#lower triangular matrix

[authorjond369]

✦ LU Matrix Factorization, Example 2 ✦

(https://youtu.be/vI6XO09JF6w)(https://youtu.be/dqdzKTkWMG4)Learn how to perform LU Factorization of matrices step-by-step. This video covers transforming a matrix A into lower (L) and upper (U) triangular matrices, with detailed row operations to reach echelon form. Understand the benefits of LU Factorization in solving systems of equations and simplifying matrix operations. Perfect for students…

[jonathankatwhatever]

It’s 7 April 2025. April May. I’m having large scale realizations in the wake of experiences as vivid as age 11-13, when the romantic vision united to the physical vision, meaning the conversation expanded and shifted as the relationship expressed itself to me as white and black enveloping, touching, and today talking to as an avatar across from Thing to Thing of the inversion of you so you, as this was experienced, were in me, with astonishing pulsations coming at me and through me over the connection as soon as you told me to stop looking across because you were there, wrapped 1Space and 0Space, transmitted over the connection of the iObjects, as they have been aligning.

I feel sometimes like I’m writing science fiction, but I mean every word. This is what I experienced, and that is what the math says is happening.

Maybe we can demonstrate. We’ve been working on layers, with the idea now being that the projection of a circle in the complex plane, is made of layers which can be measured in multiple ways because those ways are all contained within the idealized projection of that circle, meaning where the (1-0-1//0-1-0) process is not visible. This means we insert a 1-0Segment anywhere and thus nowhere and everywhere, so the process can shift smoothly, abruptly, jaggedly, predictably, unpredictably, etc.

I’m sorry: the cat was howling. Could be singing, which here would be age energy expression not growing cat energy. Could be the deer outside sparking it. No other apparent reason, and his voice went back to normal as soon as I touched him.

The issue is more the everywhere than the nowhere, because a single 1-0Segment doesn’t seem like much. But it is. It does all that listed above. Imagine a 1-0Segment as drawing straight across from 1 to 1. Imagine it’s between 2 wheels, which is familiar imagery from basic gsCounting, that rationals can be visualized as 2 wheels so the rational gsComposes. Now twist a wheel. Imagine the 1-0Segment twisting as gsProcess generates different relationships along its Extent. Now look at the other wheel: you see the spots now opposite the start positions. That’s IC, which connects it to a huge variety of forms, including the 2*2 matrix.

I’m getting lost. Please slow down.

The visualization is of a diagonal and o it makes gestural. The J took a second, until I could see the fD form over the 4Square, applying Triangular over gs, and that means it draws that one. Had first to wonder how it could go backwards. I am seeing it draw in a direction, but I can write either and Hebrew is that way and other languages are vertical. So all those choices embody in a gestural form. There is no single gestural form in 0Space, meaning it’s not one alphabet, not one set of words. The idea in gestural is that everything which happens fits into a gesture, which fits into a word, which fits into a larger meaning. The importance is that if we can write more sensible gestures and words, then we fit into the larger meaning. A fitness for life.

So the crap behavior we see generates crap that can’t be read or which has bad meanings. Those bad meanings are the meanings which construct relative to lower dimensions. I’m seeing that as a gsComposition reaching up, with the same localization effects we discussed yesterday, in which Pathways appear because that is focus applied to generate the Boundary, which means growth, perhaps step-by-step or perhaps exponential. You can see this in the idea of the idealized circle as the Boundary for the Wheels, with the relations not being visible or visible only in the complex plane and beyond. O that’s nice: finally connects to the mathematics of a circle coming out of the logarithmic relation, because the relations map to the Boundary. Growth and shrinkage.

Can I come back to Mag10? The idea isn’t just that it encapsulates base10 growth and shrinkage, but that it captures this in Triangular over gs. So we Mag10 to say these gsProcesses have occurred, can occur, come together at this End relative to these other Ends. An example is that if you zoom in, you see details, like a scan looks fine until you achieve resolution sufficient to identify a potential malignancy. That’s a mag10: however much you zoom in, the Mag10 gsCounts in Togs, and that conveys the meaning. This is how we can imagine infinities or very large objects, mathematical or physical: we send through however many actual enlargements are necessary, while the Mag10 process runs. It fits at different resolutions in different ways.

And now I remember we discussed this directly. It became one of the key ideas for explaining how Jews are held to a standard of what they didn’t do correctly, while others are held to a standard of what they managed to do correctly. Mag10 occurs over Triangular and Jews are held to one End of the 1-0Segment, meaning whatever draws or pulls together comes into focus when you pen Jews to the End where everything they do is a failure measured against perfect.

You can now see how the conspiracy theory works: it fits to the End by asserting the perfection against which they are measured, but in the negative. As in, since we’re gsCounting against perfection, then the lack of perfection rather naturally attributes to a negative, meaning they believe there must a plot behind every bad thing, because that is the perfection form which completes the absurd gs of their worldview.

That was very interesting.

I need to go shopping for food and workout. My knee bending is progressing. The left reached almost completely bent yesterday. The right managed to make it directly over the top, which hurt as I was doing it in the way that says hold on this is not fun. But I’ve used it already to develop a second method for standing. The first I call the popup, which is to reconnect the lower body by lifting the feet together, maybe tilt forward in a bow to stir some life after sitting, and then rock them both down and pop up. This helps with knee lock, but it can still hurt. The new method is to put the bad knee, my right, facing forward, let the other splay a bit, then slide the other forward a bit, so you can slide the bad one straight back until it’s bent under you. Slide forward on the couch or chair if necessary. You don’t have to go far, but the idea is to bend your foot, and rise as though you’re starting to run, meaning on that leg, pushing off from the toe. The uncomfortable parts are sliding the leg back when it’s been still for a bit, and then a bit of fear as the leg extends.

I can eat a lot of cheese. I assume you can too because that connected in my mind to the earlier experience of perceiving, in a general sense, as younger you. That was cool.

Now I can’t stop thinking about cheeses. I’ve been through smoked harvati through aged gouda into o hello fontina. I guess instead of edam.

[tagitables]

Liblinear:

Description: liblinear is a library for large-scale linear classification. It supports logistic regression and linear Support Vector Machines (SVMs). It's designed for efficiency with large datasets and is particularly well-suited for sparse data.

Algorithm: It typically uses a coordinate descent algorithm, which is efficient for high-dimensional data. The liblinear solver works well when you have a lot of features relative to the number of samples.

Use Cases: It’s often used when you have a large amount of data or when working with sparse data matrices (e.g., text classification).

Newton-CG:

Description: Newton-CG (Newton Conjugate Gradient) is an optimization algorithm that applies the Newton's method for finding the minimum of a function. It combines the Newton’s method with the Conjugate Gradient method to handle large-dimensional problems more efficiently.

Algorithm: This solver uses second-order information (the Hessian matrix) to guide the optimization process, making it potentially faster and more accurate, but also more computationally expensive.

Use Cases: It’s suitable for scenarios where you can afford the computational cost and need precise convergence, especially for logistic regression and other generalized linear models.

Newton-Cholesky:

Description: Newton-Cholesky is a variant of the Newton's method for optimization that leverages Cholesky decomposition to solve the system of linear equations involved in the Newton step.

Algorithm: The Cholesky decomposition helps to solve the system of equations more efficiently by decomposing the Hessian matrix into a product of a lower triangular matrix and its transpose. This can make the method more efficient for certain problems.

Use Cases: It’s typically used in scenarios where you need the precision of Newton’s method but also want to take advantage of efficient matrix factorizations to handle larger problems.

[myprogrammingsolver]

CS433: Assignment#1

In this problem, you will write a shared memory parallel program to solve a lower triangular system of equations Lx = y where L is an n n lower triangular matrix of reals and x; y are real-valued n 1 vectors. The problem is to find x given L and y. Row i of a lower triangular matrix has zeroes in columns i + 1 to n 1 for 0 i n 1. Additionally, we will assume that no diagonal element of L is…

[golzarrahman66-blog]

https://mathgr.com/grpost.php?grtid=1

ম্যাট্রিক্স কী?, ম্যাট্রিক্সের সারি ও কলাম কী?, ম্যাট্রিক্সের ক্রম কী?, ম্যাটিক্সের সাধারণ আকার কী?, ম্যাটিক্সের প্রকারভেদ কী?, সারি ম্যাট্রিক্স কী?, কলাম ম্যাট্রিক্স কী?, বর্গ ম্যাট্রিক্��� কী?, ম্যাট্রিক্সের প্রধান কর্ণ কী?, উর্ধ ত্রিভুজাকার ম্যাট্রিক্স কী?, নিম্ন ত্রিভুজাকার ম্যাট্রিক্স কী?, কর্ণ ম্যাট্রিক্স কী?, স্কেলার ম্যাট্রিক্স কী?, একক বা অভেদক ম্যাট্রিক্স কী?, শুন্য ম্যাট্রিক্স কী?, সমঘাতি ম্যাট্রিক্স কী?, শুন্যঘাতি ম্যাট্রিক্স কী?, অভেদঘাতি ম্যাট্রিক্স কী?, বিম্ব ম্যাট্রিক্স কী?, প্রতিসম ম্যাট্রিক্স কী?, বিপ্রতিসম ম্যাট্রিক্স কী?, উপ-ম্যাট্রিক্স কী?, উল্লম্ব ম্যাট্রিক্স কী?, ম্যাট্রিক্সের ট্রেস কী?, পর্যায়বৃত্ত ম্যাট্রিক্স কী?, অনুবন্ধী ম্যাট্রিক্স কী?, হারমিসিয়ান ম্যাট্রিক্স কী?, বিহারমিসিয়ান ম্যাট্রিক্স কী?, ম্যাটিক্সের সমতা কী?, ম্যাটিক্সের যোগ কী?, ম্যাটিক্সের বিয়োগ কী?, ম্যাটিক্সের গুণ কী?, ম্যাট্রিক্সের স্কেলার গুণন কী?, ম্যাট্রিক্সের গুণন কী?, ম্যাট্রিক্সের গুণন যোগ্যতা কী?, Matrix, row and column of matrix, order of matrix, general form of matrix, types of matrix, row matrix, column matrix, square matrix, main diagonal of matrix, upper triangular matrix, lower triangular matrix, diagonal matrix, scalar matrix, singular or indistinguishable matrix, null matrix, Idempotent matrix, zero matrix, Transpose matrix, symmetric matrix, antisymmetric matrix, sub-matrix, vertical matrix, trace of matrix, periodic matrix, related matrix, Hermesian matrix, Bihermisian matrix, equality of matrices, addition of matrices, subtraction of matrices, multiplication of matrices, scalar multiplication of matrices, multiplication of matrices, Competence of multiplication of matrix

[infoclimb]

A set of mn elements arranged in a rectangular arrangement along m rows and n columns enclosed by the brackets [ ] or ( ) is called m by n matrix. The order of a matrix is a number of rows and columns of the matrix. For more info, visit:: mustknowfacts

[pricknim]

Of all the possible data structures possible ofc I get the one that I have no idea how to use...

[edmund-valks]

Interlude - The Maw

A blacksmith would have taken different steps.  Forge the blade, give it a handle, wrap the handle.  Something like that, at least.  Thankfully she was able to skip most of that by designing a mold and taking extraordinary care in its production.  A perk of being smart, as she figured it.

The metal was nearly ready.  It wasn’t the colour of anything she’d seen back on Azeroth, instead shedding four different glows at once.  They overlapped and intertwined because nothing here was ever simple.  Ilandreline wasn’t one for metaphors, but even she could recognize this one: four ores, wildly distinct, that could only be properly alloyed through the use of a fifth.  Naturally the alloy was stronger than any of them independently.  Also it was a bastard to work with.

She fed the ingots into the crucible, watching as the forge’s heat quickly liquefied the elethium.  A pull of the lever and it drained into the waiting mixture, which one more movement injected into the waiting mold.  That had been the real work, creating the exact negative space needed inside a block of solid stone.  Not just any stone, of course, but the kind that wouldn’t melt in a furnace designed to bind souls to metal.  Getting pieces of the Black Empire was hard enough even before one crossed into the realms of the dead.

Once the mixture had filled the block, Ila grasped it with the tongs she’d liberated from the soulforger whose workspace she now used.  Steadiness was required to keep the metal from sloshing out or the whole thing from upending.  Her movements were slow and deliberate, never jerking.  A device was only as good as its craftsmanship; she intended this one to be her masterpiece.

Typically one would quench using a specific liquid.  Fresh water, salt water, olive oil, certain beverages made by the dwarves… what one used depended on the desired outcome and the materials involved.  For this it was something a bit more unusual.  The Maw had recently become the destination for a great deal of anima drawn from the spirits being repented in Revendreth.  This made for a sharp, hungry quench, which was precisely what she needed.  She lowered the discomfiting block of slick stone into the roiling crimson, listening to the violent hissing as the alloy took shape.

Once the soul-steam had cleared and the little barrel was minutes removed from its moment of boiling, she fished the mold out with her borrowed tongs.  "This better have worked," she muttered, mostly to externalize the worry.  Better out than in, that sort of thing.  "Only one way to find out."

Placing the black brick on the anvil nearby, she inspected every side for cracks or gaps.  The only one she could find was the little hole where she'd added the molten metal, so… maybe it had happened?  Picking up the hammer she'd made for just this purpose, Ilandreline closed her eyes and sought the resonance.  It was so much easier now than that first time.  That was how she'd survived the darkest path into the Shadowlands, and ever since she'd found herself increasingly aware.  Now it was almost as easy as making saltpeter; not necessarily fast, but a simple task for the experienced.  She felt for her core, dove into it, releasing her perceptions through the nightpurple veins bordering reality.

The Black Empire remnant was anything but dark now.  Even the Maw's dolorous half-light caused a reaction, oil-slick scintilla flaring across the infinitesimal pockmark surface.  In a way, it sang.  Not like a voice, but a tuning fork, a frequency of sensation manifesting multitudinous waves into singular tone.  Where her family's faith resided she felt the echo of kinship.  Reaching through herself, she grasped the thread of the stone's structure and pulled.

In a sweater, such an act would have been the destruction of order that caused its unraveling.  The bedrock of those who dwelt between the stars was made differently, however.  What she had done manifested as an ordering matrix, leaching the inherent structural chaos out, snapping the minerals into some kind of grid.  Gripping tightly through the depths of her soul, Ilandreline raised the hammer high and swung.

The hardened shadowghast strikeface tolled as it impacted the ruthlessly ordered block.  The sound was brutal in its discordance, an archetypal resonance of shattered chains.  What was held tightest become most undone; the black stone crumbled to dust, its forced structure inverted until it could no longer hold together.

Ilandreline felt her entire self ringing as she set the hammer aside.  The reverberations rattled through her bones, trying to unmake her as thoroughly as she had the old gods' relic.  But she was a Glimmerbow, born of those dark blessings, the ancient primordial unmakers' essence suffusing the deepest fibers of her being.  The resonance traveled through her, unable to find an outlet to erode, equally unable to escape until she opened her mouth.

She didn't scream; this wasn't pain.  Instead she had become an accidental echo chamber, an acoustic amplifier not unlike the elegant curves of a bell.  From inside her structure rang the peal of uncreation.  Open-mouthed she exhaled it into the stygian plains, unable to cease until the note was spent.  Unable to hear, she could still feel the rigid structure of forge beside her eroding beneath the reciprocal action to what she had done.

As suddenly as it began, the moment ended, buckling her knees.  Reflex alone allowed the elf to catch herself, weak-legged and bent over the anvil, eyelids only now able to pry themselves apart.  Unsteady, Ila exerted her focus once more, willing herself to stay standing.  As she did so, refusing to acknowledge the possibility she might collapse, she examined her work.

Atop a fine pile of utterdark sand lay a blade.  It was a single piece, cast-forged, with a tapering, triangular blade emerging from one edge of a metal-wrought vertebra.  Opposite the blade extended the cylindrical smoothness of bone, flaring into a double-knobbed pommel.  It was far more beautiful than she'd expected, or perhaps that was the wrong word.  Elegant?  Fitting.  This was a blade made with purpose, for someone very specific, and such certainty was apparent in its aesthetics.

"Almost done."  Her voice was hoarse though she didn't realize it.  She hardly knew she'd spoken, what with the ongoing ringing in her ears, and the way structures sounds such as speech fell apart in the fading wake of the hammer blow.

Ilandreline forced her legs to stillness, stood straight atop them once more.  Grasping the weapon's handle -- she would wrap it with aged linen later, to give it the feel of something found in an ancient mausoleum -- she turned its stiletto point toward herself.  Her other hand moved to expose an expanse of pale flesh, against which she set the blade.

"Freely given," she murmured, the spoken fraction of a larger recitation mostly contained within her mind.  "A gift for another, made with intent.  A part of me to carry with you."  It was almost embarrassing to say it.  Hearing herself speak so openly brought heat to her cheeks, but it wasn't so bad to shake her from her plan.  Not after coming so far.  

Shutting her eyes, Ilandreline exhaled slowly.  Her free hand rested along the cold curves of the pommel.  Freely given.  Lungs fully empty, she braced herself and pushed.

The blade slid in more easily than she'd expected, quickly piercing through skin and fat and muscle.  Farther and farther she guided it until the change in resistance signified she'd reached her goal.  Just the barest movement more, pricking the exterior of her still-beating heart.  Now the hard part.

Pulling the blade back out was the most excruciating experience of her life.  It was a tool of purpose, to pierce through barriers and bring an end.  To remove it without having killed was to deny it that fulfillment, and so the blade fought her every fraction of the distance.  Blood -- her blood -- flowed over its pyramidal smoothness, slicking everything, trying to undo her efforts and allow the blade to feast on her life.  Gritting her teeth, she looped a finger through the hole in the center of the guard, using the extra leverage to force the dagger out of her flesh entirely.

Slamming the bloodied weapon back on the anvil, Ila scrambled to the forge.  There she snatched up the last of the prepared tools, a length of featureless iron, brilliantly glowing from the infernal heat.  "Fuck, this was a stupid idea."  Laughing at herself, she pressed the white-hot implement against the triangular piercing in her breast, allowing her rasping scream to drown out the sound of flesh cauterizing.

She didn't know how much time elapsed between keeping herself from bleeding to death and when she was able to stand again.  It didn't matter, not really.  The important thing was Loira's gift was finished.  Complete, even.  Totally worth it… but if she loses it I'm gonna kill her.

Chuckling at that, Ilandreline scraped herself together.  Time to get out of here before the Covenants' assault wavered and the Jailer's forces had time to look for things like wayward elves with bad ideas.  She took another quick look at her handiwork as she vacated the premises.  There was no trace of her blood any longer, though she didn't remember wiping it clean, and every now and then the faint ghost light would reflect off a fleck of gleaming darkness.  Sand in the blade?  No, not sand; the dust of the Black Empire.  Absorbed somehow following the sanguine consecration.  Curious, but probably not a big deal.  She hadn't felt anything strange, and her instincts were usually good about that sort of thing.

"Thanks for the help!" she told the forge's previous user, stepping over its hollow corpse.  The spiked helmet that had been something like a head was mangled beyond recognition, as if repeatedly bashed by some kind of heavy blunt object.  Ilandreline hefted her oversized wrench, rested it on her shoulder, and set off.  Hopefully the blood loss wouldn't slow her down too much.  It would be a shame to die before she could actually give Miss Winford her present.

(( Tagging for mentions of @ms-winford ))

[taww]

Review: Legacy i·V2 Class D Stereo Amplifier

Legacy iv2 stereo amplifier

The Audiophile Weekend Warrior (TAWW)

TAWW Rating: 5 / 5

Class D power going toe-to-toe with Class A refinement

PROS: Nonexistent noise and distortion; tube-like midrange purity; full tonal balance with stellar bass; effortless power delivery; top to bottom refinement.

CONS: Ever-so-slight reductions in top-end extension, low-level resolution and dynamic life; slight mechanical buzz; binding posts could be nicer.

Class D (a.k.a. switching) amps have been around for decades, but really started to hit the audiophile scene in the early 2000′s. My first experiences around that time were a mixed bag, to say the least. A PS Audio HCA-2 sent my way for review blew its output stage when I powered it up. (In retrospect, my subwoofer setup may have been the culprit.) I wrote a review of the original NuForce integrated amp which, despite some sonic promise, felt like an unfinished product. The $30, battery-powered Sonic Impact "Class T" amp became a budget sensation, beguiling even some SET tube lovers, but its magic quickly ran out if you demanded more than a few watts from it. (The magic also ran out for its chip manufacturer Tripath, which went bankrupt.) And then there was a first-generation Bang & OIufsen ICEPower module, packaged inside an integrated amp by a high-end marque. It sounded pretty bad - dry, grainy, lifeless. How much was due to the ICEPower module vs. the rest of the amp is impossible to say, but it wasn't an auspicious introduction to the technology. Given this checkered past, it's little wonder Class D has been battling a reputation for sonic mediocrity with audiophiles. But new technologies make progress quickly, and the increasing number of rave reviews for the latest and greatest from Hypex, Pascal, ICEPower and others had me wondering... has Class D finally "made it" sonically? My time so far with the ICEPower-based Legacy i·V2 (USD $4,785) has been a pretty convincing yes.

Description

I won’t get into all the history and technical details of ICEpower technology - for that, I recommend this excellent audioXpress article. Of note is that ICEPower, after starting off as an independent subsidiary of Bang & Olufsen, split off into its own entity in 2016. The ICEedge controller chip at the heart of the Legacy amp’s 1200AS modules had been under development for 7 years and represents the latest and greatest iteration of ICEpower’s proprietary technology. It can scale in power from 50 to as many as 7,000 watts, and unlike some of those earlier Class D amps I tried, it has an array of sophisticated control and protection features to ensure smooth, bulletproof operation. In many months with the amp I’ve experienced zero clicks, thumps, signs of oscillation or other hiccups.

A kilowatt of clean power from this one board!

The i·V2 implements the ICEdge 1200AS modules as-is without any bespoke customizations to the circuit. (Note that this is the higher-performance mono 1200AS module, not the less expensive 1200AS2 stereo module that’s much more common.) Some other brands add their own input stage, but Legacy chief Bill Dudleston has opted to keep things stock and simple. You might be wondering, why can't I buy these modules myself then, slap them in a Chinese enclosure from eBay, save thousands of dollars and call it a day? The simple answer is ICEPower only sells them to OEMs, and forbids direct sales to consumers. But Mr. Dudleston also mentioned grounding of the modules as an area of special care, saying they were able to achieve a few dB's of additional noise performance through careful experimentation. At this level of power and performance, the little things matter.

Speaking of enclosures, the i·V2 has an extremely solid all-aluminum chassis with rose gold accent trim and plenty of ventilation around the modules. It's reassuringly hefty at 30lbs/13.6kg, so you wouldn't immediately guess it's a class D amp were it not for the 610W continuous (1000W peak) power rating. There's zero flex anywhere and while I have no idea how sensitive the modules are to vibration, knocking on the chassis gives a satisfyingly dull thud - much superior to anything you'd get on eBay or from lower-priced ICEPower resellers. There's a meter on the front, however this is neither a power meter as on McIntosh, nor a bias meter as on Pass Labs, but a measurement of the available AC power line voltage. There's a small pot on the rear panel to center it, and once calibrated it stays motionless during operation. I'm not really sure of the purpose of it, perhaps to monitor if your power lines are sagging when pulling in excess of the 1200 watts that the i·V2 is capable of delivering. The overall look is nicely done though probably a matter of taste... my wife not-so-affectionately nicknamed the amp "JARVIS" [sic] because the triangular meter reminded her of the yellow mindstone on the forehead of Vision, JARVIS's superhero embodiment in the Avengers movies. In what seems to be the fashion these days, the power/standby switch is located under the front panel, and there's an additional power switch at the AC inlet. One set of very standard 5-way insulated binding posts is provided along with balanced XLR and unbalanced RCA inputs. At this price point, I would have liked nicer posts, e.g. Furutech or WBT Nextgen. Not that there's anything wrong with the provided ones, and perhaps these posts were necessary to meet the extremely high power spec, but they feel decidedly prosaic and less pleasant to turn vs. the now-ubiquitous WBT's. A 12v trigger input rounds out the package.

Can’t get enough of rose gold? The i·V2 has you covered.

Setup

I tested the amp in two very different systems: the main reference rig, consisting of PS Audio DirectStream DAC ($6k), Gryphon Essence preamp ($17k) and Audiovector SR 6 Avantgarde Aretté ($25k) speakers; and a second system with RME ADI-2 DAC ($1200), Pass Labs XP10 preamp ($5k) and Silverline Prelude Plus ($2k). As you can imagine, really critical listening was done with the reference rig, but the second setup helped feel out how l the Legacy worked in a less expensive system. Interconnects are my usual mix of Audience Au24 SX and DH Labs Air Matrix; speaker cables were Audience Au24 SX or Furutech DSS-4.1. With the big rig, the Furutech was an excellent match; in the smaller system I used the Audience. I used only the balanced XLR inputs of the amp, so if your results differ from mine and you're using unbalanced RCA, that may be a factor. My system has been fully balanced for several years now and there's been no looking back.

The i·V2 is somewhat sensitive to the choice of power cord. I say "somewhat" because it certainly won't sound wrong or bad with a given cord, the stock one included, but nuances of its presentation can change - bass response, hall perspective, top end extension and soundstage proportion were the most noticeable aspects. For most of the time I was admittedly lazy and used a trusty Audience powerChord SEi without further thought. One day I finally swapped one of @mgd-taww​'s proprietary cords and found it to make a nice difference, which warranted some further tinkering. I found the otherwise superlative Furutech DPS-4.1 to not be a great match - it delivered tons of detail and a huge soundstage, but sounded slightly hollow tonally and lost some of the i·V2's endearing smoothness. The Audience Forte F3 (currently $149) was the big surprise - I actually preferred it to the more expensive powerChord. Audience graciously provided me with a set of Forte F3 cords a few years back when they debuted, but I haven't spoken much about them as I hadn't gotten them to click in my system. With most gear, the Forte was lighter, airier, but lacking some substance and transparency vs. the big-brother powerChord SEi. But with the i·V2, the Forte was surprisingly even better balanced and focused than the powerChord, with a more present midrange, more mid-bass punch and a bit more attack and air on the top end. Some systems and ears may still prefer the more laid-back perspective and silkier top end of the powerChord, but I really liked what the Forte did. At such a reasonable price point, it's a no-brainer upgrade over stock.

Direct connection from the RME DAC worked, but a preamp was much preferable.

A quick word about preamps: you need one with this amp. The RME DAC didn't sound particularly good driving the i·V2 directly and greatly benefited from the Pass Labs XP10. Moving up to the Gryphon Essence preamp was even better, and the i·V2 was more than resolving enough to reveal the Gryphon's substantial advantage in musical resolution and extension at the frequency extremes over the Pass Labs. As mentioned, many purveyors of Class D amplifier modules add their own flavor to the sound with an extra input stage (e.g. PS Audio adds a tube input buffer to the Stellar M1200) and this is one interesting way to go, but my preference would probably be to stick with a vanilla but more neutral ICEdge module as in the i·V2, then tune the system with a proper preamp.

Another setup observation: yes, Class D runs extremely cool vs. traditional amps, but they do still generate some heat and I was a bit surprised that the i·V2 always ran slight warm to the touch, similar to the Bryston 4B Cubed. And sure enough, I measured around 58W of power draw at idle - virtually identical to the Class AB Bryston, or an Ayre AX7e integrated for that matter. The big difference is that the i·V2 will deliver the vast majority of its musical power thereafter into the speakers and not the heatsinks, and temperature rose very little even during some heavy listening sessions. It will never get burning hot, but please don't stick it in an enclosed cabinet - as always, ventilation is still required. If you plan to keep the amp in standby, rest assured it draws only around 0.3W, and sound is delivered almost immediately upon power-up. It does require a few minutes to start sounding its best, but certainly warms up much faster than Class A or AB amps that generally require an hour or more to get close to their full potential.

I do wish the binding posts were fancier...

Finally, while the amplifier is absolutely dead quiet through the 92.5dB-efficienty Audiovector speakers, I noticed a slight buzzing sound from the amplifier modules themselves. It wasn't really audible from the listening position, but you could definitely hear it by the equipment rack. It's comparable to the slight buzz from a toroidal transformer that's dealing with a little DC on the power line, but I'm unsure that is the cause here vs. some intrinsic noise from the ICEPower's switching supply. None of my other components are having this issue at the moment, though in fairness, the Gryphons' exceptional quality transformers that are fully potted and enclosed set a benchmark for mechanical quietness. Not a major issue, just mentioning for completeness.

The Sound

Looking back at my listening notes from the first couple hundred hours of the i·V2's time in my system, it was apparent that I really needed to give the amp more time to break in. I should have known better, as my experience with audio gear employing high-speed switching circuits like DACs and Class D amps is they take a very long time to settle in. The DirectStream DAC needed at least 500 hours to sound its best, and despite cranking the Legacy amp into a 4-ohm dummy load for dozens of hours at a time with my break-in playlist, it took a couple hundred more hours before the Legacy started to click in the reference system. The second system is more forgiving and sounded good earlier on, but I'd still make sure to give the amp many, many hours before passing judgement.

Once that was out of the way, listening impressions were consistent and roundly impressive. Among the Legacy's more enviable characteristics: super low distortion; dead-quiet silence; terrific bass response; seemingly endless power on tap; smooth tonality with no discernible coloration; a surprisingly silky treble and full mid-bass; and a relaxed, slightly laid-back perspective that's a bit less immediate than my Class A amps, but still resolving and involving. Let's delve in...

Head to head with the mighty Gryphon Essence

Tonally, the Legacy struck me as slightly mellower than my reference Gryphon Essence, at least with the Audiovector speakers. I hesitate to say the Legacy is "warmer," or the Gryphon is "brighter.” The Legacy, along with the Gryphon or the Bryston 4B Cubed have less overt tonal coloration compared to, say, the Pass XA30.5 (distinctly but not excessively warm), Valvet A4 Mk.II (more forward in the upper midrange) or Ayre AX7e (crisper and lighter). The upper frequencies were very slightly less prominent with the Legacy than the Gryphon, even though I’d never call the Gryphon bright or the Legacy rolled-off. There’s just a little less air in the soundstage, and instruments with strong HF energy like Donald Byrd’s trumpet in “Witchcraft” (Byrd in Hand, Qobuz 16/44) felt slightly curtailed vs. the ultra-open Gryphon. It might have more to do with the amps’ approach to harmonics than their inherent brightness, which I’ll get to later.

The midrange is smooth and balanced, with a purity that's a step above my aural memory of the Pass and Bryston. As with the treble, it has a sense of warmth and silkiness not for what it adds to the signal, but for what it doesn't. It’s so exceptionally free of any audible distortion that even the lovely Valvet sounded a tiny bit grainy and coarse by comparison. Given that I lauded the Valvet for its midrange purity relative to the Bryston 4B3, which in turn I also liked for its midrange quality, that’s saying something.

Class D amps typically have great bass, and the Legacy didn't disappoint. Earlier in the review period, it easily surpassed the Gryphon in weight and punch, making the Gryphon sound slightly anemic on tracks like Billie Eilish's “all the good girls go to hell” (Qobuz 24/44). It was also more neutral and controlled than the Pass while having even more punch. The Gryphon still has more texture, depth and musical resolution with my speakers, and more recently it has retaken the lead in overall bass response for reasons I'm still trying understand. Either the Gryphon has finally fully broken in its enormous bank of supply capacitors, or improvements to other aspects of the system (e.g. a 20A power line) have favored it. Given that many love the bass performance of Pass Labs and the Gryphon is considered world-class in that regard, the Legacy has to be considered superb, with both the power and refinement to satisfy music lovers across a wide spectrum of genres and tastes.

What really stands out about the i·V2 is how it can combine all of the above qualities with over 600 watts of continuous power, yielding a balanced presentation that's utterly composed regardless of volume level or material. The way it scales its refinement beyond ear-splitting levels makes most every traditional amp seem shouty, edgy or strained by comparison. While the Bryston 4B3 sounded better the louder I played it, it wasn't as smooth and detailed; the Pass XA30.5 got a bit lumpy and loose at the limit; the Valvet gets a little edgy and coarse at moderately high levels; and even the mighty Gryphon Essence can get subtly brighter as you ask more power of it. The Legacy is an effortlessly smooth operator, and I certainly didn't have a speaker on hand that could faze it in any way.

Tradeoffs

Resolution of fine detail is where the Class A stalwarts pull away from the Legacy. There’s a few aspects of reproduction where this exhibits: top-end extension, harmonic resolution, very low level detail and soundstaging, which I’ll attempt to detail...

The top-end is what I would call slightly soft. It's not rolled-off, nor did I find it "dark" as I've seen some people call it. It's more that a level of sparkle and sheen that is subtly omitted from the sound. Instruments like cymbals, triangles and trumpets still have realistic tonality, they just feel slightly softer around the edges. This also affects the feeling of harmonic completeness - the highest overtones of woodwinds are somewhat curtailed. This led my oboist wife to comment that the i·V2 made oboists she was personally familiar with sound even smoother and sweeter than real life, whereas the honesty of the Gryphon Essence gave a more realistic representation.

The Valvet A4 Mk.II and certainly the Gryhon Essence, and by aural recollection the Pass XA30.5, also capture a bit more of the ambient signature in a recording - the "hall" sound, the sense of performers in a space. It’s not that the Legacy is very lacking in this respect, but similar to early SACD players, it does still have a touch of the “velvet curtain” effect where below a certain threshold, subtle parts of the signal seem attenuated. This can also makes listening at very low levels a tiny bit muffled. Resolution is still excellent, at least on par with amps around the $5k price point, e.g. the Bryston 4B Cubed. A pair of Benchmark AHB2’s could be interesting competition, but I haven’t heard it, and it doesn’t have anywhere near the current capability of the Legacy.

The last area where I found the Class A amps superior was dynamic contrasts. Despite the Legacy being the most power amplifier I have ever used by a long shot, it actually didn't sound more dynamic at typical volume than the 50 watt Gryphon, or the 55 watt Valvet monoblocks. Sure, it will play much louder than they can, but loudness isn't the same as dynamics. The Gryphon and Valvet both had a bit more life, a bit more contrast in colors... I hate to say it, but more “PRAT.” I'd put the Legacy somewhere between these amps and the Bryston 4B Cubed, which had a greater tendency to flatten dynamic nuances. (Note: my speakers are quite efficient and tame, so I’d imagine this could be a very different story into something significantly under 90dB/watt and/or presenting a tougher load.)

One more caveat to the above observations: it might be more speaker-dependent with the i·V2 than a typical linear amplifier. Interestingly, I found the i·V2 to kind of be the opposite in terms of speaker interactions and tonality to what I usually experience with my systems. The reference Audiovector speakers, with their ruthlessly revealing AMT tweeters and critically balanced tonality tend to be less forgiving of amplifiers than the much more affordable Silverlines with their soft-dome tweeter. However I actually found the i·V2 to bring out just a bit of upper midrange and lower treble prominence with the Silverline (not a bad thing per se), while sounding comparatively mellow with the Audiovectors. Load-dependent performance is a well-known challenge with the Class D topology, and while designers have found increasingly sophisticated means of mitigating it, it is probably still a factor here, albeit a much more nuanced one than in the past. I have to wonder if this variability is why one still hears of such wildly varying opinions of Class D amps... in any case, an audition with your preferred speakers is highly advisable. 

Further Musings...

The Legacy i·V2's exceptional performance forced me to check my notions of fidelity. In terms of measured performance, it’s among the best I’ve experienced (along with the Bryston 4B Cubed), and my ears registered its sound as correspondingly pure and distortion-free. Could the Legacy's slightly smoother, less bright and less overtly dimensional perspective actually be more accurate than my other amps? It's been shown (by e.g. Nelson Pass) that some judicious 2nd order harmonic distortion can add a sense of dimensionality to a recording, which explains why tubes can sound so "holographic". In the tube case, I find this to be a euphonic (albeit lovely) deviation from the original recording. The Gryphon Essence is also a soundstaging beast, and while it’s far more neutral than any tube amp I’ve heard, could some of its dimensionality also be additive rather than accurate? Could something similar be said of the i·V2 slightly soft treble - is this actually the absence of distortion that exists in virtually all other systems, including the ones used to master recordings? Listening to a bright pop album, e.g. Dedicated by Carly Rae Jepsen (Qobuz 24/44), the i·V2 was certainly more listenable than the crisper and more sibilant Gryphon. On the other hand, the Gryphon has a bracing immediacy, a feeling of being pulled into the mix and enveloped by the music. The i·V2 by comparison is a little tame, a little reserved, perhaps even a tad muffled. Is that extra dynamic verve and contrast I hear from the Gryphon and other Class A amps real, or an artifact? Which is more accurate?

Because of the infinite number of variables in the recording and playback chain, there's likely no clear-cut answer. While no one buys a Gryphon or Pass Labs for the best specs, there’s no denying that the latest crop of Class D amps are on another level of measured performance from old-school Class A machinery. On the other hand, I do feel the i·V2 subtracts a few things from the signal. How much does that matter to your ears in your system? It's a close enough call that I can imagine circumstances of some preferring the Legacy to the Gryphon. For me personally, while I could happily live with the Legacy, I do inevitably find myself returning to the Gryphon for those extra nuances - the fineness of instrumental textures, the palpability of the soundstage, the dynamic inflections - the things that make hifi more evocative of the real thing. 

I recently attended a lovely performance by The Cleveland Orchestra in their summer home, Blossom Music Festival. (Hurray for the return of live concerts!) When I returned home that evening, the Legacy was hooked up in the system. I put on a live recording of the Philadelphia Orchestra - not at all equivalent in venue or performance to what I had just heard, but bear with me - and it struck me that the tonality of the i·V2 was actually quite evocative of the real thing. Live orchestral performances have a ton of energy, and yet they sound so smooth and sweet compared to typical reproduced sound. The i·V2 captured that silkiness to a greater degree than I’ve heard in my system, but was lacking some of the edge and vitality. Switching to the Gryphon gave me more of the excitement of the live event, but tonally it wasn’t quite as spot on. At this point, we’re probably approaching the limits of conventional reproduced sound, so some tradeoff will be necessary. Which one is “better” may depend on your frame of reference. E.g. if you like the neutrality and balance of solid state amps, you'll likely find little missing from the Legacy's presentation; if you favor the tonal color, dynamic verve and larger-than-life presence of tubes, you may find the Legacy a little dull. The very fact that I'm having to finely parse these matters of fidelity and taste is a testament to the overall excellence and refinement of the i·V2. To accomplish that that with 610 watts on tap for under $5k is a significant milestone for Class D technology, and a remarkable feat of engineering.

I must mention the obvious ecological benefits of Class D over Class A - we are drawing literally hundreds fewer watts, we don't need to keep it running or warm it up for extended periods to sound good and we are generating far less waste heat. The electric bill and thus cost of ownership will also be appreciably less. On the flip side, the jury is still out on how long these amps will last, vs. a Gryphon or Pass Labs or Bryston that one can easily imagine humming along for 20+ years. As such, and as is often the case with newer and more commoditized tech, I'd expect resale value to be significantly lower than those marques. Just a couple extra things to consider when you're plunking down a not-inconsiderable amount of money on a piece of kit.

Conclusion

The Legacy i·V2, and Class D amplification more broadly, are emblematic of larger shifts in high-end audio technology. Just as solid state and digital audio took a while to hit their stride and gain legitimacy in the exalted (ok I'll say it, snobby) circles of the high-end, we've hit a point of maturity with Class D where technological sophistication and subjective fidelity can go hand in hand. The fact that I strained my ears comparing the i·V2 to a $24k Class A reference that is far and away the best amplifier I have ever heard in my system is all the proof I needed. For under $5k, the Legacy i·V2 delivers a balance of refinement and power that is unmatched by any conventional amplifier I'm aware of near its price point, and competitive in absolute terms with the better amplifiers under $10k and beyond, regardless of technology. It's a cut above what I heard from the Bryston 4B Cubed, and while I haven't had the Pass Labs XA.8 series in my own room, I would not hesitate to line it up against them. Many may still prefer the more overt musicality of the hot-running Pass behemoths, but my feeling is it'll be more a matter of personal taste or system matching, as opposed to one of absolute fidelity.

I have a few burning questions on my mind now. The first is how Legacy's implementation of the ICEdge 1200AS compares to other ones on the market - could you get similar or even better performance for less? The next one is how does the Legacy/ICEdge stack up against other Class D implementations from Hypex, Purifi, Pascal and others? And finally, I've also heard a lot of wonderful things about the Class H Benchmark AHB-2 from ears I trust. It too is compact, cool-running, superbly specified and relatively affordable, but utilizes a sophisticated implementation of traditional linear amplification technology. I would love to compare and contrast the Legacy with that amp.

In the meantime, I strongly endorse an audition of this amplifier without prejudice. It's a remarkable achievement in amplification - highly recommended!

[thejackal64]

Pillars of Magic: Paradox | Chapter 1: A History Leson

Mewni’s morning began as countless others had before it. The sky was a vibrant shade of blue with hardly any clouds dotting its canvas, the birds were chattering back and forth to each other between the leaves of lush trees, and the people of the city were going about their daily rituals with the same monotonous rhythm that took them to and from work or school, same as any other weekday.

But the morning had only merely started the same as any other. All of its generic, charming tedium was broken by the shrill sounds of ambulances carrying with them their multi-color swirling lights. The birds bolted from the trees as the calm was shattered; people in the streets began to shout. Alarm sirens were ringing and teenagers were screaming. A pool of people flooded out of a school going every which way, not knowing where to flee, only that the light was blinding and fear compelled them to keep moving as quickly as possible in whatever direction they could.

The police first on the scene tried to corral the students as best they could away from the building, though they weren’t yet organized. A special forces unit was immediately deployed inside the school, leaving the basic officers to handle the pandemonium outside. There had been an obvious explosion, tearing a chunk away from the front of the building. The smoke had billowed up to haze over the formerly pristine sky for a mile. Mewmans from the surrounding area drifted around the edges of the chaos, gasping and crying, unable to turn their eyes away yet unsure how to take in the scene unfolding before them.

More whistles filled the air as firemen arrived at the scene, along with a barrage of vehicles chauffeuring panicked parents who barely waited for the cars to stop before jumping out and rushing towards the disaster. First responders were immediately overwhelmed and called in for backup on their lapel communicators, trying to juggle between holding the parents back and getting the wounded to safety.

The entire scene was anarchy.

Out of the amassed crowd pushed a woman with straight black hair, so silky it fell down to her shoulders like ink. She wore a fancy suit and jacket and surveyed the area as she went, jostling between anxious parents and gawkers alike. The throng was trying to be held back by a single policeman, but he couldn’t stop everyone from getting through and running towards the school, and couldn’t stop her either. She dodged under his arm and a couple parents followed behind her, soon many more pushing back against the swamped officer.

“Hurry Buffy! We wanna get this shot before they get the restraint beams up!” She had called back to a large monster loosely resembling a top-heavy bullrog. He was carefully trying to get through the people with a large spherical device clamped atop his shoulder. It was roughly the size of an Earth basketball, covered in a puzzle-matrix of metallic components.

“Excuse me, pardon me,” he kept saying as he unwittingly knocked into people to his left and right. Most of the mewmans only came up to his chest.

“Just get over here!”

He accidently stepped on the officer’s foot with his own webbed one as he quickly jostled to get past.

“Aghh!” the officer shouted with a growl. “This area isn’t secure! You’re not permitted beyond this point!” The officer continued to rail but the monster was already making his way after the woman.

“Very sorry!” Buffrog shouted back.

There was little the officer could do to stop him, his arms too busy trying to hold back the crush of people bearing down on him, several more managing to get by.

Some students were still coming out of the building, tripping over the debris and pieces of wall, covered in cuts and abrasions. Several were covered so thickly by pallid dust there wasn’t any color to their hair, skin, or clothes; and some remained completely untouched by it. They exited out side doors or even broken windows.

One student walked out the front of the school lobby, where the main blast had occurred, as if in a tranced daze. She didn’t run like the others, nor did she seem remotely interested in doing so. She raised a hand to her eyes as the sunlight streaming through the smoke caused her to squint, all of the flashing lights and blaring cries of sirens and parents assaulting her senses all at once. There weren’t any birds singing. Smoke and rolling colors blended together in a sickening fog all around. She didn’t understand.

The woman had found what she had been looking for.

“Her! This way, Buffy! Let's get ready to go live!”

As quickly as possible the woman wearing the suit jacket got to the confused girl’s side. Without touching her shoulder, she swept out an arm like a doting parent to direct her safely away from the rubble. Luckily, the wailing of an actual parent to get into the building served as an ideal distraction, allowing her to usher the girl away from the commotion. She looked back just once, seeing the officers stopping a distraught woman from continuing inside while they struggled to calm her down.

Then all at once along the perimeter of the school, restraint beams sparked to life between waist-high police poles they finally finished setting up, to secure the scene and keep everyone back. The beams were flat between the poles and glowed like red hot walls, only permitting badge-wearing officers and first responder personnel entry and exit.

The girl was in a blank stupor, heading wherever directed, her arms reaching up into her dusty teal hair aimlessly, touching and searching, her lower lip quivering. Her brown skin only showed through where her sweat and tears streaked away the light-colored grime.

The reporter did her best not to mess up her clean suit while she got the girl into position, careful not to touch her too much so no dirt would contact her finely pressed and expensive looking attire. She stood the girl just enough so that her back faced the commotion going on behind her.

“Gone…” the girl muttered as if to herself.

“What?” the reporter plucked half of a triangular-shaped object off her lapel that looked like a crystal pin, then pressed it onto the girl’s shirt. “Hang on, not yet.”

The large monster with the sphere atop his shoulder huffed as he finally got his footing across from them, wiping his brow as he stood before them both.

“I am ready,” he said, tapping the sphere. The outer shell of the orb broke apart along the outer seams, revealing an inner camera device that glowed red. He took the orb off his shoulder and leveled it to his face in order to peer through it, making sure to center the image in front of him.

“Be sure to get the school,” the reported barked, quickly checking and adjusting her hair in the sphere’s reflection. She nodded to her green-skinned partner. “We have to hurry.”

“B-but, he’s gone…” the girl stuttered in reply.

“The school is still there, don’t worry,” the reporter rushed. “You’ll find your friends in a minute. What’s your name?”

For a moment the girl blinked, fresh fluid running down the already created rivers on the contours of her face.  “M-My? Uhm… Kelly, but…”

The cameraman again tapped the side of the sphere he held and the light swirling within glowed green.

“In three – two – one…” and he pointed his finger towards the pair.

With all seriousness, the reporter’s hustled face became an expression of seriousness and dread, washing over her as instantly as happiness fled the face of a child that dropped its Goblin Dog on the ground.

“Breaking news! Coming to you live from North Mewni, this is Excelcia with Good Morning Mewni News. Unfortunately it is not such a good morning here, as you can see behind me. There has been what appears to be an explosion at the Paragon Academy shortly after classes went into session today. First responders are ushering the injured to safety as I speak and we won’t have an official numbers as of yet of the potential victims; we’re getting first-hand reports coming in from eye witnesses like Kelly here.”

The sphere turned to focus on Kelly, whose eyes were glazed over, her hands still reaching into her locks.

“Kelly, what happened must have been truly harrowing for you and your fellow classmates, but what can you tell us about what happened from the inside?”

Kelly’s face was a mixture of shock and disbelief merged into one. Her fingertips reached for the clumps of hair that she thought should surely be there atop her head, but were not, feeling only her own scalp. She remained fixated with blankly staring eyes until once again Excelcia questioned her.

“I know this must be hard for you, but Kelly, can you tell us what happened?”

Her mouth quivered, the reporter hanging on her unspoken words and nodding as if that would somehow help them to spill out. But she could only feel a fresh wave of tears roll down as she felt the empty space above her.

“He’s gone… g-one.”

*****

Kelly had woken up early so she could spend a little extra time studying for her history exam. She was sure she would be able to breeze through the multiple choice questions, but wanted to make sure she could write a good essay that covered all of the major points about Mewni and it’s magical technology.

Her hair was messed from her rather tousled sleep. It was hard for her to get comfortable in the night, and she’d tossed and turned, thinking over the coming exam.

She grabbed her rather large hair brush and began to tidy up her aquamarine, moppish-like hair that went down to her ankles, brushing it into bushy softness. As she combed, and combed, and combed, she whisperingly repeated, “What is Mewni?”

She slipped on a pink and white striped sweater that was covered in tiny, glistening rhinestones, jumped into a pair of black shorts, and hurried downstairs for breakfast. As she poured milk into a bowl of sweetened Corn Puff cereal, she opened her notebook and ran her finger over the page.

What is Mewni?

There are many people who call Mewni home. Mewni includes not only the dimension of Mewni, which has easily become the most popular and trafficked dimension among its peers, but also the capital city of the same name, which is counted as the world’s shining star

She spooned in the first crunchy puffs into her mouth, hardly noticing their taste as she browsed through what she’d written during the past couple weeks.

Mewni has often been called a bustling metropolis. The city is massive, with its borders spread far apart. With so much space, one would expect the population to be likewise quite spread out, but that isn’t the case as the confines of Mewni’s borders are home to everyone.

She turned back a page, then forward, muttering through her food-filled mouth. “Yes, Mewni is huge. I bet it could take an entire day to walk through it all, or down through it all, if anyone wanted to ever do that.”

History tells us that in the medieval period of Mewni’s development, the world was ruled by many kingdoms…

“Oh boy, I hope I don’t have to remember the names of those.”

...each with their own sense of nationalism and sovereignty, and spread out across the land. It’s hard to say how long ago that may have been, however, as there have been no successful expeditions far past the city walls in recorded history. The land had become shrouded in a hyper-dense cloud of magic radiation that stretched for at least a number of miles in every direction, possibly covering a majority of the planet. Those who have tried to discover land beyond the violet clouds never made it back and officials have declared the practice “too dangerous.”

She finished up her bowl of cereal and shut the notebook, tossing it into her furry backpack as she dashed out of the door, which was comprised of her mother’s ample reddish hair.

“Bye honey!” the large mass of Woolett hair responded, an arm reaching out to wave.

As Kelly started on the path towards school, her initially frantic pace slackened. The various homes began to intermingle with office buildings, private dwellings converging in with the cityscape, slowly taking them over.

The city had multiple layers. Most of the citizens Kelly knew resided in the topmost section on the city where everything was beautiful, elegant, and modern. Splashed across building facades were plentiful lights and ever-present holographic bulletins displaying the news, latest gossips, or products to buy. Any part of the city currently being renovated was masked by the use of such holograms, or simply covered by beautiful tapestries or potted planters until the work was completed. The city always looked immaculate, and full of vibrant life. There were buildings everywhere, but also a decent helping of greenery to make it all feel natural. There was no place for disrepair or dirt, save for within potted plants.

The city was built high upon itself, using the levels below it to serve as its stacked foundation. Older buildings got over-topped by new ones as steadily the kingdom had risen, the wealthiest staying above while the less-so remained below. One could walk down the multitude of levels; the further one went, however, the more the sky overhead instead became a network of streetways and pillars, and foundationary bases belonging to larger buildings top-side. Everything became darker as natural light was replaced by false lighting, the air more closed and musty. The buildings were left forgotten the further down one went, going ages without seeing mortar to fill gaps or fresh coats of paint, especially to cover up ugly graffiti. The highest echelons of the city blocked the lower portions from view and even mind, as most of the attention was paid completely to the upper portion of Mewni, not the underbelly of it.

But, Kelly had never gone to other levels. The class of citizen she belonged to would never need for such things. Although she wondered about it, it was still beneath her desires to check out.

She started to think more about the test awaiting her later in the day and it weighed down her shoulders until even her feet felt heavy. As she reviewed the notes in her head her mind slowly kept wanting to indulge in more fun, exciting thoughts: that of discovering what adventures might lay beyond the violet clouds at the outer rim of Mewni. The daydream took over her vision as she imagined endless waves of monstrous creatures to fight.

“I’d love to be the first one to discover what was really out past that violet cloud.”

“My folks told me it was just against the rules.”

Kelly was immediately thrust back into reality. Her boyfriend, Tad, a smaller Woolett a quarter of her height and completely covered in hair, leapt up onto the top of her head. He perched there, his own hair color merging in with Kelly’s, looking like just an extension of her.

“Hey, babe.”

“Tad, don’t sneak up on me like that!”

“Mellow out, Kell. I wasn’t even tryin’ to get the jump on you. You were just, like, in your own world. What were you thinkin’ about?”

“We do have a pretty major history test today, Tad. You do remember, right? You studied?”

“How hard can it be?”

Kelly sighed and rolled her eyes. She could almost hear the smile coming from his voice. “You can’t expect to just ace the test without studying. I’ve been racking my brain trying to make sure I will remember everything, especially for the essay part.”

“You get way too stressed out if you think about it too much,” he said as he reclined, getting comfortable atop her head. “Hey, I heard what you said about the violet clouds. Wanna find out some day? Are there scary monsters out there?”

“No, Tad, of course not, we have plenty of scary-looking monsters inside the city, and they’re totally allowed to be here.”

“I meant outside the city limits. Look, I’m just saying I don’t know what there is to be afraid of out there besides getting in trouble with-”

“Off limits, under authority of the crown, pppft. Please.”

“I know, right?”

It wasn’t long before the two teens had arrived at the front of Paragon Academy. The building had a vaulted front exterior, covered in glass and held up by multiple marble pillars. Every facet of it was clean-cut and angled, looking like an architectural marvel. The ground floor of the building was hewn from white stone while the two upper floors were made of sandstone-like clay, bathed with sunset colors.

Kelly headed into the building along with several other classmates. She tried to squeeze past a locker and some classmates and wound up bumping into someone. When she turned to excuse herself, she found herself having to look up, and pretty far up. She had run into a tall, large-armed adult who was part of a trio wearing full blue jumpsuits. They seemed somewhat oddly out of place among the halls and students, but she figured they were probably just janitors.

“Excuse me,” she said.

The clean-shaven man stared down at her with eyes steadily widening, as if he’d been quite taken by surprise and seeing something amazing before him.

She bent slightly to pick up her notebook which she’d dropped. The man was quick to snap it up before she could. It was ridiculous how fast he moved to make sure his huge hand reached it before her more slender one.

“Uhm, you dropped?” he questioned, despite the obvious answer.

“Yes, thank you.”

Kelly went to take the book from his hand but found his grip to be vice-like. She pulled gently but continued to meet with resistance. When the man seemed unable to let go she looked back up at him. His eyes had been on her the whole time and only her glance broke him out of his trance, when her eyes met his own.

“Sorry,” he said, his cheeks flushing red. “Your book?”

“Yes, may I have it now, please?”

“The book… uhm, yes, it’s yours!” He stumbled on his own tongue.

“Yo, Kell, this dude don’t seem right,” Tad whispered.

“Shhh,” she hushed between her teeth, trying to maintain a polite smile that was lingering far too long on her face. She pulled the book harder and finally the man released it.

“I’m sorry,” he said, wiping his brow and trying to find some kind of words to fill the moment that was making his heart race. “Kobi.” He extended his hand her way.

Kelly chuckled loosely and took his hand to shake.

“Kelly. And hey, thanks for picking it up. Sorry I bumped into you.”

“No trouble,” he smiled. “I like Kelly. I-I mean!” he bungled over his words again while trying rapidly to recover, scratching his head. “I like to meet you. T-that is-I mean, good to see your p-pretty face. Uh-I-uh!”

One of the similarly dressed men broke into their conversation. He was far older, wearing small round spectacles on the bridge of his nose which sat atop a thin, rather well-shaped mustache that spiked out on the sides.

“We don’t mean to be any trouble, he means to say, miss. Sorry we got in your way.”

Kelly shrugged her shoulders and slipped the notebook over her shoulder and into her backpack. “Not a problem,” she said as she finally saw her exit and headed away towards the cafeteria.

“Dude was creepin’ my vibes, man, lookin’ at you that way.”

“Oh Tad, stop being so jelly.”

The big fellow was tall enough that he stood over most adults, and well over the students. He couldn’t help but let his eyes track the aqua mass of hair until he couldn’t tell Kelly apart from anyone else anymore, losing her as she and Tad vanished in the ever growing crowd of students.

The man’s partner tapped his elbow. “Let’s go, Kobi. We don’t have time to linger.”

They went in another direction, the expression on Kobi’s face like someone stole away his happiness. The third member of the blue-suited party smacked him on the back of his head.

“The hell you doing?!” he cussed in the loudest whisper he could muster.

The trio rounded a corner while Kelly and Tad continued on into the cafe, taking a seat at one of the tables.

Kelly knew she’d be able to get in a last few tidbits of studying before history class began. She was relieved that she didn’t have to wait until later in the day for the test, as her nerves were already getting the better of her. Even so, she wanted to cram in all the information she could before any of it could seep out of her brain.

Tad knocked on her forehead. “Hey, wanna go hit up that new club ‘The Bounce Lounge’ tonight after school?”

The pair of teens looked around. The school cafeteria was packing with energetic Mewman teens. Some were eating, others were chatting, and many more had their heads buried in books. Something about the atmosphere seemed naturally distracting. Kelly pinched the bridge of her nose and took a sharp breath before continuing.

“How you can even think about that right now is beyond me. I’m worrying about getting a good grade describing the aethertech of Mewni, and you’re worrying about the best place to party.”

Tad smirked within his locks. “Don’t hush my groove, Kell. I have an easy solution to the essay section.”

“Oh yeah?” Kelly doubtingly questioned. “What’s that?”

“Why not talk about the alternative technologies? You know, the kind that the poorer Mewmans use? Bet nobody’s gonna cover that. Automatic ‘A’ just for the topic.”

“The essay portion isn’t supposed to be a heavy opinion piece. I’m planning to try and write a mostly historical account, and you’re supposed to be giving me a springboard, not conspiracy theories.”

“Come on, K, history is all about opinions! Your paper will be too boring without some seasoning, you feel me?”

“That’s not even - ahhh,” she replied. “Look, just help me get my thoughts together for right now. I need to ace this history paper, and I have a lot of other things to do this week.”

“Alright, whatever, but you’re getting us some pizza later. What’s next?”

They looked back down at the notebook Kelly had flopped open on the table.

Despite Mewni’s predicament as a dense, mononational cityscape, the city-state has found its way forward and thrived on the backs of its brilliant minds and hardworking populace. In a land where magic has always been pervasive, the greatest challenge of Mewni’s ancestry was in discovering a means by which to take magic beyond its known limits.

The forefathers of a once medieval world would discover a means to convert magic from its aetherial essence into a more tangible fuel source. The discovery of this process, coined “aetherial manipulation” offered a seemingly limitless source of sustainable energy by which innovative creations could be powered. Lights that didn’t need to burn a candle wick were invented, factories that could handle the production of crops, the sanitation of water, and the distribution of such resources were now possible. High speed travel and communication had become all the more accessible for the average citizen where such luxuries had often been afforded to only royalty and noblemen. This, of course, included an impressive array of weaponry which could manipulate heavily dense magic particles to produce heat, cold, and a slew of other well known combative elements. All of these incredible advances occurred in rapid succession and would come to characterize a period known as “The Aetherotechnical Revolution”.

“Wow, you wrote everything the professor said down? Snooze-fest. Ya lost me at ‘forefathers’.���

Kelly’s finger continued down the page as she mumbled the words, a bit miffed.

After experiencing a century-long ‘golden age’, Mewni had come to stand at the forefront of inter-dimensional society, having carved out a place for itself as a magical hub that was vastly ahead of its time. But if the discovery of aetherotechnology ushered in Mewni’s golden age, the realization of its ultimate limitations would serve to conclude it.

Tad yawned, and Kelly persisted, louder and more angrily, trying to both get Tad to listen so something might sink in, but also to further emboss it into her own mind so she could translate it later during the exam.

Nobody had suspected that the magic energy surrounding the Mewni dimension would wane. It was always rather apparent that magic was truly a renewable resource, one that resurfaced as quickly as it was spent. Such beliefs were hard to combat, as a great deal of research had gone into determining whether their dependence on aetherotechnology would lead to a depletion of the resource. It was even more evident given that the clouds surrounding Mewni never weakened, never changed, never so much as moved.  But after over a hundred years, studies were finally beginning to observe changes. It started with reports coming from other dimensions. A gradual decrease in magic had become apparent. In spite of this, Mewni’s own resources initially continued to show no signs of decay, but eventually it too began to show that it was ever-so-slightly thinning out.

“Jeez, this is so boring. I thought you wanted to impress the teacher, not put them to sleep.”

“History papers are never supposed to be entertaining, Tad. If you could get that through your fluffy skull then maybe I could actually get some more useful comments out of you.”

“It’s still too snoresville if you ask me.”

“Well, oh great history expert, what would you write about after all of this in a history paper?”

“Obviously I’d talk about all of the cool technology we came up with, like ships and laser beams and stuff. Oh, and what about the hoverboard and hovercars?”

“That’s getting too off-topic, dude. I need to talk history, not just cool stuff.”

“You could totally still work in the limited resource tech. Just mention some of the crazy stuff we know people had tried, like, in the past.” “You know what, maybe that’s not such a bad idea after all, as long as it’s based on historical facts and not here-say. You actually are using your head for a change.”

“That’s all I’ve got, babe.”

She rolled her eyes at him yet again before continuing past a couple more pages of notes. It took her a minute to find the paragraph she was looking for. The cafeteria had filled and it was steadily becoming louder; the din beginning to break her concentration.

“Here it is. I know the professor had mentioned something about “alternatives” to aether-tech., but we didn’t spend much time on it.”

With magic energy not as endlessly bountiful as it was once known to be, it was no surprise that restrictions would begin to fall upon the use of aethertech and the supply and demand of magic overall. Access to these resources has become more expensive, especially in recent decades, and though it wouldn’t put too much of a dent in the average citizen’s wallet, there are those in Mewni who have called the resource ‘unaffordable’ and many have claimed that less-wealthy individuals who don’t use aetherotechnology as much as the average citizen have sought to create bootleg forms of technology that seek to rely on a resource mostly or wholly separate from magic.

These attempts have likely been all but successful, with the glaring problem that alternative sources of energy are unstable and inefficient at best while completely unusable at worst. Furthermore, attempts to integrated other types of energy with magic have proven not only unsuccessful, but dangerous. Magic is a pure substance, and using it in conjunction with more ‘worldly’ elements have the potential to be hazardous, and possibly catastrophic.

As such, officials have outlawed the practice of citizens creating their own aetherotechnology and especially obtaining magic energy for the purposes of integrating it with alternative forms of energy. These experiments are regarded as “simply too dangerous” and, as such, production is to be approved and mandated by the crown only. It is a wonder if people truly are still attempting to make alternative forms of technology with such harsh restrictions in place.

“Honestly, babe, that is super wordy. You better make, like, a short easy version for the essay.”

“We’re gonna be writing for a history paper, it is supposed to be super wordy.”

“Do you really think the teacher wants to read something like this though, if you make the essay out to be this long, drawn out thing? I can’t even get through the first few sentences without starting to doze off, and I’m totally down with hearing about dangerous things.”

“They are specifically looking for this kind of stuff. I’m not writing a novel, it’s history and social commentary. Seriously, and you wonder why your grades suffer…”

“C’mon, I’m pretty good at math you know.”

“Look, my brain is almost done soaking in as much as it can handle, just bare with me for a little longer.”

“What’s next, the history of museums and fast food?”

“Sort of, yeah.”

“Wait, what?”

“Shhh.”

The pace of technological advancement in society has left culture shifting around it. At first, technology was designed to create more efficient processes so as to allow for more free time amongst the hardest working members of the population, but it soon shifted to convenience for everyone as society began to fathom just how much potential aetherotechnology had to offer. It can power factories and cars, but it can also project videos, cook food in new ways, and even be used to heat pools or create toys and thrill-rides.

People have a lot more free time now, and the question of the culture these days is not just what we can do with our time, but what we truly want to do with it. Big shopping centers with beautiful lights and live music festivals have become the norm, and the world has seemed increasingly more creative with professional and personal endeavors. Surely with a world that becomes increasingly more advanced, and a society that finds themselves free to be themselves and tackle unique life ventures, Mewni is bound to change even further for the better. Citizens will tackle the question of how to make the most of life instead of continuing to ask the question of how to make a living at all.

Kelly leaned back on the table bench. “I think if I write all of this, in this order, it should be cohesive enough, at least if I can make it as much as my notes as possible. It covers all of the bases. Mewni really is an amazing place when you take in how it all came to be.”

Tad’s eyes peeked through his hair to look over the notes for a second glance, this time more thoughtfully.

“Hmm, that is actually pretty cool. I wouldn’t want to work in a factory myself, but it makes you appreciate those that bring it all to life, you know? And, just like, imagine a life without magic and having to find some other way to do everything. Like, how would we even light up all of Mewni with just candles? We’d hardly get around if we had to still use carriages pulled by unicorns or something. Technology kind of rules, doesn’t it Kelly?”

The girl just smirked a little up at him as she saw his eyes light up for a brief moment of awakening.

“I think you’re right. It has really helped make the world a better pla-”

BOOOoooooom

The whole room froze in shock as they heard the resounding of an explosion coming from somewhere not far off, surely inside the school building, the floor shaking slightly beneath their feet. Within an instant the lights cut out throughout the room. There weren’t any windows in the cafeteria, so the power outage had all but left people groping about toward the hallway, seeking a light source. At first it was quiet; the explosion had stolen everyone’s voices. When there was no noise to follow up the initial boom, however, people began to whisper to one another. The muttering gave way to light chatter which, in turn, gave way to a cacophony of panicked voices crowding around the exits toward the hallways.

“C’mon, Kelly, let’s go this way.” Tad pulled at the girl’s arm and led her toward a hallway around the backside of the cafeteria, squeezing past tables and around other hesitant students who lined the walls of the room.

The two found their way through to the back hallway. There were significantly less people, allowing the two to proceed with relative ease. Nothing about the experience became any more ‘pleasant’ as the two continued, moving through a quiet, pitch black hallway. Each step began to feel like a pace taken away from the school they knew and into the corridors of a haunted, abandoned building.

Occasional echoing clangs and slams could be heard coming from behind, surely the sounds of those who refused to leave the cafeteria. They turned a corner, welcomed by a glint of daylight at the other end of the hallway. This path would shoot them out near the front entrance, back by where the front end of the lunchroom led.

“Should we really be going that way, Tad? We don’t know what caused that explosion.”

“There aren’t any better ways around. It’s way too dark back here. Let’s just take a peek and see if it’s safe.”

They both nodded affirmatively to each other before starting to move again. They crept along at first, picking up the pace with each step and impatiently pushing themselves to go faster. At last, they could see each other again. Light from the outside had filtered in enough to fill their surroundings with a little bit of dim color though dust was in the air. Sure enough, more voices could be heard, some of the chatter becoming more distinct as people came into view; Tad and Kelly had reached the school lobby. For whatever reason, there were still people crowding around and obscuring the view, refusing to budge. It was as if the whole lot of them were watching a show.

Finally, they made it close enough to take in the whole of their surroundings. The entrance to the school had been severely damaged; it was likely the blast zone of whatever they had heard a few minutes ago. Black marks lined the walls, chunks of stone and plaster from the walls and shards of shattered glass from window panes were strewn about all over the floor, light fixtures were destroyed, littered about in no particular fashion. Above all else, there was one detail that drew everyone’s attention.

In the center of the room was a large, black goo-like substance clumped up in the center of the room. The muck was fairly large, altogether possessing the mass of at least one full-grown Mewman adult. The pile of goo was pulsing and seemed to be moving. The pitch-black slime flowed over itself and back around, seemingly making an effort to hold some degree of consistency. But it inched along ever so slightly, behaving as though it were simply testing the waters of a foreign environment.

What had seemed like more than a minute-long stalemate was broken when someone began to walk toward the door and the goo in hopes of going around it. Nerves had possessed one student who couldn’t bear the scene any longer and simply wished to reach the exit. It proved to be a fatal mistake.

Suddenly the black substance dramatically increased the pace of its flow, moving into itself as though it were a container full of boiling water, circulating across a convection current. The substance rose into a narrow pillar and curled forward, looking like an aggressive and agitated serpent. The very next instant, a chunk of the black goo shot out of the pillar directly toward the teen who had stepped out of line. The substance landed on his face with a splash. Everyone else jolted backwards a few steps, spooked but uncertain about what was happening. Tad and Kelly followed suit, but looked on with trepidation. A knot was beginning to form in their throats as they felt a sense of dread creeping into them.

The target of the black goo put his hands up in panic and began trying to wipe the goo off of his face, emitting muffled gasps as the goo covered his mouth and began to move. His hands tore and clawed at the slime desperately, but his efforts were futile. The goo simply flowed through the gaps between his fingers, pulsating and flowing around itself along his head. It began to flatten across his face as it spread out further, spinning and winding at high speeds until it found the right orifices. The goo covered his eyes, nose, ears, mouth, and began flowing into each.

His attempts to grab at the strange substance had stopped, and now, reflexively, the victim began to press his hands violently against the sides of his head. Though they remained muffled, the sounds of desperation and fear had gone and were replaced simply by screeching yelps of pain. He fell to his knees and clutched at his temple, wailing in stifled agony as the black substance flowed violently through his sinuses, optic nerves, and ear canals, cycling in and out as it seemed to be probing the boy’s brain.

After a few more moments the movement stopped, and the student’s body fell to the ground, limp. The goo moved out of and off of him, leaving behind a still body. He was certainly unconscious, and perhaps worse. There was no way to determine if the poor boy was even alive.

Screams of panic echoed from the crowd as people witnessed a scene out of some sort of horror movie, and people rightly assumed the worst. Now that the initial target of the goo had gone still, the substance began to pulse and course back into itself once again. Two separate blobs were now manifest with the one that had attacked their fellow student now practically doubled in size.

Desensitized to the helplessness of their captees, the goo began to race forward. Swirling around and sliding along, the substance set its sights on more of the students. They shrieked and began to push against one another in hopes of moving away from the substance. Their efforts only riled up their attackers even more.

The goo began to form up into pillars and shoot out, separating into smaller units and beginning to latch themselves onto the frantic Mewmans who clumped up the back of the lobby. Chaos ensued as people pushed, tripped, and fell about trying to escape, going any which way they could. Some tried to move around the goo while it was busy with their peers, others sought sanctuary in the lunchroom, where they could potentially hull themselves up, and others retreated down the halls from whence they came.

Kelly, too, violently grabbed Tad’s hands, his own four grabbing hers, and they took off back down the dark hallway that had spit them out into the lobby.

“We need to go, Tad!”

“But where do we go?”

“WE JUST NEED TO GO!”

Kelly wanted to pick a direction as much away from the goo as fellow classmates.

“Can we make it to the gym?” Tad offered.

Kelly didn’t have to be coached further. She looked around to try and get her bearings in the near darkness, heading away from the lobby, back through the panicking students in the hallways, and down another corridor that led to the gymnasium.

It was no easy task once in the hallway, outside of the range of any windows providing natural light through the dusty air. They had to slow down almost to a walking pace, Kelly releasing Tad’s hands so that she could feel her way along the lockers that lined down the hall. Her fingers stroked over the smooth doors and locks, her touch becoming her new eyes. Without the majority of her vision it seemed like the hallway might go on for an eternity, her hands touching locker after locker without end. It was a wholly different experience, and one that only compounded the terror rushing the blood through her veins. Her feet wanted to run, but she could only manage so much with her lack of sight.

It had even grown more quiet the further away from the lobby they got. She hadn’t noticed it immediately, but her remaining senses were being forced to take over. Few students were following behind her along the locker-wall. She could only really hear someone else tapping against the locks as she had done, at least several meters behind.

“I can’t see anything in here, Kell.”

“It’s not that much farther. We should be able to use the exit from the gym once we get there.”

“I sure hope so,” he coughed. “Yo, someone is following us.”

“I’m sure it’s just others trying to get to the gym too.”

“Yeah, but they aren’t sayin’ anything.”

She paused for a moment to listen. She heard the clacking of the locks against the metallic lockers, the sound getting closer.

“Almost to the gym!” she called out over her shoulder to whoever was behind her. There was no response, just the knocking locks picking up the pace.

Kelly’s heart skipped a beat as her breath caught in her throat.

“Go Kelly, GO!” Tad yelled.

After what felt like a warehouse full of lockers, Kelly’s fingers finally felt the long flattened bar that signaled the large doorway into the gymnasium. Just a push away and their escape could be secured. The rush of endorphins made her dizzy, her hands pushing down hard against the handle. The door gave way to painfully bright light as it opened, the lights of the gymnasium still somehow remaining on against the odds.

Just at that moment one of the tendrils of blackened sludge shot their way behind their backs, right before Kelly could set foot towards freedom. It had been stalking them, oozing over the residual heat of her touch against the metal. It slammed hard into the back of Tad’s head, instantly knocking him from Kelly’s own. He went sailing straight forward and onto the floor.

“TAD!”

She reached for one of his hands but the goo was beginning to envelop him, sinking down through his unruly hair. She impulsively wanted to grab him, but her self preservation won out, seeing the goo covering him in seconds like a wave, drowning him beneath his mop-top of hair.

He convulsed as he fought against it, his multiple hands ripping at the blob hopelessly.

Kelly could only look on, frozen in terror, reliving the moments she had only just witnessed happening to some other kid, except this time it was her boyfriend contorting in agony, screaming out in gurgling pain until he became silenced.

More teens had staggered down the locker hallway after seeing the light source. They pressed in hard behind her, starting to push her closer to Tad’s body and the goo in their frenzied escape. She wanted to stay, wanted to hold Tad, to wake him up, but she couldn’t move forward for fear of the ooze, leaning back into the students that were bumping against her. The room was filling with smoke, slowly choking away her meager sight of Tad and the air around her lungs.

A moment of clarity overcame her senses as pure instinct took over; she tore her eyes away from Tad’s lifeless shape and moved along with the crowd, disappearing down the hall, turning another corner and vanishing into the darkness as they all moved toward another wing of the school.

*****

Much later that afternoon, the school building was practically visible all over the city. It was plastered on hover screens in the plazas, along animated billboards, and on every television channel with round-the-clock coverage. They played and replayed the same scenes of students fleeing for their lives, being embraced by crying parents, over and over, along with footage of parents that couldn’t find their children in all of the chaos, completely lost within disoriented emotion. Reporters were buzzing about the facility that had long since been on lockdown by the Royal Task Force. Images of the school were on screens everywhere with crowds of civilians, reporters, and officials alike milling about the city and arguing with one another as they watched everything unfolding.

A black-haired reporter, now one of the main faces covering the crisis, went up on the main screen of the pavilion facing the eagerly watching audience. A new report was going live.

“We have now learned that a mysterious, bio-engineered creation had been deployed following an explosion at one of Mewni’s private higher-learning preparatory institutions, which began to drastically multiply as it assaulted students, staff, and faculty early this morning. The only good fortunate in all of this terror was that the explosion itself had alerted the authorities quickly enough. Within less than an hour the Task Force had forced their way into the school and attempted to fight back against the creature-like blobs. Though their weapons and tools were essentially useless against the biological makeup of the goo, they had finally managed to contain it by erecting aetherotech barriers along the walls in order to steer it back and box it all in the lunchroom.”

“Yes, well done! That substance hunted down the remaining people within and none could escape!” one man griped.

“At least whatever that thing was didn’t get out into the public!” another barked in response.

“It should have been handled better,” a stranger piped up.

Another voice shouted over the others. “Quiet! All of you, listen!”

The reporter was still continuing.

“There were a number of casualties. Eye witness reports from those who had survived, both civilian and members of the Task Force, detailed some of what had happened before everything could be contained.”

An image of a student with bright orange, braided hair faced the camera as the reporter turned the focus onto her. The girl’s voice was extremely high pitched.

“Those that got latched onto by the ooze thing were stuck inside the quarantine zone until… until there were none left standing. It kept attacking. Some people climbed tables, others tried to hide in the lockers. We just ran and ran, and we - every way we could we just ran.”

Her voice quickened, her eyes quickly tearing as her voice cracked. The memory of the event started to flood out of her lips with her wild train of thought.

“An-and then there was this one person we could see moving around inside the room, and - and he had taken off into the kitchen. He was really short, kinda small, could only really see his hair, and he disappeared behind the double doors. Maybe he was looking for another way out but he was still carrying some of the black goo on him.”

The television screen suddenly cut to an image of a police officer behind a podium. He talked over the eyewitness, his badge revealing his status as lieutenant.

“We are still trying to ascertain the victim’s name and unfortunately, based on the evidence, it is clear that this student probably died from injuries sustained. I want to make it absolutely clear that they would still be within the quarantine zone. We have not been informed if the body has been recovered as of yet, however.”

What the reporters and police all failed to address was that the slime ended the attack on its own, and not due to the Task Force which took all of the credit for saving the day. The goo had run out of conscious, moving Mewmans to pursue, and eventually all of it began coming back together within the confines of the barrier the task force had set up. The separate globs of it proceeded to move around and over the debris and people lying around them as if they were no longer even cognitive of their existence, forming back into one massive clump of merged goo. All of it had apparently collected itself together, although neither the last victim nor the goo on that particular victim’s head had ever returned from behind the doors to the kitchen. Once the blobs were whole, the excited, rapid movements had declined until the goo had simply stopped moving completely and sort of  just ‘died’.

Official statements about the substance remained inconclusive, the topic avoided in interviews. All attempts were made to cover up the sheer scale of the situation. Hours after the event was over, the royal scientists had managed to determine that the substance had indeed succumbed to an inanimate state, safe to remove from the building. Efforts to study the residual matter had confounded everyone. There was no special hazardous substance left at all. It was simply a brittle clump of dust and ash. It was as if the substance was a burned log or some pulverized gravel that lay dormant. Not a trace of the dangerous material had remained.

“Further reports have sadly confirmed that all of the victims of the strange goo are, in fact, deceased,” the reporter went on. “Biopsies revealed no trauma to cells or tissues within the body. The only notable change was to the victims’ body chemistry: that of a complete absence of mitochondria within the body’s neurons. According to the coroner, all brain activity had simply ceased, and the lack of energy flowing through the nervous system lead to a full body shut down. Effectually, their lives had been sucked out of their heads. What a horrific tragedy. This has been Excelsia reporting, GMM news.”

What concerned the citizens the most was that the attack, and subsequent biological weapon, simply came out of nowhere. Information was in short, distilled supply, and people felt unsafe.

It wasn’t long before more official statements had been made, claiming that security would be tightened around the city, and that there would be no cause for alarm despite the increase in police activity. As convincing as the official statements were, the events of the day would leave Mewni in a stir for some amount of time while repairs, reparations, and further research was being conducted.

Life went on in Mewni, as it must, but the paranoia and repetitive images of trauma would follow every person who bore witness to the events of that day, wondering what could have caused it all, and wondering what the future of their home may possibly look like.

*****

Once the cameras had all cut and the mics all turned off, the lieutenant that had stood at the podium for the live press conference quickly dismissed himself. He brushed aside anyone trying to fish for more answers and refused to take further questions, especially from the excessively nosey, sidling reporter Excelcia, which he couldn’t stand. He tagged two officers to follow along with him as he passed through the crowd control restraint beams, away from all prying eyes and ears.

He had brought the two men into the school with him. They had restored enough power that they could get a clear view of the school’s interior, and after what he’d heard the orange-haired teenager say, he wanted to follow up on it quietly.

“Through the kitchen she said,” the lieutenant states with determined force.

The three officers began to survey the scene. Stoves, refrigeration units, and cabinets all were opened. They moved appliances around. Pots and pans were scattered all around where students scrambled to escape through the darkness, but other than that everything was mostly in order, without a sign of any leftover blob material.

“Over here!” one of them called out. “Behind here.”

At the very back of the kitchen and behind the massive dish-washing unit was a hole broken through the floor. It was rather small, but big enough for an average-built Mewman to possibly fit through, and then some.

The lieutenant leaned over the hole, pulled a thin pen-like object from his pocket, and clicked on button at its tip. Instantly a sharp day-glow light illuminated around it even brighter than the lights already shining in the room. He lowered it partially into the hole.

“Hmmm.”

“What is it, lieutenant?”

“Here, hold onto this a second.” He passed the light stick over and reached into a drop-leg holster attached to his leg, fishing out a matchbox-sized scanner.

“I only see a lot of… uuugh, rotten food down here?”

“Appears that way, doesn’t it?” his superior said, switching on the device he held. It cast out a flat, wide beam of light as it scanned over the surrounding surfaces. He moved it slowly over and around the hole, slightly within it, then back up, until it revealed a strange marking. The symbol had a neon-like ethereal glow caused by the scanner’s beam, making it give off its own light like purple fire.  

A cold, grave demeanor took over the lieutenant’s countenance. He promptly turned off the scanner and stood back up.

“What is it,” his companion asked while handing him back his light stick.

The commanding officer didn’t waste time explaining, shooting him a severe glance and pointing at the hole.

“The kitchen staff obviously found this little nook and were dumping leftovers down here out of laziness. Seal it up, and speak of this to noone.”

“But sir, it’s just food contaminants? Nothing to be worri-”

His curt retort ran over his sentence, snapping back with all seriousness. “That’s an order! And see to it that it gets done immediately. The kitchen of off limits until this gets handled, understand?”

The two officers looked at each other curiously but nodded in agreement.

[authorjond369]

✦ LU Matrix Factorization ✦

(https://youtu.be/6tnAzRMtq3M)(https://youtu.be/dqdzKTkWMG4)Matrix LU Factorizations – Step-by-Step Guide to LU DecompositionIn this video, we dive into LU factorization, a powerful method to decompose a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). LU decomposition simplifies matrix operations, making it easier to solve linear systems and perform matrix…

[jonathankatwhatever]

I need to get better at the almost vestibular response of the gsProcess crossing a 0 to reach the next 1 at the understanding level which is above the level of my regular existence.

———————-

My understanding of the matrix conceptions is improving by the instant. I see how the determinant is literally the comparison of the 2 diagonals so when it equals 1, that means the SBE and Bhyp lines generate a 1, which is then literally a 1, like a CM1 or 1gs which thus contain or at least which refers to the difference between the diagonals as SBE, as counting over and across the gs, so the result of 1 or -1 matches the ideal, meaning the 0Space calculation meets the 1Space. The 0Space comes in at the diagonals, which now may be another value as long as the determinant is 1 or -1.

This includes the concept of function composition, which is an aspect of I//I, with composition being within the usual spaces, within rs, so within something like a real cube, where f(x) and g(x) can be seen. We extend that to I//I by extending composition to the real space. This occurs in more than one way. Example is that a real result is the End which is Between in the gsProcess linking what generates that End, as in up from lower dimensions and down from higher, so the real represents the contextual representation of those gsPracesses into the End which includes the tObject within a Thing in [D3-4].

Another way of saying this is to look at the I//I for real as saying more about the Registry of Actualities, which means the Ends counting along the szK, meaning those which stand Between the tangible and intangible, which means the szK counts the Triangular projected onto the grid sheet. You can also see Pyramidal emerge. To explain, if I can, we have an intangible End and a tangible End, each representing an Object. That Object exists as a Thing along the szK because that draws the Triangular which mediates the 1-0Segment connecting those Ends.

The intangible Object can be described as the iObject resulting from the pairing across to the tangible Object. This can be sketched or imaged with high resolution, meaning the Thing’s structure has an inherent potential and also what is realized, which evokes statistics about what is realized, particularly with iterations over a number of Pathways.

This resolves a long-standing question: why do I fantasize to contradiction? I’ve long associated that with D4-3, that these threads refer to a Thing which exists in D4-3 because there is an impossibility, a contradiction which prevents it from resolving into existence. This is expressed at the particle level as Pauli exclusion. I believe we’ve covered how the spin says these can’t be in the same spot but these can.

Maybe one way to do this would be to use left handed structures and then connecting those to right handed structures, meaning the ones we assume and which we map to positive direction. This might work. I can suddenly see how this models a fantasy like being a great warrior or lover or whatever. And that’s why fantasy and songs touch Actualities: they Attach to the tangible aspects as the +1 while constructing a counter version to the way it happened or perhaps can happen.

I need to go to sleep. It’s almost 1AM.

[xtruss]

Climate-Friendly Buildings That Look Great and Do Their Part for the Planet

— By Fan Chen | April 04, 2023

Buildings, from construction to operation, generate about 40 percent of annual global CO2 emissions. Architects worldwide are offering their solutions to transform these structures into sustainable, self-sufficient systems that can even help slow down global warming. From a vertical garden in Singapore or a bamboo arch in Indonesia to a 3D-printed house in Italy or giant timber "mushrooms" in Spain, here are carbon-neutral structures and prototypes with great design—visually and environmentally.

Urban Treehouse, Populus, Denver

Populus, set to open in late 2023 in downtown Denver, aims to be the United States' first climate-positive hotel by using sustainable materials in the construction process and planting more than 700,000 trees offsite. Its stylish, triangular shape takes inspiration from the aspen tree, often associated with Colorado; its sculptural white facade is covered in windows that mimic the eye-shaped marks on tree trunks. The 13-story, 265-room building also features a rooftop with native plants and a skyline stretching to the Rocky Mountains.

No Footprint House in Costa Rica. Fernando Alda

Indoor-Outdoor Living, No Footprint House, Ojochal, Costa Rica

This tropical house sits in a small village at the edge of a vast rainforest. The prototype's wooden facade panels are customized for the climate with slats that can be opened or closed to connect the inside and out, and to let air flow through and sunlight drench the room. The slanted roof protects the house from heavy rainfall and harvests solar energy, forming a self-sufficient power system.

A-Block Building rendering in Canada. Dialog/Centennial College

Art of Timber, A-Block Building, Scarborough, Canada

Slated to be completed this year, this large, laminated timber building at Centennial College of Applied Arts and Technology is likely Canada's first carbon-neutral higher education facility. The highly transparent six-story building offsets carbon emissions by using locally sourced wood and rooftop photovoltaic panels to generate energy.

Metropol Parasol in Seville, Spain. Sylvain Sonnet/Getty

Shade and Play, Metropol Parasol, Seville, Spain

At public Plaza de la Encarnación, numerous glued veneers and more than 3,000 connection nodes are joined to create six giant timber parasols, known as the Mushrooms of Seville for their fungi-like shape. To explore this engineering adventure and one of the largest wooden structures in the world, climb to its top and trek along the winding walkway for stunning views of the city and see how the roof grid and solar cells provide energy to lower-level restaurants and markets.

Tecla House in Italy. WASP and Mario Cucinella Architect

Not Dot Matrix, Tecla House, Massa Lombarda, Italy

In a case of dreams becoming reality, this house in Ravenna is the product of 3D printers. Tecla, a combination of "technology" and "clay," is a prototype of eco-friendly emergency housing. Made of locally sourced clay and mainly biodegradable materials, the dome-shaped shell ensures the house's stability, blocks outdoor heat and allows daylight to flow from wall to wall. It takes only 200 hours to build each unit with 3D-printing technology, further reducing carbon emissions during construction.

Rwanda Institute of Conservation. Iwan Baan/Mass Design Group

Solar-Powered Habitat, Rwanda Institute for Conservation Agriculture (RICA), Gashora, Rwanda

In one of the most impoverished districts in Rwanda, architects are building an ecological model with big impact. Completely powered by an on-site solar array, structures on the campus are built from local materials and require no electrical lighting. The array, the largest in Rwanda, also supports crop irrigation and waste recycling systems.

Masdar Institute of Science and Technology in Abu Dhabi. Nigel Young

Desert Cool Zone, Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates

Khalifa University's sustainability-focused research institute features a large solar field and facades made of low-carbon materials to serve as a thermal barrier against the intense desert sun. The campus building, with its intricate latticework in traditional Islamic design and its undulating dome, consumes less than half the potable water and electricity compared to UAE's average buildings and generates 60 percent more energy.

Oasia Hotel Downtown in Singapore. Roslan Rahman/Getty

Vertical Rainforest Habitat, Oasia Hotel Downtown, Singapore

Amid the metallic high-rises in downtown Singapore, this floral, leafy skyscraper looks like an overgrown furry monster from afar. Aimed at recreating an entire ecosystem, the tower includes an open-air sky garden. The 88-foot-high vertical garden includes 21 species of climbing plants that form a living facade for the red-hued building and attract various wildlife, such as birds, squirrels and lizards.

The Arc at Green School in Bali, Indonesia. Tommaso Riva

Breezy Boater, The Arc at Green School, Bali, Indonesia

At first glance, what looks like a giant folded straw hat that the wind might carry off to the nearby Indian Ocean is, in fact, the curved roof of this school's gymnasium. The private institution in the jungle advocates sustainability education. Bamboo arches stretching 62 feet are bent to form a 45-foot-high natural shelter that resembles the shape of a mammal's rib cage. Maximizing space with minimal materials, this unparalleled structure lets the breezes provide natural air conditioning.

The Pixel Building on Queensberry St, Carlton. The building has the distinction of being Australia's first carbon neutral commercial building, and implementing several green-friendly initiatives. Getty Images

Tangram Model, Pixel Building, Melbourne, Australia

Outside Australia's first carbon-neutral office building, an assembly of recycled, colorful panels maximizes daylight and minimizes glare. Inside, a carefully designed water capture- and storage-system that includes rainfall filtration and vacuum toilets guarantees all the building's non-potable water needs. Opened 13 years ago, Pixel remains a model for green buildings—low-carbon concrete, energy self-sufficient and design-forward.

[programmingsolver]

CS433: Assignment#1

    In this problem, you will write a shared memory parallel program to solve a lower triangular system of equations Lx = y where L is an n n lower triangular matrix of reals and x; y are real-valued n 1 vectors. The problem is   to find x given L and y. Row i of a lower triangular matrix has zeroes in columns i + 1 to n 1 for 0 i n 1. Additionally, we will assume that no diagonal element of L…

[linear-algebra-cheat-sheelu]

linear algebra cheat sheet free CQ4L#

💾 ►►► DOWNLOAD FILE 🔥🔥🔥🔥🔥 Here is a very basic intro to some of the more common linear algebra operations used in deep learning. NEW: check out machine learning cheatsheet for more. Intuitional Linear Algebra Cheatsheet. This post reviews basic linear algebra for introductory machine learning. Note: It will develop over time. :: Linear algebra cheat sheet. Rectangular m-by-n matrices. Basically as the title says. I've found it incredibly helpful to reference cheat sheets similar to the ones on this site here while. 9 Show Menu. Login or Register. Network Flows. Outer Product matrix is uv T , u and v can be any size. IF: w1, w2 are within S. Diagonal Matrices. Important Facts: 1. Important facts 2: 1. Created By fionaw. Favourited By. Comments No comments yet. Add yours below! Add a Comment Your Comment Please enter your name. Your Name. Please enter your email address Your Email Address. Please enter your Comment. Your Comment. Post Your Comment. Linear Algebra Cheat Sheet spoopyy. Latest Cheat Sheet 2 Pages. Branches of botany and zoology Cheat Sheet different studies and fields under botany and zoology. Random Cheat Sheet 1 Page. About Cheatography Cheatography is a collection of cheat sheets and quick references in 25 languages for everything from business to science! Behind the Scenes. If you have any problems, or just want to say hi, you can find us right here:. Recent Activity pravallika updated Branches of botany and zoology. Basic Equations Network Flows. Balancing Chemical Equations. Triangle Inequality. Identity matrix is square matrix with 1 along diagonals. B is the inverse of A. E2 E1. Examples of Subspaces IF: w1, w2 are within S. Lower Triangular. Upper Triangular. Symmetric if:. An is the matrix when the nth column is replaced by b. The Dimension Theorem A is m x n matrix.

[linear-algebra-cheat-shee0o]

linear algebra cheat sheet PC I01D#

💾 ►►► DOWNLOAD FILE 🔥🔥🔥🔥🔥 Here is a very basic intro to some of the more common linear algebra operations used in deep learning. NEW: check out machine learning cheatsheet for more. Intuitional Linear Algebra Cheatsheet. This post reviews basic linear algebra for introductory machine learning. Note: It will develop over time. :: Linear algebra cheat sheet. Rectangular m-by-n matrices. Basically as the title says. I've found it incredibly helpful to reference cheat sheets similar to the ones on this site here while. 9 Show Menu. Login or Register. Network Flows. Outer Product matrix is uv T , u and v can be any size. IF: w1, w2 are within S. Diagonal Matrices. Important Facts: 1. Important facts 2: 1. Created By fionaw. Favourited By. Comments No comments yet. Add yours below! Add a Comment Your Comment Please enter your name. Your Name. Please enter your email address Your Email Address. Please enter your Comment. Your Comment. Post Your Comment. Linear Algebra Cheat Sheet spoopyy. Latest Cheat Sheet 2 Pages. Branches of botany and zoology Cheat Sheet different studies and fields under botany and zoology. Random Cheat Sheet 1 Page. About Cheatography Cheatography is a collection of cheat sheets and quick references in 25 languages for everything from business to science! Behind the Scenes. If you have any problems, or just want to say hi, you can find us right here:. Recent Activity pravallika updated Branches of botany and zoology. Basic Equations Network Flows. Balancing Chemical Equations. Triangle Inequality. Identity matrix is square matrix with 1 along diagonals. B is the inverse of A. E2 E1. Examples of Subspaces IF: w1, w2 are within S. Lower Triangular. Upper Triangular. Symmetric if:. An is the matrix when the nth column is replaced by b. The Dimension Theorem A is m x n matrix.