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 global 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]

One axiom may admit more than one typed physical reading. Completeness means classifying every output-relevant admitted alternative, not forcing the family to contain one member.

No total or physically complete reading family is claimed. Global decoder uniqueness is not a program requirement. Scoped uniqueness and nonuniqueness questions remain local to their declared classes. 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 ordinary quantum run QASM exactly in Z[ζ₈] · no cryogenics, no rounding 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 M_J = [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.

Program rule: a successful physical description may be a classified family of typed readings rather than one unique decoder. Every output-relevant alternative, overlap and equivalence must be explicit, and no reading may be selected after seeing the result it is used to explain. 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 sin²θ_W = 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 n_s − 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.