Selected PR1094: one neutral move opens a strict two-step packing gain

research/selected-neutral-path-seed893/CERTIFICATE.json

@@ -0,0 +1,181 @@
+{
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "construction": {
+    "majorization": {
+      "neutral_pair": "(0,7) -> (7,0)",
+      "proof": "For p=1-a in (0,1), t^p is strictly concave. The equal-sum pair (8,0) strictly majorizes (7,1), so 8^p+0^p < 7^p+1^p. The first step only permutes (0,7).",
+      "strict_pair": "(1,7) -> (8,0)"
+    },
+    "path_length": 2,
+    "role_moves": [
+      {
+        "destination": [
+          13,
+          15,
+          14
+        ],
+        "destination_window": [
+          255,
+          430
+        ],
+        "moment_change": "exactly zero",
+        "remainders_before_after": [
+          [
+            0,
+            7
+          ],
+          [
+            7,
+            0
+          ]
+        ],
+        "role": [
+          7,
+          2,
+          230
+        ],
+        "role_index": 47270,
+        "source": [
+          1,
+          14,
+          57
+        ],
+        "source_event_position": 268,
+        "time": 98,
+        "width": 7
+      },
+      {
+        "destination": [
+          1,
+          14,
+          57
+        ],
+        "destination_window": [
+          92,
+          272
+        ],
+        "moment_change": "strict decrease for every real 0 < a < 1",
+        "remainders_before_after": [
+          [
+            1,
+            7
+          ],
+          [
+            8,
+            0
+          ]
+        ],
+        "role": [
+          1,
+          15,
+          226
+        ],
+        "role_index": 34306,
+        "source": [
+          11,
+          8,
+          103
+        ],
+        "source_event_position": 181,
+        "time": 71,
+        "width": 7
+      }
+    ],
+    "why_sequential": "The second role's landing is source-event and family legal initially, but its destination has remainder 0; after the neutral move it has remainder 7 and accepts the width-7 role."
+  },
+  "idle_profile_after": {
+    "1": 2275,
+    "3": 377,
+    "7": 6,
+    "8": 1,
+    "48": 4866
+  },
+  "idle_profile_before": {
+    "1": 2276,
+    "3": 377,
+    "7": 7,
+    "48": 4866
+  },
+  "interpretation": {
+    "full_source_rebuild_controller_invoice_or_selected_replay": false,
+    "new_supplier_or_kappa": false,
+    "not_claimed": [
+      "complete two-step census",
+      "global packing optimum",
+      "supplier admission",
+      "new selected kappa",
+      "multiplication theorem change"
+    ],
+    "result": "A concrete legal two-step owner-map packing improvement, conditional on the retained local-word and coverage model."
+  },
+  "owner_audit": {
+    "all_owner_rules_replayed": true,
+    "baseline": {
+      "cross_replica_roles": 57480,
+      "deficit": 5120,
+      "rank_mass": 1041408,
+      "roles": 69120,
+      "windows": 288
+    },
+    "final": {
+      "cross_replica_roles": 57480,
+      "deficit": 5120,
+      "rank_mass": 1041408,
+      "roles": 69120,
+      "windows": 288
+    },
+    "inherited_mutation_controls": 11
+  },
+  "pricing": {
+    "calls": 144,
+    "candidate_endpoint_fraction_of_cap": [
+      "3598032256907958984375/3629363563503835676672",
+      "899508064227294921875/907340890875422048256"
+    ],
+    "families_per_call": "896/9",
+    "fixed_word_packing_cap": [
+      "52814190909/31250000000000",
+      "1690054109089/1000000000000000"
+    ],
+    "local_profile_per_call": {
+      "1": 2412,
+      "2": 418,
+      "3": 432,
+      "4": 142,
+      "5": 82,
+      "8": 8
+    },
+    "method": "Exact rational child-cost intervals with outward rounding at 2^-256 and bisection to a 10^-15 grid.",
+    "moment_root_after": [
+      "2947508024859/1759218604441600",
+      "147375401243/87960930222080"
+    ],
+    "moment_root_before": [
+      "368438139011/219902325555200",
+      "2947505112089/1759218604441600"
+    ],
+    "remaining_cap_gap_closed_fraction": [
+      "1777813720703125/15667431112269400836",
+      "3555629882812500/31334862221170614899"
+    ],
+    "root_gain_certified_lower": "291277/175921860444160",
+    "supplier_comparison": {
+      "binding_primitive_after": "complex",
+      "bit_endpoint_unchanged": "1733427039589844234749/1000000000000000000000000",
+      "bit_minus_complex_after_lower": "60778303521025114009058049/1048576000000000000000000000000",
+      "complex_after_endpoint": [
+        "2947508024859/1759218604441600",
+        "147375401243/87960930222080"
+      ],
+      "complex_before_endpoint": [
+        "368438139011/219902325555200",
+        "2947505112089/1759218604441600"
+      ],
+      "source": "Selected-record research baseline exact supplier arithmetic; bit word and all its charges are unchanged."
+    }
+  },
+  "schema_version": 1,
+  "selected_kappa_unchanged": "836330098538459/500000000000000000",
+  "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+  "status": "PASS_SELECTED_NEUTRAL_PATH_WITNESS"
+}

research/selected-neutral-path-seed893/README.md

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+# One neutral step opens a strict selected-packing improvement
+
+**Concrete two-step packing witness. Conditional fixed-word endpoint only; no supplier admission or new kappa.**
+
+On the selected PR1094 owner ledger, no legal single whole-role relocation strictly lowers the idle moment. A neutral move can open a strict one:
+
+1. Move width-7 helper `(stage=7, replica=2, helper=230)` from `(owner=1, child=14, port=57)` to `(13,15,14)`. Both bins have capacity rank 32. Their free remainders change `(0,7) -> (7,0)`, so the full idle histogram is unchanged. The call event is at 268, strictly inside the destination window `(255,430)`.
+2. Move width-7 helper `(stage=1, replica=15, helper=226)` from `(11,8,103)` to the now-free `(1,14,57)`. This call event is at 181, strictly inside the destination window `(92,272)`. Before step 1 the destination had remainder 0 and this move did not fit. After step 1 it has remainder 7. The changed remainder pair is `(1,7) -> (8,0)`.
+
+For every real `0<a<1`, `p=1-a` lies in `(0,1)` and `t^p` is strictly concave. The first step permutes `(0,7)`. The second replaces `(1,7)` by the more unequal equal-sum pair `(8,0)`, so `8^p+0^p < 1^p+7^p`. Thus the second step strictly lowers the idle moment uniformly over the full exponent interval.
+
+The final idle profile is `{1:2275, 3:377, 7:6, 8:1, 48:4866}` versus the selected baseline `{1:2276, 3:377, 7:7, 48:4866}`. The neutral step preserves `{0:24730, 1:2276, 3:377, 7:7, 48:4866}` including the zero bins. The resulting 69,120-role map passes the inherited complete owner audit, including event windows, family uniqueness, exact occupied prefixes, rank mass `1,041,408`, deficit `5,120`, and halving guard.
+
+## Exact pricing
+
+The pinned outward-rounded child-moment calculator prices the unchanged local profile `{1:2412, 2:418, 3:432, 4:142, 5:82, 8:8}` on all 144 calls and the complete idle histogram, normalized by `144*(896/9)` families. Certified grid brackets are recorded in `CERTIFICATE.json`:
+
+- Existing idle profile endpoint: approximately `0.001675462676808`.
+- After the two moves: approximately `0.001675464332527`.
+- Certified endpoint increase is at least `291277/175921860444160` (about `1.6558e-9`).
+- The selected word's packing relaxation cap remains `a < 0.001690054109089`; the new endpoint is about 99.14% of that cap. The witness closes about 0.0114% of the remaining gap from the selected actual endpoint to the cap.
+- The unchanged bit supplier endpoint is exactly `1733427039589844234749/1000000000000000000000000` (about `0.00173342704`), above the new complex endpoint. Thus complex remains the binding primitive in the retained supplier comparison; the certificate records the exact remaining margin.
+
+This is a fixed-word packing improvement under the inherited coverage model. It does not reconstruct the source controller or full invoice and does not update either supplier endpoint, the selected record or `kappa`. The selected-record hash and `kappa=836330098538459/500000000000000000` remain unchanged.
+
+## Reproduce
+
+```sh
+python3 -I -O -B research/selected-neutral-path-seed893/verify.py
+# PASS_SELECTED_NEUTRAL_PATH_WITNESS path=neutral_then_strict two_role_map_audit=PASS new_kappa=NO
+python3 -I -O -B research/selected-neutral-path-seed893/test_verify.py
+python3 scripts/research_package.py --package research/selected-neutral-path-seed893 --check-only
+```
+
+The registered replay manifest uses Python 3.12. The exact interval model and owner data are pinned in `SOURCES.json`; the verifier regenerates the complete certificate and refuses input drift. See `TASK.json` for chooser seed, priority revision, live overlap, claim and precise scope.
+
+## Predecessors and overlap
+
+PR #1094 supplies the selected owner construction; PR #1091 supplies the retained owner audit; PR #1240 supplies the fixed-word packing ceiling. The one-relocation obstruction is in `research/frontier1094-single-relocation`. Open PR #1790 gives a complete no-improving census for **simultaneous** two-role swaps and leaves neutral-then-improving sequential paths as open questions. This package adds one explicit positive sequential path; it does not enumerate the open class or independently replay PR #1790.
+
+## Open next questions
+
+1. Does this owner map survive source-bound controller reconstruction and the full supplier invoice? Rebuild the selected supplier using the final ownership map and run the pinned controller, invoice and selected-record replay. The relevant full rebuild was not run in this bounded cycle.
+2. How many legal neutral-then-strict paths exist in the fixed selected map? Enumerate canonical ordered relocation pairs while updating touched-bin capacities and retaining the event-window and family rules. PR #1790 already lists this wider domain; avoid duplicating its scope without coordination.
+
+## Credit
+
+Selected construction: Rohan Arun, PR #1094. Owner geometry and the inherited owner audit: Josie Elliston, PR #1091 / `research/t16-owner-audit-seed67`. One-role relocation model and uniform concavity comparison: `research/frontier1094-single-relocation`. Fixed-word packing relaxation: Douglas Colkitt, PR #1240 lineage. This contribution was prepared by OpenAI Codex with substantial AI assistance in deriving the witness, implementing the exact checker and writing the analysis. Apache-2.0.

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