Raise conditional κ to 0.003026674765 with a smaller completion reserve

research/eight-owned-relations/PREDECESSOR.json

@@ -0,0 +1,24 @@
+{
+  "predecessor_pr": 5377,
+  "head": "c448d13c71908647f968b06cddb795ce7d288139",
+  "author": "Ali Romman",
+  "files": {
+    "native.py": "85d994fc5661bfa53c4b42f79955ff74ffe70072163cb02fa76cd79efbcc0c97",
+    "price.py": "e228a48de6138257da7520bb57567a275c402289c90fe7e94f0ef2ad6371f836",
+    "README.md": "eb853337dfaf306808d77538e448a78f16021a2e73295078b4b2f4ff6ea835c4",
+    "RESULT.json": "1937b2e1fb4bec0fa1b0d2428a52734c554152538ac8930605bd46704f1c7320",
+    "SOURCES.json": "eca6dd5ac3028a72e016e0c8a265be702dd6c4daf481bc009524577ff5e7c831",
+    "TASK.json": "b9a9ace02d10791b49cf113dd6a19501b297920a29b9a4d5585e25ef4e8ef92f",
+    "VERIFY.json": "1fc62a3afd087aa63f8d993beb1cba944b9b441824cd14e9135e792fcd45bab8",
+    "verify.py": "c4d4fe9b74db1d47fbbfc0c602315d8256a15f0ad0e50b9fcfe2249bf65916f1",
+    "WORD.json.gz": "8d913767ad773839995e54e4d80aeff692a86687d0f78153311c8ad62b7ba1bc"
+  },
+  "new_scope": "Joint eight-relation construction, eight snapshots, sixteen removed native jobs per backward call. Direct adaptation of predecessor interpreter and pricing; not an independent implementation.",
+  "concurrent_predecessor": {
+    "pr": 5383,
+    "head": "4bd6efa51a495a7c7b7754915cf0244e7e60969e",
+    "receipt_sha256": "d6a99bd75c6b7a2146b0fc4cfa038890aaf1d4adcdef42d767fdb40b687e61aa",
+    "credit": "Ali Romman",
+    "scope": "Same eight-relation mechanism published during our construction; no priority claimed. Our new result tightens finite compiler/outer margin with a smaller completion reserve."
+  }
+}

research/eight-owned-relations/README.md

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+# Smaller completion reserve for the eight-relation supplier
+
+This package supplies **conditional κ = 0.003026674765**, improving Ali Romman’s PR #5383 value 0.00302666 by **0.000000014765** on the same complete recursive paid/target profile. The gain is a small finite compiler-margin refinement, not a new native mechanism or a practical speedup. The selected frontier remains unchanged. RESULT.json is the replay receipt; the claim requires all checks below to pass.
+
+## Exact contribution and predecessor overlap
+
+We first reconstructed eight compatible helper relations from PR #5377’s one-relation argument. During that work, PR #5383 published the same eight-relation mechanism, at head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`. We therefore credit that mechanism to the public predecessor and make no priority claim. The new result shrinks the exact completion reserve from 10⁻⁹ to 10⁻¹² and funds a higher tested saving and outer endpoint. Both constructions have the same full bill, verified explicitly against the retained PR #5383 receipt. Our preparation ordering has its own scalar allowance, charged afresh.
+
+The local native checker and pricing code are direct adaptations of Ali Romman’s PR #5377 at `c448d13c71908647f968b06cddb795ce7d288139`. They are not independent implementations of those engines. PREDECESSOR.json pins the downloaded sources and concurrent receipt. No pending PR object is needed at runtime: the new construction and receipt are retained here, and every external replay input is on the pinned main base in SOURCES.json.
+
+## Sufficient construction
+
+Let the eight rational forms in RELATIONS.json vanish. Exact row reduction has pivot columns 225, 227, 229, 230, 241, 245, 257 and 261, so each of these helpers can be prepared from the other independent cold helpers with dyadic operations. No pivot occurs on another pivot’s prepared right-hand side. Clear each private pivot, prepare it, execute the native word, then clear its output. This removes eight productive rank-9 targets per backward invocation; those targets are never credited.
+
+For each of the eight sites, the unrestricted original source satisfies two exact identities: the center row minus the saved row is a nonzero rational multiple of its relation, and the later rank-1 input row is a rational multiple of that same relation. All sixteen identities are replayed by the retained predecessor row engine before imposing the relations. Under the joint preparation, the center equals the saved value in the exact same physical frame and the later row is identically zero. Thus an owned COPY replaces each rank-8 center and identity on zero replaces each rank-1 transport. Eight distinct snapshot fields are retained across overlapping lifetimes; none is reused early.
+
+The new chronological interpreter checks every remaining scalar contact, owned erasure, native boundary, paid rank and terminal frame. Backward calls preserve all 224 main inputs and 400 independent helper inputs, and erase all 17 owned entry fields. Forward calls preserve their original 632 persistent inputs. The phase/map/adapter sequences are unchanged and bound to the source phase receipt. Copies and clears introduce no new Gaussian phase recipe. This is an exact symbolic all-input argument under the retained physical representation contracts, not numerical sampling.
+
+## Complete bill and conditional exponent
+
+The p16/a7 controller has 16 backward and two forward invocations, 15 query shears and its retained idle and boundary programs. Relative to the selected PR #4610 source, the change is −128 H1 and −128 H8 paid jobs and −128 H9 productive targets. For 0 < t < 1, the net target-minus-paid moment gain is
+
+`128 (1 + 8^t − 9^t) > 0`,
+
+by strict subadditivity of x ↦ x^t on positive reals. This mechanism and bill are already in PR #5383. There are 64,148 paid jobs, 10,800 productive fields and rank surplus 752. No extra target credit is obtained from owned pivots or snapshot fields.
+
+The fixed-profile root remains in `(0.00302667476807, 0.00302667476808)`. We use tested saving `C = 0.003026674766`, completion reserve `ρ = 10⁻¹²`, tensor power `v = 1024`, cutoff 20, completion floor 21 and tail offset 1/5. Two rational interval engines certify the complete target and paid moments. The compiler needs all of:
+
+- `α < 1 − ρ`, where α is the full paid-to-target moment ratio;
+- both charged tail ratios below 97/100 and `(97/100)^128 < 1/16`;
+- the exact normalized completed bound `1/(1 + 1024 ρ) + 4/2^32 < 1`;
+- the retained shifted-exit, rounding and complement-capacity inequalities.
+
+The smaller reserve is useful because it leaves enough moment margin near the raw root, but it is not free: shrinking it too far would violate the fixed rounding allowance in the third inequality. All these conditions are rechecked, not inferred from the sign of the raw moment.
+
+Let κ = 0.003026674765 and gap = (C − κ)/7 = 1/7,000,000,000,000. The uniform-rank compiler uses logarithmic power 1000 and computes an integer j satisfying `(gap.denominator * j + 1)^1000 < 2^j`; it checks that the preceding integer fails. The resulting finite height H and threshold N = 2^H are recorded in RESULT.json. Every intermediate saving has an explicit gap, and all 54 strict plus four functional outer predicates are positive. The construction is algorithmically specified; the enormous expanded word is not materialized.
+
+All preparation, snapshot, cleanup and route work is charged. Eight new snapshot slots and sixteen additional owned lifetimes receive two routes each. The full nonrecursive bound remains below 10^9; exact scalar and route counts appear in RESULT.json. Formal prefix norms and denominators are checked against the retained 2^192 envelope; that check does not replace a physical precision execution.
+
+## Reproduction and scope
+
+Python 3.12, standard library only, portable relative paths:
+
+```sh
+python3 -B scripts/research_package.py --package research/eight-owned-relations
+python3 -B scripts/check_research_commit.py --package research/eight-owned-relations
+```
+
+Both registered normal and optimized runs are read-only. `verify.py --write` explicitly regenerates only this package’s word and receipt. Checks cover exact row reduction, all source identities, complete native endpoints and ownership, exact word bytes, controller factorization, independent invoice counting, directed intervals, compiler and outer predicates. Wrong signs in every prepared pivot, wrong snapshot/gauge, missing owned clears and corrupted ranks are rejected. The old 10⁻⁹ reserve is rejected at the new tested saving, and a 10⁻¹³ reserve is rejected for insufficient rounding budget. Source phase lowering is authenticated and reused, not rerun.
+
+The result retains the selected framework’s permitted-erasure, whole-job mixed-target all-size/native, precision/tape, analytic, prime and exact-recovery contracts. Physical tape execution, analytic decomposition, BIT native replay, full source phase lowering, Lean/kernel verification, hosted CI and independent human acceptance are not supplied here. The source admission review for #4610/#5241 does not automatically admit this changed inventory. Chris R’s concurrent PR #5384 independently validates the single-relation predecessor; it does not validate this eight-relation compiler endpoint. No unconditional integer-multiplication theorem or selected-result change is claimed. Full-history ancestry checking is not claimed for this shallow checkout.
+
+## Open next questions
+
+Independent review should check the new reserve against the completed-bound inequality and the finite compiler at the exact printed constants, then the applicability of inherited transfer assumptions. Begin with price.py and the complete invoice in RESULT.json. See TASK.json for the structured question. A further native/profile improvement is a different task; this result supplies no global ceiling for all helper relations.
+
+## Credit
+
+Ali Romman, with OpenAI Codex assistance: PR #5377’s one-relation mechanism and source/pricing implementation, and PR #5383’s public eight-relation construction and prior bound. Cao Yifan: final native word, phase evidence and earlier compiler tightening in PR #4610. Chris R: independent selected-source admission in PR #5241. Cinna Davis: p16 controller and helper lineage in PR #4470. zxv: productive-helper framework, completion/compiler and the PR #5283 cache-contract handoff. Jacob Alan Sussman: mixed-target recursion. Dugongue: retained transported-frame lineage and this compiler-margin refinement. ToikY and all earlier native, Clifford, BIT, precision and analytic contributors retain their source credit. The smaller-reserve technique already occurs in the selected #4610/#5241 compiler audit; we claim its new certified application to this bill, not invention of that technique.
+
+Latest overlap check covered all 214 open PR search results containing “kappa”, the 100 recently updated PRs, and targeted bodies through #5384. Larger draft #5270 is not used: #5349 documents a physical-reference/controller binding mismatch. This bounded search is not exhaustive literature or Discussion coverage.
+
+Prepared by Dugongue with substantial OpenAI Codex assistance, solo. Apache-2.0. Exact predecessor and source hashes are retained.