Independent verification: PR589 paid rank ledger by exact rational projectors (no new kappa)

research/bit589-projector-ledger/README.md

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+# Independent exact-projector audit of the PR589 bit ledger
+
+**Independent finite audit; no new supplier, packing bound, endpoint or κ.**
+The source-to-ledger check passes for both the untuned PR555 word and the
+retained PR589 word. Exact rational orthogonal projectors recover every local
+paid rank. The nine-stage schedule and frozen selection recover the global
+histogram without using that histogram to infer the idle capacities.
+
+This deliberately corroborates existing results using a separate implementation.
+The original `xcheck_p.py`, `wlib.py` and record exporter already check the local
+word; this package does not claim discovery of its correctness or a defect in
+those checkers. The additional artifact is a compact independent path from the
+two source words to the selected bit invoice, with a different geometric method
+and explicit failure controls.
+
+## Result
+
+Both words have 636 frames in **Q⁸**, 661 scalar registers over **F₂**, and one
+clean, restored COPY temporary. Each forward or reverse record stream has:
+
+| Item | Count |
+|---|---:|
+| MOVE records | 2,911 |
+| Common-frame ADD records | 24,305 |
+| COPY / ERASE records | 9 / 9 |
+| Total records | 27,234 |
+| Symbolic dirty-input columns | 661 |
+| Local paid rank mass, including COPY | 5,129 |
+
+The exact local profiles are:
+
+```text
+PR555: {1:1321, 2:1342, 3:80, 4:47, 5:102, 6:10, 7:18}
+PR589: {1:1323, 2:1342, 3:79, 4:44, 5:102, 6:11, 7:19}
+delta: +2 H1 - H3 - 3 H4 + H6 + H7
+```
+
+All nine copies have rank seven. Every ordinary input, including all 439 dirty
+helper inputs, is represented by a distinct symbolic bit. Both orientations
+restore sources and helpers and implement `y_t -> y_t + x_t` on all targets.
+The COPY temporary starts and ends at zero in each lifetime.
+
+The selected nine-stage parameters are `L=9, K=4, T=32, m=64, v=111`.
+There are 288 local invocations and 28,416 live data roles. The independently
+derived idle remainder per replica is
+`{2:435, 4:444, 6:444, 7:666, 42:9}`. Therefore:
+
+```text
+global = 288 * local_PR589 + 32 * idle_per_replica
+       = {1:381024, 2:400416, 3:22752, 4:26880,
+          5:29376, 6:17376, 7:26784, 42:288}
+rank mass = 1,808,352
+64 * 28,416 - 1,808,352 = 10,272
+```
+
+[RESULT.json](RESULT.json) records both complete profiles, every idle window,
+COPY ranks, per-phase ADD counts, exact projector and record-byte digests, and
+the 16 rejected controls. It is recomputed and compared on every normal replay;
+normal replay writes no package files.
+
+## Why the projector calculation certifies each local rank
+
+The label form is one half the standard dot product. Multiplying an inner
+product by a positive scalar leaves its orthogonal projectors unchanged.
+For each rational frame span F, exact Gram–Schmidt gives nonzero orthogonal
+vectors `u_i`; form
+
+`P_F = Σ_i u_i u_iᵀ / (u_iᵀ u_i)`.
+
+The checker stores this as an integer matrix `M/d`, and checks symmetry,
+`M²=dM` and `tr(M)=d dim(F)` by integer arithmetic. It also checks that the
+frame lists **exactly** the live labels fixed by this projector. No modular
+rank, floating point, or numerical tolerance is used.
+
+For two orthogonal projectors P and Q, the test `PQ=P` proves nesting. Taking
+transposes gives `QP=P`, so
+
+`(Q-P)² = Q-P`, and `rank(Q-P) = tr(Q)-tr(P)`.
+
+An idempotent over Q has eigenvalues zero or one, which justifies the last
+equality. Every chronological MOVE must pass this matrix identity and have
+positive rank. Reverse replay uses `I-P` and reverses the record order;
+`(I-P)-(I-Q)=Q-P` preserves the charge. COPY and ERASE swap roles in reverse.
+All ADDs separately require matching current frame IDs, and COPY lifetimes
+require an unchanged center and clean temporary restoration.
+
+The source and target boundary spans contribute `2v(8-1)` to the telescoping
+MOVE rank mass; helpers contribute `8R`. Adding the nine COPY charges gives
+`2*111*7 + 8*439 + 63 = 5129`. This identity is a cross-check, not a substitute
+for reconstructing the individual ranks.
+
+One control changes the first A gate's frame from the first source line to
+the second source line. It leaves the scalar program and the **entire
+dimension-only histogram** unchanged. The projector test rejects the first
+non-nested transition. This delimits a weakened dimension-only check; the
+retained supplier checkers are not alleged to accept this mutation.
+
+## Independent global decomposition
+
+The pinned `global_k.py` recipe, its `adapt9p.py` parameterization, and the
+replica configuration specify the nine local calls per replica. The independent
+transcription aligns pair levels before each bridge and derives the ordered
+idle capacities
+
+`14, 7, 28, 7, 42, 7, 42, 28, 14, 0`.
+
+For each idle child, a backward scan stops at the last local/bridge touch of
+its pair and records the permissible intervening stages. This is a separate
+implementation of the pinned `hosting_core.py` window definition. Each positive
+capacity has `2v=222` family copies. The frozen selection is checked for family
+coverage, allowed stages, pattern capacity, width-eight helper inventory, and
+agreement between pattern counts and stage allocations. It assigns all 439
+helpers in each of the nine stages.
+
+The pending capacity is 41,958 per replica; 3,951 hosted width-eight helpers
+consume 31,608. The remaining mass is 10,350. Consequently,
+
+`288*5129 + 32*10350 = 1808352`,
+
+and the deficit also equals `32*(2*4*111 - 9*63)=10272`.
+Only **after** reconstruction are the published local/global histograms read
+as expected values. The selected assembly's immutable input digest, PR589
+identity and COPY deficit bind this comparison to its retained bit source.
+The global result is a fixed-selection accounting audit: it does not construct
+or replay the physical owners.
+
+## Reproduce and controls
+
+Python 3.12, standard library, no network or dependency installation:
+
+```sh
+python3 -I -B research/bit589-projector-ledger/verify.py
+python3 -I -B research/bit589-projector-ledger/test_verify.py
+python3 -B scripts/research_package.py --package research/bit589-projector-ledger --check-only
+python3 -B scripts/research_package.py --package research/bit589-projector-ledger
+```
+
+Expected audit output:
+
+```text
+PASS_BIT589_PROJECTOR_LEDGER local_mass=5129 global_mass=1808352 deficit=10272 controls=16
+```
+
+The seven tests cover six explicit exact-projector fixtures and a differential
+check of both full literal record exports and all exported basis/annihilator
+operators. The latter invokes the pinned predecessor exporter only as a
+secondary compatibility check; `verify.py` does not import or execute it.
+Temporary differential outputs are removed on test completion.
+
+The 16 controls reject non-nesting with equal dimensions, the same-histogram
+gate mutation, wrong MOVE/COPY/ERASE charges, omitted dirty restoration or
+compensation, wrong scatter frames, missing temporary erasure, idle overfill,
+missing families/helpers, an illegal stage window, wrong replica multiplicity,
+a rank-mass-preserving histogram change, and a corrupt source pin. Exact
+rejection reasons are checked. The verifier uses explicit exceptions, so its
+checks remain active with `python3 -O`.
+
+## Sources, scope and overlap
+
+Base: `bce54fb3f895cbe5cd4c0eb477c3afeed100190f`.
+Retained PR589: `a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46`.
+Selected PR1094: `0fc329d0bec93ca7cd288eaea1295172e8789810`.
+Exact SHA256 and Git-blob pins are in [SOURCES.json](SOURCES.json). Catalogue
+and selected-record pins are historical provenance; implementation inputs are
+checked against their working bytes. The source-aware package runner needs
+the base commit in Git history. Frozen sources are unchanged.
+
+The chooser's `independent-moment` card is refined to this source ledger, as
+recorded in [TASK.json](TASK.json). Coordination is in discussion #1166.
+No pending implementation is imported. Nearby work is explicitly credited:
+
+- PR1262 independently reconstructs the **complex** emitted ledger.
+- PR1293 audits published supplier histograms, endpoint arithmetic and D/E.
+  PR1405 separately audits that pending package's logarithm enclosure; no
+  numerical engine or conclusion from either package is used here.
+- PR1329 supplies the retained-bit identity guard. Here identity checks only
+  bind the distinct chronological ledger calculation.
+- This account's PR1307 checks cross-child physical pending projectors. The
+  present selection recount is corroboration, not another physical audit.
+- Cinna Davis's PR1351/1371 check one physical family's address operators,
+  using complete matrix replay and projector algebra respectively. Here the
+  projectors describe local eight-dimensional label frames and their complete
+  chronological rank invoice, not that physical family map.
+- PR1344 checks the scalar matrix of a particular frame-509 replacement;
+  PR1345 prices a transport census from per-register frame paths. Those local
+  arithmetic/path checks are predecessors, not new findings claimed here.
+- The incorporated `bit589-width-packing` package already proves the no-bank
+  packing optimum. This package makes no new packing-ceiling claim.
+
+Unchecked obligations: complete selected cold replay; native cohort checkers;
+the generator's recovery of these frozen compact words; full E8 lattice
+classification; every H1–H5 implication; physical owner/chart realization and
+global emitted-program equivalence; finite precision; all-size compilation;
+moment/surcharge/outer analytic transfer; Lean or a complete multiplication
+theorem. The schedule rules are a pinned, reviewed-source transcription,
+not a proof of the Python compiler for all parameters. Source hashes establish
+identity, not mathematical correctness of these inherited obligations.
+
+## Open next questions
+
+The structured questions are in [TASK.json](TASK.json).
+
+1. Connect this independently derived invoice to each call and remainder of a
+   source-bound emitted physical program. First pin a complete PR589 replay
+   capsule and compare its call expansion against this receipt, using PR1307's
+   separate pending-axis audit. The blocker is the capsule and the full
+   physical realization contract; matching accounting alone cannot discharge it.
+2. Apply this check to one distinct changed bit word before pricing its saving.
+   This can separate scalar ADD reductions from changes to paid children. A
+   candidate still needs its own H1–H5 or replacement-interface proof, hosting
+   and precision evidence; none is supplied by this audit.
+
+## Credit
+
+Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance.
+Assistance covered research, implementation, proof explanation, checks and
+writing; no independent human review is claimed. New material is Apache-2.0.
+
+DreamingOfClouds: PR589 tuning and PR545/510/463 geometry and templates.
+eumemic: PR555/543/493 scalar words and interface lineage. DaysSky: PR442
+hosting. Dylan Crow: record format/exporter. Zhihao Chen, chafreaky, Jacob
+Sussman, Dugongue, Rohan Arun and the retained source authors: preceding
+geometry, circuits and transports. Sagar Thakrar: nearby ledger/packing audits;
+Navinor: PR1293. Cinna Davis: the nearby local-matrix and physical-family audits.
+Original source notices and licenses remain untouched.