lnq 👨🏿‍🦱: knottheory
👨🏿‍🦱
Showing posts with label knottheory. Show all posts
Showing posts with label knottheory. Show all posts

/ link

link :== coupler of two or more objects. Topologically, a link is a non-intersecting collection of knots🪢. A link is also a single element comprising a chain. -- Additionally, it refers to a discrete brane 'hyperlinked' to other branes in some cellular automata scheme.
/// Likewise, we can describe a knot as a link with one (1) component.

--------

Metrically, a link* (symbol: L) :== the standardized cent-to-calorie conversion -- our derived cryptocurrent unit^ in juking expressed as some value of ¢ents🪙. ** Named after 🧑🏿Link Starbureiy. ^^ Links can be conjoined🔗 (get it?) to yield an energy🔋 signature.

As 💱spreadable@ crypto🧩, a link (Q♭) :== minima fibor as a control [fret = 0.000384615385¢~ (≈ $1.00 cap)] in trades. @@ ie. strategies get extrapolated to other fibors. ~~ ie. 1/26 of initial penny fret to get $1.00. This is our Q♯🎶 entrée [part of the standard opening for encryption], which acts as the default (however interchangeable) ballet on UUe's rotisserie. (see +list, QQ, 🧑🏿lnq, stew, juke tax, residue, token, MONEY, penny fret, toy, font, c@$#tag, 🧑🏿lnq's bubblegum)

/ fruut

Fruut :== a class of transformers sourced from STU, and translated into the mesh geometrical primitives: rectangle, circle, and triangle. For identification purposes, we like to say that each shape corresponds to a 'fruit'; respectively: berry (alpha helix), banana🍌 (beta sheet), and lime🍋 (gamma delta) [colloquialized as 'bag'].

The fruut are part of the Stewdio's kit (complementing the flageolet) for transcoding (the parameters of) twistor fields so as to establish both intonation+melody/groove of The Origamic Symphony🎶. (see starberry)
TOS /// +It is prerequisite that mathematics begin with primitive notions. Hence, when postulating, we start at some angle and navigate from there.
+Geometric primitives are called such because they are the building blocks for other forms and shapes.
+The melody is a secondary actor in stew choreography (ie. essential for closing🔒 a loopstring➿ generated from its walk).
+Rule of thumb: fruut is for folding, and the flageolet is a metronome for pencil generation.


In time signatorial mode, fruut are the tools used for folding stews to derive (arrive at) a fibor. (see patch)

It is assumed that the shapes are true (ie. two-dimensional) by default, and can occupy higher dimensions of uuater (world volume).

/ twistor

In a folding scenario, the twistor (u,u) :== a complex transform* of STU solved from stew choreography.** Defined by a tight (≤ handicap) walk.

Twistors are derivatives of unique plays embedded in twistorspace that are hedged from tablature. Statistically, twistors act as complexity catalysts and can have negative (vacuum) or non-negative (bubble) potential.

Let (u,u) be any two (2) leaves sequenced for stewcing. A twistor is an operator that associates a stewcable dyad (egg,epp) in a finite field with curvature which is coded to eventually become a zero-bubble. Twistors are measured with ¢ent🪙 values that are typically small (ie. frets).
/// All twistors are assumed to be fit. We stewc (hedge) in order to identify those folds which are ideal/most fit.
Function map: stew choreographytwistor

/ fibor

A fibor :== an automaton that is a unique and totally twistable ||f(u,u)=0|| crypto mesh* (cluster) of links (L) which is subject to stewcing.** There are two (2) classes of fibor: MONEY and bubblegum. This is a tertiary (stereo) isoform of Egglepple.

Fibor^ is a functional component (dyadic fluctuator) of twist economics; hashed (from an algorithm of mathemusic) to output some image.^^ Each fibor is both its own structural formula and memory address. As part of the endgame🏁, we care mainly for the ludological aspect(s) of stewcing (topology, rhetoric, mechanics, etc.), as they relate to identification and function attribution. (see minor, major, fibor bundle, fibor mutation, stew, zero-bubble, walk, stewc tax)
/// +Mathematically, fibors are trivial zeroes (compared to stews which are non-trivial zeroes).
+Fibor is the 'print' (or vending) stage. This would be the total algorithm input assigned from stew choreography. Gameplay-wise, stewcers should aim to get here as quickly as possible.
+For purposes of imaging, the loopstring➿ may be a simple topological schematic, serving to illustrate some animation directive.
+Just to reiterate, our primary interests are not in figuring out the science (eg. chemistry, biology, physics, etc.) behind the folding (chemical bonding, dipole moments, things of this nature are left to such experts). We are chiefly concerned with "writing a playbook", so to speak, that will enable anyone to generate algorithms (plays) for configuring polymorphisms and coordinating meshes.
+We must be careful with our vocabulary. Yes, fibor is stringy, but it is not a requirement that it be physical, per se. It just necessarily assumes the properties (namely that it can vibrate in multiple dimensions) of strings as it propagates into worldspace. In this case, we are concerned strictly with string dynamics (incorporating the landscape vacua philosophy). However, fibor - in the mold of stew choreography - is open/closed in some arbitrary volume, whence it is attached to a dynamical mem(brane). Oddly, however, there exists a method to start with Planck data, and work our way up to normalization with g-folding.

Function map: minormajorfiborfibor bundle

/ coverage

A spread's coverage [cover-patch identity]* :== the twistorspace posture (knot🪢 formation) for statistically graphing a [supersymmetric] zone on(to) some pitch (ie. fibor-bundling a set of BIG + SMALL branes). Since there are 100 different covers (0-99) that can be patched 26 different ways (a-z), there exists a total of 2,600 discrete coverages.** An example would be something like [(cover-34,patch.g) = coverage 34g].

As cryptographic shape schemes [puzzles🧩], coverages are fundamentally combinatorial; spanning the entire range of branes(SMALL + BIG). A coverage can be (strategically) both preventive and responsive. (see #coverage, toonlight, 🔋e:e statistics, patchwork, cassette, Honne Bay🪱)

/ twistorspace

Ludologically, twistorspace or "slot" :== 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 (secured🔐 with crypto) these conformations (bubble or vacuum); without such a (force) field, the signal (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 handicap, juke field, coverage)

/ ¢ent🪙

mathemusical cent Mathemusically, a ¢ent🪙 :== quantum measure as the ratio* of two (2) (close) frequencies.** Made from stew choreography. For the ratio (a:b) to remain constant over the frequency spectrum, the frequency range encompassed by a ¢ent must be proportional to those frequencies. Scaled🎚, an equally tempered semitone spans 100 ¢ents (a dollar) by definition.

According to The Origamic Symphony🎶, an octave^ - the unit of frequency level when the base logarithm = [font size × font weight] - spans twenty-six (26) semitones (intervals/measures), and therefore, 2600 ¢ents.^^ The interval between the first and second harmonics of the harmonics series. Because raising a frequency by one (1) ¢ent is equivalent to multiplying this constant ¢ent value, and 2600 ¢ents doubles a frequency, the ratio of frequencies one ¢ent apart is calculated as the 2600th root of 2 (~ 1.00026663)!.!! pip = .00026663. (see ¢ent formula, crypto, fibor, juke tax, MONEY, stew choreography, residue, u-u economics, link, 🌞funshine)
TOS /// Economically, the ¢ent (cachecredit) is the rudimentary u-u crypto object (used to measure/determine the size of twistorspace). Reward function-wise, ¢ents are transacted in the twist economy as the negotiable instrument [ie. purchase, pairing, etc.].
+Physically, ¢ents are the practical universal currency.

/ loop➰

Mathematically, a loop➰ :== a closed🔒 string with no knots or tanglements whose path initiates and terminates at the same point.

Ludologically, a loop is a simple infinite walk (ie. circuit); 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.

/ 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).

/ hypocurrency

Hypocurrency is tokenage held* by a merchant (think 'cache' or 'debit'💵).Not in circulation. (compare hypercurrency. See also hyperlink, residue)

/ braid

/ tangle