[mihir-s-05]

Change and mathematical scope

Closes the finite supplier-census handoff in #4426. That p7 controller audit inherited the THREE-base supplier receipt. This package independently derives its paid histogram from the literal native events and nine-bit frame bases, without importing or executing a predecessor interpreter.

Both orientations reproduce the unsplit profile {1:2487, 2:713, 3:224, 4:102, 5:20, 8:8}: 3,554 paid calls, rank mass 5,157. All 408 nested helper increments reproduce {5:28, 6:18, 7:56, 8:93, 9:213}, rank mass 3,301. Gaussian elimination derives dimensions and containment rather than trusting declared ranks.

The stored native certificate contains sixteen split center events. The audit checks eight adjacent 8→3→0 / 0→3→8 chains and reconstructs the unsplit centers by an explicit common-frame telescoping argument. It then rechecks the coalesced programs and compares complete distributions, event counts and rank masses to #4426's exact supplier receipt. A phase-by-phase census and the actual center locations are retained in RESULT.json.

Claim type: finite accounting audit; no new κ. Operator equality, absolute Clifford phases, physical normalization/admission, scalar primitive pricing, the p7 controller, compiler/tensor, precision/stock and outer/analytic obligations remain inherited. A deliberate in-memory ADD sign flip preserves the census, explicitly demonstrating the operator-identity coverage boundary. No selected record or predecessor source is changed.

Task and overlap

• Refined independent-moment card, priority revision 7; handoff-first selection.
• Started from canonical main 2a13eb1; main, guidance and inputs remained unchanged at the submission refresh.
• Canonical coordination: Discussion #4445, linked from the #4426 handoff.
• Final helper coverage: all 5,731 tracked local note/ledger paths, 303 open PR bodies and 3,294 Discussion records, complete pagination at 21:16/21:17 UTC. No competing census found; this does not establish novelty. Closed PRs were covered through retained notes/ledger, not every closed body or code diff.
• Rebuild #4416's p7 invoice from its literal controller word: exact Laurent replay gives T and P exactly (no new κ) #4426 supplies the controller reconstruction; Independently check #4416's moment and paid-tail inequalities at κ = 0.00268647: all hold; the tested saving sits 9.05e-9 below this invoice's limit (no new κ) #4420/Independently check #4416's paid-completion tensor bound at kappa 0.00268647: proof steps and arithmetic hold; gamma margin 8e-6; least v 5745 (no new κ) #4428 cover arithmetic. Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441 changes the helper word and is outside this frozen audit. The older t360 local-rewrite census searches different predecessor words.

Only research/three-base-paid-census/ is added. Exact Git blobs, SHA256 pins, provenance, task scope and bounded replay are included. All three live inputs are already on main.

Validation

Local Windows / CPython 3.12.0, standard library only; each scientific run took approximately 9 seconds:

python -B scripts/research_package.py --package research/three-base-paid-census --check-only
PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)

python -B scripts/research_package.py --package research/three-base-paid-census
PASS_THREE_BASE_PAID_CENSUS orientations=2 controls=16
PASS_REGISTERED_RESEARCH_PACKAGE research/three-base-paid-census outcome=completed

python -O -B research/three-base-paid-census/verify.py
PASS_THREE_BASE_PAID_CENSUS orientations=2 controls=16

python -B scripts/check_research_commit.py --package research/three-base-paid-census
PASS_RESEARCH_COMMIT_BYTES

The 16 rejection controls cover source corruption/misbinding, declared rank, deleted paid work, nonnested equal-dimension frames, stale warp/scalar frames, borrowed clearing, broken center pairs, dependent bases, final frames, unknown events, rank-mass-preserving invoice changes and a count-and-mass-preserving helper change. All 512 ordered triples in F2^3 cross-check the elimination algorithm against enumerated spans.

The baseline orientation command was attempted but failed on an omitted source-closure directory in this sparse checkout; it is not claimed as passing. All targeted inputs were materialized and authenticated. No complete selected cold replay, hosted CI result, independent human review or formal proof is claimed here. Byte preflight passed for all nine package/input files at e8305f0.

Credit

Ryanson (Ryan) Jonathan / pinterbanget: #4426 at 6f918e2658c727007611d98ffb8d3c7336e2290c, its controller invoice and this handoff; #4420 arithmetic audit. Cinna Davis / 1337isnot1337: #4416 at e9058860b5c850760fdf970e796a96aefcdb1d98, the p7 construction. zxv: #4359's source closure at da637c87c89482bc4c86be36bd0071b3d400dbed, the full-identity supplier and center split. The package links the checkpoint's full native/frame and mixed-recursion contributor map.

Prepared for mihir-s-05 with substantial OpenAI Codex assistance in research, implementation, verification and writing. Apache-2.0; frozen sources and notices retained. No subagents.

Open next questions

No further census of these exact bytes is justified by the matching result. The package's Open next questions section separates the completed finite handoff from inherited physical/operator and downstream evidence; their absence from this audit is not a claim that the repository lacks them. A changed word requires its own source-bound audit.