H3V7N5QF

Genesis-Ongoing: 25 blind finite derivations from small edits of one seed, each recording what follows and what does not.

Each derivation starts from a short seed about terms, assertions xry and a fixed list of changes. It is carried out blind: only this repository is used, the body of each paper uses only the seed's words, and nothing is steered toward a known theory. Every notion is recorded as given, chosen, derived, computed, refuted or open. Every alternative that is not eliminated by a proof is kept. The results are Python computations written to evidence/, Lean 4 theorems with #print axioms reports, and a claim ledger per derivation that names, for each claim, its evidence and what would falsify it.

---

Part of a three-repository programme

This is the second of three public repositories by the same author. They use different methods and make different kinds of claim. This section says how they connect, and where the connection is a recorded gap and not a derivation.

Repository	Role
19L57G1, Genesis	A blind, sealed, finite derivation from an opaque seed, and the point where it stops: the minimum response is tied across readings L and F.
H3V7N5QF (this repository), Genesis-Ongoing	25 further blind derivations, each from its own seed, on terms, assertions and a short list of changes: obstruction and answer, fewest changes, counted assertions, two relations, an admission gate, and three operator-targeted climbing rounds.
theory_of_finite_quantum_mechanics, finite QM	A derivation graph of 892 nodes in 35 stages. It starts from the inert inscription <>, passes through Pre-Genesis, Genesis, S(n) and MSS-N, the witnessed-difference programme (WDP), L1 and L1 to L2, and asks how far finite exact constructions reach toward finite QM. Every node carries a status and an evidence grade E0 to E4.

How this repository relates to Genesis. It continues the method, not the code. It shares the bookkeeping discipline, the claim ledger with falsifiers, local gates, and a prose-watchlist gate that was ported from 19L57G1 (paper/second/change_log.md, item 15). Its code and Lean do not import 19L57G1. The seed is a different one. A comparison of the two event languages is in meta/immune_system/genesis_correspondence.md, outside any derivation. It is a table of chosen analogies, refuted identifications and open bridges, and it identifies nothing.

How it connects to finite QM. At finite QM commit 8f1f7ca (2026-10-22), 16 nodes of the derivation graph cite this repository. 14 are in the GENESIS stage, 1 is in COMPUTATION and 1 is in WDP. 12 are PROVED_LEAN, 2 are OPEN, 1 is COMPUTATIONALLY_CHECKED and 1 is DEFINITION.

Finite QM node	Status	What it records
PG-GEN-IRREFLEXIVE-DISTINCT	PROVED_LEAN	First: a and b are two terms, and bra is independent.
PG-GEN-ONGOING-OBSTRUCTION	PROVED_LEAN	First: exactly two kinds of change are obstructed.
PG-GEN-ONGOING-FEWEST-CHANGES	PROVED_LEAN	First: the closed formula for the fewest changes.
PG-GEN-REWRITING-COMMUTATION	PROVED_LEAN	Lean in the second derivation's library: changes commute with injective rewriting of terms.
PGW-GO-REACH-CEILING	PROVED_LEAN	First: every finite legal state with a term is a result.
PGW-GO-CONTRACTION-STEP2-STEP3	PROVED_LEAN	Second and third: striking changes from the base seed.
PGW-GO-MULTIPLICITY-MONOTONE	PROVED_LEAN	Fourth: counted assertions never fall along a sequence.
PGW-GO-TWO-RELATIONS-SWAP	PROVED_LEAN	Eighth and ninth: a second relation, and the exchange of the two.
PGW-GO-LEFTOVER-UNBOUNDEDNESS	PROVED_LEAN	Tenth and sixteenth: admitting a recorded leftover does not terminate.
PGW-GO-ADMISSION-GATE	DEFINITION	Fifteenth: reaching a result does not admit it.
PG-GEN-SAMENESS-REFINEMENTS	COMPUTATIONALLY_CHECKED	Sameness readings: excess, plain and together arrays, cancellation cost, bounded two-term rewriting orbits.
PGW-GO-H1-CANCELLATION-EXCESS	PROVED_LEAN	Twenty-second (climbing round H1).
PGW-GO-H2-STATE-RAISING-GAUGE	PROVED_LEAN	Twenty-third (climbing round H2).
PGW-GO-H3-TWIN-FILLS-HOLONOMY	PROVED_LEAN

The route from the H3 node into PGW-WDP-BRIDGE-ONGOING-TO-WINDOW is GAP_NO_DERIVATION. None of the 25 papers states a derivation of a Born rule, a complex field, an inner product or any other structure of finite QM. The finite QM graph cites this repository by a sibling path and not by a pinned commit. 14 of the 16 nodes are grade E0 in finite QM's evidence map, which means that map's checkout has no counted evidence file for them. Mostly that is because the Lean and code they cite are here, not there. A name check of the 45 Lean references that name a declaration finds 42 whose file exists here and whose last name component occurs in it. That is a citation check. It is not a replay of the Lean and not a review that each theorem states its node's claim. The other three cite lean4/Second/Rename.lean under names that do not occur in this repository.

This is the beginning of the README. Read the rest at the original. Read the full README ↗