TWIST-J

A finite rule with unbounded evolution.

Can physical reality be modeled as a closed, exact, deterministic system of integers? Not approximated by them. Made of them.

One algebraic axiom is assumed. A discrete architecture is declared separately. Every physical reading must be derived, scoped, or left open.

What the system is and what we read off it are two different things.

what it is A declared autonomous integer architecture: an unbounded counter joined to a finite F56 checkpoint and advanced by one exact map U. declared J = 1 + j² kernel step Multiplication by J acts on four integers using four additions, no multiplication, no rounding and no drift. [T] what we read Time is a counter. Space is read through commutators. The modulus and argument of J are read as two abelian force channels; no uniqueness or completeness is claimed. [D]
the decoder
forward U-orbit→ matter→ geometry→ clock

no output returns to the autonomous update

A typed partial interface, ordered as matter, then geometry, then clock. Its outputs never feed back into U. declared

Its registered reading legs form a dictionary, not a completeness theorem.[D]

No total, unique or complete decoder is claimed. The specific open obligations are tracked in the Frontier.

The kernel identities are proved at their declared scope. The decoder is the work, and it is where the program can fail. Every claim on this site carries its own status.

core the kernel · starting identities, the matrix, the step rule demo lab kernel-inspired dynamics, pentaplex, fractal · illustrations, not canon evidence manifest the public commitment of the method · en + cs canon Public Canon · active ledger papers mathematics + gravity, on ORCID code verify it yourself

the kernel

axiom J = 1 + j² = (1, 0, 1, 0) step (a, b, c, d) ↦ (a−c+d, b−c, a, b−c+d) matrix MJ = [1 0 −1 1; 0 1 −1 0; 1 0 0 0; 0 1 −1 1] basis (1, j, j², j³)

j is the twist unit, the primitive fifth root of unity: j⁵ = 1. Four additions per step, zero multiplications, exact integer arithmetic, zero drift. Kernel reference.

Ansatz: a successful complete decoder should be forced by the declared architecture, not selected by fit. That forcing and uniqueness are not yet proved. The declared architecture contains no fitted dimensionless parameter; its one SI calibration anchor is the electron mass.

The public ledger commits, each claim with its label:

all seven standard model hypercharges exactly in Q[T] the electroweak tree value sin²θW = 3/13[T] committed form 3/13 + 1/(32π²φ⁴)[D] FRW continuity alone does not select a unique rational dark-energy density character[T] the committed form w = −14/15 is a target and consistency witness, not a density-character selector[D] typed homogeneous selection of that density character remains open[O] the scalar tilt ns − 1 = −5α, which CMB-S4 can kill[H] the frozen photon-window Κ route is falsified at its universal occupancy lemma; roughening remains undecided and no physical-photon conclusion follows[F]

Proof, exact computation and experiment decide.

No summary here is stronger than its row in the Canon. Read the head directly: canon/CANON.md, raw Markdown at the repository head.

A. M. Thorn · J = 1 + j² ·