Conditional κ = 0.001673677688974651 through repeated T16 augmentations

research/t16-repeated-augmentations/PROOF.md

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+# Scoped repeated construction
+
+The predecessor is authenticated PR3388 at `684d347c0e6e578b8ab600d2e680ad6701cf7fa0`. Retained source evidence reconstructs its original canonical source patch and subsequent explicit recipes. Its conditional assumptions, fixed-word ceiling and full source attribution carry forward.
+
+The new construction has twenty-five stages: eleven neutral donor preparations, eleven improving augmenting paths and three further exchanges. Every move names a logical call/helper identity and checks its width and source bin before assigning the destination. Simultaneous movement and deterministic compaction preserve whole helpers and disjoint contiguous slices. Canonical before/after hashes bind every intermediate map. The full owner auditor independently checks strict physical source-event windows, capacities and family uniqueness at every stage.
+
+No chronology changes occur in this extension. Neutral preparation preserves the exact idle histogram. Each path concentrates two rank3 residuals into one rank6, and each final exchange replaces rank3 and rank6 with rank1 and rank8. Summing all stages gives `3H1 - 25H3 + 8H6 + 3H8`, which has zero rank-mass difference. Each priced improvement is checked by the exact supplier engines; search heuristics and floating estimates are not verification evidence.
+
+The full eleven-stage admission derives the actual controller and physical invoice, prices both suppliers, checks all47 strict outer margins and runs69 admission,12 bit-supplier,15 controller and6 independent T16 rejection controls. Package tests additionally check source identity, malformed moves and orders, whole-owner mutations and the retained explicit-order lift. The independent auditor checks actual chart identities and both prefix and row reserves.
+
+Complete typed invoice comparison checks every field. Only three file-binding hashes and the order of the same complete144 call records are normalized; generated evidence is checked against those bindings. The final call order is also bound directly to the candidate plan. No additional resource cost is silently omitted.
+
+The result is a finite construction under the inherited conditional framework. It is not a proof of global packing optimality, an all-size compiler or the entire multiplication theorem, and it does not select a new canonical frontier.

research/t16-repeated-augmentations/README.md

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+# Conditional κ through repeated T16 augmentations
+
+This package improves exact [PR3388](https://github.com/CrocSwap/integer-mult-bounds/pull/3388), commit `684d347c0e6e578b8ab600d2e680ad6701cf7fa0`, by repeating a neutral-donor/augmenting-path construction eleven times and then applying three residual consolidations. Exact conditional κ rises from **0.001673648366462479** to **0.001673677688974651**, a gain of **2.9322512172×10⁻⁸**. Conservative κ is **0.001673677686121868**. The complex supplier remains binding.
+
+The aggregate paid-profile change is **`3 H1 - 25 H3 + 8 H6 + 3 H8`**. Each of eleven improving paths changes `-2 H3 + H6`; each of three final exchanges changes `H1 - H3 - H6 + H8`. Neutral preparation creates the required donor configurations. The twenty-five explicit stages preserve the exact PR3388 call order and all previous gains. Whole-helper roles, rank mass1,041,408, deficit5,120 and144 complete invocations are unchanged.
+
+`REPAIRS.json` records logical `(stage, replica, helper)` identities, exact width and source/destination preimages, and canonical intermediate owner hashes. Every stage is reconstructed and fully owner-audited. No optimizer or private helper tooling runs in verification. The predecessor is reconstructed from retained source evidence rather than an unauthenticated map or headline.
+
+Verification recomputes both supplier prices and runs the complete eleven-stage admission. The retained T16 lift, physical controller, invoice and independent audit are unchanged from3388. Full typed invoice comparison allows only cryptographic source bindings and the actual order of identical complete call records; all cost fields remain equal. The actual chart count, prefix reserve, row coefficient and exact price are recorded in RESULT.json.
+
+Run `python3 scripts/research_package.py --package research/t16-repeated-augmentations`. See `PROOF.md`, `VALIDATION.json` and the source manifests. This is a finite conditional packing improvement, not a complete multiplication theorem or a global optimum. It does not alter selected results or frozen predecessor packages.
+
+Credit is preserved for Hao Yan's (@FanPUYen) T16 controller and independent audit, Philippe Van Velzen's strict admission, and the PR3308/3338/3354/3359/3366/3375/3381/3388 lineage. Source-specific attribution is retained in predecessor documents. Prepared by Pierre (hexapode) with substantial OpenAI Codex assistance; no independent human review is claimed.
+
+## Open next questions
+
+Can the new rank6 and rank8 residuals be consolidated further without losing the earlier gains? Start from the exact final map and preserve each helper's invocation, width, strict window and unique family. A bounded search stopping after eleven successes is not a proof that no further path exists; alternative neutral preparation and weaker published contributions remain candidates for composition.