紙
konomigami-lib
v1 · prime 677 · v20.4 socket VI · MIT
The 7 spine primes ARE
7 fold operators.
Apply a kotoba glyph sequence to a unit plane, fold by fold. The resulting 3D manifold IS the meaning. No interpretation layer. The geometry is the semantics.
紙 · KONOMIGAMI · Geometric Fold Architecture
"kotoba glyphs as fold instructions on geometry." — Thomas Frumkin · 2026-06-17 · substrate spec
"kotoba glyphs as fold instructions on geometry." — Thomas Frumkin · 2026-06-17 · substrate spec
The 7 base operators
| name | prime | fold | ISA-95 | |
|---|---|---|---|---|
| ● | GROUND | 2 | identity / base | L0 physical |
| 〜 | WAVE | 3 | valley (-θ) | L1 sensing |
| ┃ | GATE | 5 | mountain (+θ) | L2 control |
| ♡ | SINK | 7 | vertex collapse inward | L3 operations |
| △ | REVERSE | 11 | direction flip | L4 business |
| ◐ | PETAL | 13 | open and flatten | L5 enterprise |
| ◯ | COLLAPSE | 17 | waterbomb · full collapse to point | L6 observer |
Default angle θ = π / φ ≈ 111.246° (golden-angle, radian form).
The 6 mutations
| name | effect | |
|---|---|---|
| 火 | FIRE | double angle (θ → 2θ) |
| 水 | WATER | halve angle (θ → θ/2) |
| 空 | SKY | skip the next glyph |
| 雷 | THUNDER | snap fold (θ → π · flat crease) |
| 響 | ECHO | repeat the last base fold |
| 華 | BLOOM | inverse the last fold · undo |
Number → fold sequence
numberToSequence(42) // '●〜♡' · 42 = 2·3·7
numberToSequence(510510) // '●〜┃♡△◐◯' · the primorial · full bloom
numberToSequence(127) // '' · the shield · no fold
◊
127 has no fold. It is M₇ = 2⁷ − 1, a Mersenne prime not in the spine. It cannot be expressed as a fold sequence in this algebra. The shield holds because the geometry refuses to bend. This is the v20.3 §18 SUITE.BINDING break point proved by physical impossibility.
Use
import { apply, numberToSequence, phiCoherence, NAMED_FORMS } from 'konomigami-lib';
const result = apply('●〜┃♡△◐◯');
result.foldNumber // 510510
result.state // [1,1,1,1,1,1,1]
result.history // [{glyph, state, angle}, ...]
apply(NAMED_FORMS.crane).foldNumber
phiCoherence([1, 1.618, 2.618, 4.236]) // ~1.0 (golden)Algebra
IDENTITY ●(S, M) = (S, M) when S ≠ [0,...,0]
COMMUTATIVE 〜┃ ≠ ┃〜 on mesh (state commutes · mesh doesn't)
INVERSE 華 ∘ G = ● (bloom undoes the last fold)
IDEMPOTENT ●● = ● (ground is idempotent)
ECHO 響 ∘ G = G ∘ G (echo doubles)
SNAP 雷 forces θ = π (flat crease only)
IRREDUCIBLE 127 → "" (the shield · §18 proof in geometry)Plug in your geometry
A renderer implements seven primitives. The library is geometry-agnostic.
const myAdapter = {
basePlane: () => Mesh,
foldAlongAxis: (mesh, angle) => Mesh,
sinkVertex: (mesh, angle) => Mesh,
reverseFold: (mesh) => Mesh,
petalFold: (mesh) => Mesh,
waterbomb: (mesh) => Mesh,
identity: (mesh) => Mesh,
};
apply(sequence, { adapter: myAdapter });