Simulating Reality from the First Recognition Event: The Stage Papers

We are building a simulation of reality that starts from the first recognition event and runs forward exactly, carrying every lawful branch rather than sampling one. It advances in stages. Each stage adds one physical ingredient, and its results are proved before the next stage builds on them. This record collects one paper per stage. Each paper defines its objects in classical mathematics, proves its results with their conditions stated, gives the exact numbers the simulation computes, and says what remains open. Every result stated in these papers has been checked against a machine-verified formal proof. This version contains the papers for stages 0 to 5, the stages that are built. Stages 1 and 4 rest on premises that are adopted, not yet derived, and each paper states them where its results appear. Papers for the later stages will be added to this record as they are completed. The live simulation, with every result and its status, is at recognitionphysics.org/simulation. Stage 0. Before the First Event: The Empty Record. The starting state, derived from what a beginning requires. Before anything is compared or posted, the record costs nothing and owes nothing. It is an origin of time and the unique least record, and it is distinct from the void. Stage 1. The First Recognition Event and Its Price. The cheapest first change is one unit post, entered with its reciprocal. If a post is the unit source of a field obeying the hyperbolic-sine Gauss law, a unit bond on no cycle of the field's graph gives the post price φ − 3/2 and the first-event price √5 − 2. Which graph carries the field is open. Stage 2. Every Lawful History, Carried at Once. On a three-account ledger, n posts write exactly C(n+5, 5) records, and 44,730 of the 68 eight-post histories end balanced. Under the native voxel law, every record of up to 24 ticks carries a proved enclosure of its weight. Stage 3. The First Complete Eight-Tick Pass. No complete pass over the eight corners of the parity cube takes fewer than eight ticks. Twelve eight-tick tours leave the empty record, and 3,072 of the 68 eight-post histories follow one. Stage 4. How Branches Weigh: The Native Voxel Law. Four adopted conditions on the chances of one tick admit exactly one law. It settles every start into the weight φ−9−‖s‖₁ and, from the empty record, is within 9(1 − 0.00836)n of it after n ticks. Stage 5. The Amplitude Register: An Exact Update, One Open Choice and Two Bits of Order. The exact update of the eight complex amplitudes a recognizer carries, one per tick of its cycle. Eight versions of the update meet every stated law, and a replayed history keeps at most two bits about the order of its posts.