Knot Theory Playground

Family

Invariants

Complexity

gnosis-math / finite trace bridge
What the picture is measuring
score rope units = components + crossings + bridge + genus + reserve
curve carrier deltas project to amplitude; equal heights can still be different knots
proof layer GlobalKnotCode plus finite Reidemeister traces normalize to one code form
boundary not arbitrary classical diagram recognition yet; this is the encoded finite ledger
Apotheosis circles: the visible small circles are the 54 shell loops of the trihexenneon box, factored as 3 x 2 x 3 x 3. The ledger row is 54 components + 3 crossings + 1 reserve = 58. The circles are components, not crossing marks.

Polynomials (gnosis-math witnesses)

Rope-Length Catalog

Ashley Book Map

Reidemeister

moves: 0

B5 Braid -- FoldedKnot traits

try 3
choose 2
commit 4
letGo 1
learn 3

NP ≠ P UNKNOT ∈ NP

The runtime lives in unknot regions. Knots are walls.
Box: Trihexenneon [3,2,3,3] = 54-torus
Boundary: apotheosis wall (knotty)
Interior: smooth unknot
Cert: Reidemeister sequence (Hass-Lagarias-Pippenger 1999)
Circles: 54 shell components on an enclosing sphere. Apotheosis adds the formal +3 crossing band and +1 reserve in the rope ledger.
aeon --/120 · phase -- · breath --s
QUEUE REGIME queue 0 · done 0/0 · slot 0
c = 3   target 3