Conditional κ = 0.001673648366462479 by concentrating T16 buffers

research/t16-buffer-concentration/PROOF.md

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+# Scoped construction and replay argument
+
+The source is the exact pending PR3381 commit `ef1f7b1f9cb582767e448dc047b2359ded28076f`. Its authenticated retained source reconstructs PR3375 from a canonical selected-map patch, then replays the six3381 stages. This avoids assuming an unreviewed headline or treating a compressed container as its mathematical payload.
+
+Each new stage identifies roles by `(stage, replica, helper)`, verifies their width and source bin, applies simultaneous destinations and compacts each affected bin. Canonical payload hashes bind every intermediate map. Whole-helper owner auditing checks capacity, contiguous slices, correct invocation identities, strict actual windows and distinct families within each invocation. Neutral stages preserve the exact paid profile, not just an approximate objective.
+
+Nine whole-bin evacuations move the positions of empty rank16 buffers without changing their total cost. A fullrank32 evacuation distributes four roles among three buffers; this intermediate change is priced exactly and is not asserted to be a universal concave-majorization gain. A pair swap further concentrates residuals. A neutral three-role cycle and an adjacent paired-block7 order change with neutral owner repairs then permit a nine-role augmenting chain. Two follow-on exchanges consolidate its rank6 and rank7 residuals. The final aggregate change relative to3381 is `-2 H16 + H32`, with zero change in rank mass.
+
+The one new paired-block swap is admitted under the same explicit-order rules as3381: every one of144 calls appears once, every replica retains stages0..8 in order, and the two banks remain paired. The retained lift recomputes source-event windows, provider times and the schedule digest. The unchanged independent controller audit checks the actual source-event projection rather than trusting the requested order. Rows are serialized consistently by time/helper so emitter and auditor agree on the sigma stream.
+
+The complete eleven-stage replay restores and binds the original supplier, constructs the two-bank parent, binds the explicit owner map, emits and audits the controller, derives the invoice, assembles both supplier bounds and checks all47 strict outer margins. It retains69 admission,12 bit-supplier,15 controller and6 independent T16 rejection controls, plus owner and malformed-lift controls in the package tests.
+
+Full typed invoice comparison checks that every complete call record is unchanged, allowing its actual order to follow the plan. All remaining fields are identical except three cryptographic source bindings, which are checked against the generated evidence. Actual charts, literal windows, prefix reserve and row reserve are independently audited. The unchanged supplier, cover law and guard retain the inherited fixed-word ceiling and conditional assumptions.
+
+Finite replay success does not establish global packing optimality or discharge the framework's all-size compilation and analytic obligations. No selected-frontier update or maintainer acceptance is claimed.

research/t16-buffer-concentration/README.md

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+# Conditional κ by transporting and concentrating empty buffers
+
+This package composes sixteen explicit stages with [PR3381](https://github.com/CrocSwap/integer-mult-bounds/pull/3381), exact commit `ef1f7b1f9cb582767e448dc047b2359ded28076f`. The exact conditional value increases from **0.001673636244951726** to **0.001673648366462479**, a gain of **1.2121510753×10⁻⁸**. Conservative κ is **0.001673648363609684**. The complex supplier remains binding.
+
+The aggregate paid-profile difference is particularly simple: **`-2 H16 + H32`**. The final idle profile is `{1:2382, 3:118, 16:1, 32:1, 48:4880}`. Achieving it requires a sequence of legal intermediate maps: nine neutral whole-bin evacuations transport empty rank16 buffers, one fullrank32 evacuation and a pair swap improve concentration, then a neutral cycle, paired-block7 chronology repair, augmenting chain and two further consolidations complete the construction. All 69,120 roles remain whole helpers; 144 complete calls, rank mass1,041,408 and deficit5,120 are preserved.
+
+`REPAIRS.json` records every move by stable logical call/helper identity, its width and source/destination, and canonical before/after hashes. Verification reconstructs the retained3381 predecessor and every new stage with complete owner admission. The scalar objective used in search is not trusted: both supplier prices are recomputed exactly and the entire physical admission is rerun. Search tools and external optimization dependencies are private and absent from this package.
+
+The explicit causal paired-order lift and admission wrapper are retained from3381. All downstream controller, physical invoice, supplier and independent T16 checks remain intact. Every cost field agrees with the retained complete invoice; only exact source-binding hashes and the actual permutation of identical complete call records may differ. Charged prefix remains512 and physical row coefficient16,469. The exact actual-chart count is recorded in RESULT.json.
+
+Run `python3 scripts/research_package.py --package research/t16-buffer-concentration`. See `VALIDATION.json`, `PROOF.md` and the retained source manifests. The package leaves selected results and frozen predecessors unchanged. This is a finite conditional packing improvement, not a complete multiplication theorem or global optimum.
+
+Credit is preserved for Hao Yan's (@FanPUYen) T16 controller and independent audit, Philippe Van Velzen's strict admission, and the PR3308/3338/3354/3359/3366/3375/3381 lineage. The retained predecessor documents contain the source-specific attribution. Pierre (hexapode) prepared this package with substantial OpenAI Codex assistance. No independent human review is claimed.
+
+## Open next questions
+
+Can the remaining empty16 and32 bins be transported to support a further48-bin consolidation? Begin with the exact final map and require whole-helper capacity, strict physical windows and per-call family uniqueness at every stage. Preserve weaker alternative contributions for compatible combinations. The unchanged word's ceiling remains an upper bound, not an attainable physical construction.