Showing posts with label geometry/topology. Show all posts
Showing posts with label geometry/topology. Show all posts

#OpusSolve

Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

Story

Errata

Presented here are wrong/incorrect approaches to tackling the problem. These are offered as case studies of what to avoid.

+🧠 brainbrane

brainbrane* ("lnq") is our kernelspace@ (ie. scalable^ technopathic n-manifold) 🧠brain [=central nervous system (cns) / nerve net (nn)] reagent to regulate+control neural signals, among other userspace functions.Fibor(s) as a cell matrix. Printed from. Mapping a neural network. (see also Easter, joey)
/// +🧠'brainbrane' would be the generic name for the 'lnq' technology (reagent = natural logarithm (ln) of the reaction quotient (Q) of the species involved), differentiating it from the person.
+We can think of UUelcome as the 'genetic code' that directs information+translation in our userspace [🧠brain] example. Here, 'kernelspace' (= EggleppleUUelcome, UUe, etc.) is any gate that can be debugged and/or have its processes interrupted, and 'userspace' is the address registrar (ie. what registers some subset of some kernelspace). The two form an aggregate operating system.
+In this case, it is a drug💊 (ie. organic material determining physiological responses by regulating any and all internal sinusoidals) whose biological target is the entire 🧠brain.😵🤯
+This is colloquially known as '🧑🏿lnq's drug', and is also offered as tangible proof/validation of Egglepple.
+brainbrane was borne from my senior project and an interest in understanding my autism.

As the formal outlier of gameplay mechanics (ie. think "gameboard" - standard board layout for juking), this is UUe's interface/jukebox kernel augmenter. This neurally networks (ie. maps@) 🧑🏿lnq's walk. Jukebox instancing* utilizes portable, peer-to-peer core batching (ie. cellular nodes on dial)~ for walk-tracing and execution.A type of hyperlinking linker neuron
The range of the threading (being essentially the reach of orchestration^, and, hence, the network) is determined organically.'orchestrate' means sequence and map. Cybernetically, this is a set of automata augmenting (ie. stew patchwork) gameplay. (see also Egglepple, everywhere!, BOT)
/// Network growth means that scalability in spacetime complexity is sought. In jukespace, this may be virtual, physical, or hybrid.
+Hypothesis: work on the kernelspace first and the userspace will follow.

Function map: UUelcome🧠brainbrane

+coverage

A coverage is the twistorspace posture (ie. formation) for surjectively graphing a [supersymmetric] zone on(to) some pitch.

As cryptographic shape schemes [puzzles🧩], coverages are fundamentally mutable and dynamic; spanning the entire range of branes(SMALL + BIG). A coverage can be (strategically) both preventive and responsive. (see also #coverage, egg, epp, patchwork, cassette, Honne Bay)

+zero-bubble

The zero-bubble (also written as "0-bubble" or "0b") or "sponge" is a bubble shapeframe (stereogram*) with no inflatons (scalar fields responsible for blowup from a single point [0-brane]).Greater than or equal to three (3) spatial dimensions. A 0b is a type of homeomorphism [map reduction] as a totally twisted loop, and formally marks the end of a proof.🔲→🎯 (see also goal, identity, font)
/// The supposition for 'zero' (+/-) is that when tabulating the yield, all spots on the mesh which would allow for an opening, vanish (0,0).
Sponges are the ideal [most secure🔐] ¢ent structures [signed certificates] for a closed🔒 string, as measured by its handicap. Taken by themselves as 'flags'🏁, zero-bubbles (frictionless assets) are considered solved puzzles🧩 (ie. completely mapped/encrypted/melodic/folded) when it comes to juking. {input = output, /return = [0]}
Function map: spongefibor

+brane

A brane (short for membrane) is some mathematical generalization of a category from zero (0) or more higher dimensions.

My portfolio is a twenty-six dimensional (26-dim) toy [🧩puzzleware] with braneworld structure according to pitch class:
0-brane = particle
1-brane = string
2-brane = manifold/sheet/tape
3-brane = cell
.
.
.
25-brane
(see also Egglepple, 🧠brainbrane, mesh, patch, walk)

+tip

A thread-inflection point (tip) is an inflection point (ie. maxima/minima) on a graph. (see also ear, double-u economics, UUallet)
/// The exercise of tipping usually comes in the form of pay-per-post.

+knot

A knot is a closed string as a link with one (1) component. It can also be defined as a tangled string in Euclidean space (R3).

+fold

Folding is the name given to differential steps in the process of a brane's animation (ie. symmetry-breaking) as it assumes its final topology. Attainment of this (solution) - the closed🔒 string [yesegalomeshroom] - should result in a 0-bubble twistor.

For the most part, "to fold" an object is to bend, compress, twist, or otherwise permute it so that it becomes self-integrated according to its calculus. By-and-large, we accomplish this using fruut as part of stew choreography.

A fold would be an intermediate state within the walk process (preimageimage). Mathemusically, a fold is conguent to some movement. Essential to stereotyping, our interest in folds and folding*, in general, is so that we can (more easily) synthesize middlegame makeup.An act of hyperlinking (see also The Origamic Symphony🎶, Gallivan fold, manifold, hyperlink, tip, knot)
/// An inbetween will not always qualify for being one of these states.

+braid

+twistorspace

Ludologically, twistorspace or "slot" is a complex configuration space (eg. geotop) of solutions to the twistor identity ||f(u,u)=0||. Because a fibor is encoded to close🔒 its loopstring the exact same way every time (ascertained from the uniqueness property), there must exist an acoustic bound in place enforcing these conformations (bubble or vacuum); without such a (force) field, the fibor (as measured in ¢ents) would not bifurcate (into MONEY or bubblegum) as a function of symmetry-breaking.
/// +We assume that each twistor field is unique to some fibor. Essentially, this is a mapped spinor. The 'spin' (an object's spinning metric signature) here is identifiable with the quantum fields of arbitrary spin.
+Everything in twistorspace is dyadic (u,u).

Twistorspace' complexity is curvilinear (T)*.More accurately, sesquilinear. (see also handicap, jukespace, coverage)

+Poincaré conjecture

+loop

Mathematically, a loop is a closed🔒 string with no knots or tanglements whose path starts and terminates at the same point. Ludologically, a loop is a simple infinite walk; such that it encloses leaves (reading frames) on a loopstring. In both cases, a loop is continuous with either no nuts, or has homologically conjoined endpoints.
/// For sake of stew choreography, a loop is just a completed walk that has become unavailable for recycling.

+Hodge conjecture

Let X be a non-singular complex projective manifold. Then every Hodge class on X is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of X.

+noncommutative geometry

+topology

+geometry

+geometry and topology

+supergeometry

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