A short orientation to the program
TWIST-J asks whether physical reality can be modeled as a closed, exact, deterministic integer system, with continuum, geometry, probability, and fields appearing as readings of that system.
It is a falsifiable research program, not a declaration that all of physics has already been derived. The algebraic core, the declared discrete architecture, and the physical decoder are kept as separate layers.
J is a unit in the cyclotomic integers
Z[ζ5]. Its norm is exactly one and its trace is three.
In the principal complex embedding it has two exact projections:
The Canon reads these as scale and phase channels. Their interpretation as gravity and electromagnetism is a registered physical dictionary, not an algebraic uniqueness theorem.
Multiplication by J acts on four integers using only additions and
subtractions:
The autonomous architecture joins an unbounded counter to a finite checkpoint
F56 of 56 = 15625
states. The counter supplies the Thue-Morse cut and the finite state selects one
of five exact generators.
This architecture is explicitly declared. The Canon does not claim that the
checkpoint, selector, five generators, or decoder are uniquely forced by
J.
The decoder is a typed partial interface, ordered as matter, then geometry, then clock. Its outputs never feed back into the autonomous update.
Totality, uniqueness, and completeness of this decoder remain open. This boundary is deliberate: exact finite theorems are not silently promoted into complete physical laws.
The current Canon records exact results in the cyclotomic kernel, finite dynamics, Born and measurement structures, Maxwell chain complexes, counted boosts, representation ladders, and scoped gravity and cosmology forms. It also records the dictionary legs that connect them to physical language, the obligations still open, and every route that has been falsified.
The architecture contains no fitted dimensionless parameter. Its single SI calibration anchor is the electron mass. This does not by itself prove a complete Standard Model, general relativity, a unique continuum limit, or a closed SI prediction for every constant.
No summary outranks the registry. Every serious claim should be traceable to a scope, evidence, dependency, and falsifier or decision condition.
current Canon and release pins · authoritative Core · full Canon · frontier
Time is a counter. Space is read through commutators. Exact arithmetic first. Plenum, not vacuum.