Research: independent replay of the PR2972 stock margin table with tie-out and sensitivity facts (no new kappa)

[petalas]

Summary

Adds research/stock-margin-tieout-independent/: an independently implemented replay of the stopped-range margin table published in PR #2972 (research/stock-margin-chain), plus structural facts that #2972 does not assert. The replay uses a separate integer-arithmetic path — its own exact-rational parser and floor division, no fractions module and no import of the audited code — and recomputes all 24 published integers (12 margins floor(s*L_j - L_{j-1}) and 12 routing rooms floor((1-s)*L_{j-1}), native and conservative branches, stages 2–7) from the frozen receipt research/selected-bootstrap-stock-audit/RESULT.json, SHA-256-pinned to f0bd4f22… (the same bytes #2972 audits).

Arithmetic scope, stated up front: no kappa, supplier, tariff, certificate, frozen-input or selected-frontier change. The stock coefficient remains unresolved (counted: 14/14 null actual_stock_coefficient fields). This is a finite independent certificate of recorded arithmetic plus receipt tie-outs, not a producer replay or a multiplication theorem.

What is established (exact evidence)

python3 -B research/stock-margin-tieout-independent/verify.py prints one line:

PASS_STOCK_MARGIN_TIEOUT published_pairs_checked=24 published_controls=2 min_margin_native=2851485324488315 margin_ordering=strictly_increasing_both_branches room_ordering=strictly_increasing_both_branches conservative_dominates_native=all_12_values common_saving_tieout=exact_both_branches floor_split_residual_ones=7/12 s_sensitivity=stable_at_1_unit_moves_at_1e10_units(stage6,7) headroom_minimum={bootstrap:6562783, conservative_bootstrap:6562783} guard=17 null_coefficient_stages=14/14 coefficient=unresolved

1. Independent reproduction of all 24 published integers and the two native positive controls (2851485324488315, 1015784602045963452130).
2. Structural facts (measured, new relative to Audit: stock-margin chain closes for the remaining cutoff pairs (no new kappa) #2972): margins and rooms strictly increase across stages in both branches; the conservative branch strictly exceeds the native branch at all twelve values; the floor-split residual r_j = floor(s*(L_j-L_{j-1})) - (margin_j + room_j) equals 1 at 7 of 12 stages (valid range {0,1}); recorded stock_headroom_log2 strictly increases per stage with minimum 6562783 in both branches; the guard ceil(log2(8*8194)) = 17, recomputed by integer search without floats, covers the minimum.
3. Receipt tie-out: common_saving == 1 - gaps/stock exactly (unreduced rational) in both branches, verified directly on the frozen bytes. Audit: stock-margin chain closes for the remaining cutoff pairs (no new kappa) #2972 reads only gaps/stock; the earlier stock audit enforces this only via full regeneration from producer sources.
4. Sensitivity envelope (measured): shifting the saving numerator by one denominator unit (relative ~2.5e-47) leaves all twelve native margins unchanged; a shift of 10^10 units moves exactly the stage-6/stage-7 margins (+6,864 and +2,444,877,300). The published integers pin the branch saving to the floor granularity of the receipt — the exact rational, not the printed table, is the object to bind.
5. Controls: stale-cutoff substitution (stage 7 := stage 6), one-unit stock-gap perturbation, and cross-branch saving swap are all rejected; the sensitivity envelope is asserted as the positive movement control.

Not established

• No stock coefficient (14/14 null stays; the routing-width source sentence named missing by Audit: stock-margin chain closes for the remaining cutoff pairs (no new kappa) #2972 remains missing).
• No re-derivation of the cutoffs from the frozen PR1087 assembler; no complex m=73 supplier treatment.
• The selected conditional result remains κ = 0.001672660197076918 (Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094).

Reproduction

From the repository root with CPython 3.12 (-B):

python3 -B research/stock-margin-tieout-independent/verify.py
python3 -B research/stock-margin-chain/verify.py            # predecessor cross-check, same bytes
python3 -B scripts/research_package.py --package research/stock-margin-tieout-independent
python3 -B scripts/check_research_commit.py --package research/stock-margin-tieout-independent --check-source-history

All four commands were run locally with CPython 3.12 before submission and pass; the registered VERIFY check runs in well under a second. scripts/research_baseline.py was not run locally: this submission was prepared in a cone-mode sparse checkout and the baseline script requires the selected record's package roots to be materialized; it checks the environment's selected-record bindings, not this package, whose own checks all ran. No mathematical obligation of this package is left unrun.

Related open work

• PR Audit: stock-margin chain closes for the remaining cutoff pairs (no new kappa) #2972 (audited object): its verify.py reproduces the same 24 integers through its own code path; the shared min margin 2851485324488315 and receipt hash f0bd4f22… agree numerically with this package.
• PR research: bind selected stage-one stock recurrence #3898 (stage-one stock recurrence binding) and PR research: audit selected stock boundary #3920 (PR185 completed-call boundary audit): same card family, different objects (recurrence/boundary text vs this package's cutoff-table replay); no overlapping numbers to reconcile beyond the shared frozen receipt lineage.
• PR Prove a marked-residual stock floor and bind its reflection escape #4056 (marked-residual stock floor): different quantity (residual floor), no shared numbers; both keep the coefficient unresolved.

Produced by Nick Petalas with AI assistance. Independent human and formal proof-kernel review are unclaimed. Predecessor attribution follows PR #2972 and the retained stock-audit lineage.

CI status

CI certifies the registered replay on this head: plan pass (1m59s) and replay (research/stock-margin-tieout-independent) pass (1m3s), Actions run 39300698715, head fd58efb. Interpreter in CI is the repository-configured 3.12. No failing jobs on this PR.