DEFER: selected complex diagnosis reprint (Mercator reimplementation; no new gap)

research/selected-complex-diagnosis-seed9f90/README.md

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+# Selected complex revision-3 diagnosis (independent enclosure)
+
+**Independent verification only. No new κ; the selected frontier is unchanged.**
+
+This package binds the revision-3 portfolio diagnosis in
+[autoresearch.md](../../autoresearch.md) and
+[bottleneck-brief.md](../../docs/research/bottleneck-brief.md) to the selected
+`ASSEMBLY.json` complex ledger with a **code-disjoint** exact enclosure. It does
+**not** import `research/complex-local-word-ceiling/` (atanh-successor chains).
+Logarithms use a binary `ln 2` series plus odd reduction to Mercator `ln(1+x)`;
+exponentials use Taylor series with range reduction.
+
+## Result
+
+From `research/community-frontier1094-audit/ASSEMBLY.json`:
+
+| Quantity | Exact / certified value |
+|---|---|
+| Rank mass / live width | 1,041,408 / 14,336 |
+| Deficit `D = 73·W − mass` | 5,120 |
+| Coverage identity | `mass = 72W + 64N` (N = 144) |
+| Live families per call | `896/9 ≈ 99.556` |
+| Unpaid after centre per call | `320/9 ≈ 35.556` |
+| Effective child rank `m exp(−E/mass)` | ≈ 3.9159 ∈ [3.9, 4] |
+| `a* < D/E` | yes; enclosure intersects PR1293's |
+| Packing ceiling (same model as #1240) | contains `0.001690054109089` |
+| Ideal lever multipliers | ×2.80, ×1.90, ×2.31, ×1.62, ×3.77, ×6.51 |
+| `κ` vs `a/(1+a)` | 18-decimal truncation of the binding complex transfer |
+
+Semantic controls reject an idle-rank-52 halving violation, a local mass beyond the
+coverage law, a raised ceiling after one extra rank-1 child, a bogus ×3
+centre-free multiplier, and a one-ulp kappa forgery. The local×144 + idle
+histogram rebuilds the ASSEMBLY complex profile exactly.
+
+## Reproduce
+
+Default verify is **read-only**: recomputes evidence, requires exact equality
+with committed [RESULT.json](RESULT.json), rejects forged D/status, and does not
+rewrite the receipt. Use `--write` only to regenerate.
+
+```sh
+python3 -I -B research/selected-complex-diagnosis-seed9f90/verify.py
+```
+
+Expected on stderr: `PASS_SELECTED_COMPLEX_DIAGNOSIS`
+
+Also: `python3 -B scripts/research_package.py --package research/selected-complex-diagnosis-seed9f90`.
+
+## Scope and limitations
+
+- Favorable lever relaxations omit realization cost; they are not constructions.
+- Does not rebuild the rank ledger from gate operations (see #1262 / #1421).
+- Does not re-prove the no-q-adic-selector compiler premise (PR552 / PR559).
+- Does not run `make frontier1094-verify`.
+## Open next questions
+
+1. **Can the no-q-adic-selector premise (b) of the surcharge-free complex
+   recurrence be checked from the pinned emit/controller rules rather than the
+   PR552/PR559 review prose?** It matters because the selected κ uses the
+   native (no complex surcharge) moment. First step: a code-disjoint static
+   vocabulary check on the bound `emit_local` / hosted schedule. Blocker: none
+   beyond careful reading of the pinned capsule.
+2. **Do the same diagnosis identities hold for each open complex claim whose
+   local word leaves the #1240 packing model?** It matters for portfolio
+   triage of claims above the selected κ. First step: extract one claim's
+   per-call local profile and rerun this checker. Blocked by each claim's
+   idle histogram extraction.
+
+## Credit
+
+- Douglas Colkitt: revision-3 diagnosis, packing-ceiling model (#1240).
+- Sagar Thakrar: emitted complex ledger (#1262) and bit-side levers (#1334).
+- Navinor: independent D/E diagnostic (#1293).
+- commdata2338: bit projector ledger (#1421).
+- Rohan Arun / Jeremy Kothe and the frontier1094 packing lineage.
+
+
+
+## Disposition (2026-10-14)
+
+**Defer upstream publication.** Bounded probes against live main `0b1cccf8`:
+
+| Prior | What it already proves |
+|---|---|
+| [CrocSwap/integer-mult-bounds#1240](https://github.com/CrocSwap/integer-mult-bounds/pull/1240) | Packing ceiling model and diagnosis figures |
+| [CrocSwap/integer-mult-bounds#1262](https://github.com/CrocSwap/integer-mult-bounds/pull/1262) | Emitted complex ledger rebuild |
+| [CrocSwap/integer-mult-bounds#1293](https://github.com/CrocSwap/integer-mult-bounds/pull/1293) | `a* < D/E` diagnostic |
+| [CrocSwap/integer-mult-bounds#1334](https://github.com/CrocSwap/integer-mult-bounds/pull/1334) | Bit-side lever budgets |
+| [CrocSwap/integer-mult-bounds#1421](https://github.com/CrocSwap/integer-mult-bounds/pull/1421) | Bit projector ledger |
+
+**Independence (precise):** `enclosure.py` is code-disjoint from `research/complex-local-word-ceiling/ceiling.py` (binary `ln 2` + odd reduction + Mercator `ln(1+x)` + Taylor `exp`, not atanh-successor chains). It still shares classical Mercator/Taylor range logic with earlier vendored moment engines (e.g. PR559 `engines/moment.py`). Diagnosis quantities reprint the known portfolio.
+
+**no-q-adic:** A useful check must inspect the transitive `emit_local`/controller path and inject a meaningful selector counterexample. Keyword absence / vocabulary counting is not a compiler theorem; PR559 already argues the premise in review prose. Not completed in this bounded budget.
+
+Fork PR kept for record; not submitted to CrocSwap.
+
+
+Prepared by Wentao Li (@VictorLiwentao; wentaol4@illinois.edu;
+[@Is__Victor](https://x.com/Is__Victor)) with substantial AI assistance.
+New work Apache-2.0; retain source notices.

research/selected-complex-diagnosis-seed9f90/RESULT.json

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+{
+  "author": "Wentao Li",
+  "base_commit_expected": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "chooser_seed": "9f90e3a535639d71c064e320e06118ad",
+  "controls": {
+    "assembly_declares_complex_surcharge_false": true,
+    "bogus_centre_free_multiplier_x3": "rejected",
+    "extra_rank1_lowers_ceiling": true,
+    "forged_profile_breaks_coverage_identity": true,
+    "idle_rank_52": "rejected: idle rank cap violates the halving guard",
+    "kappa_ulp_distinct": true,
+    "over_coverage": "rejected: local word pays more mass than the coverage law allows"
+  },
+  "diagnosis": {
+    "D": 5120,
+    "D_over_E_enclosure": [
+      "194599109435276979657110370148318118755048126914948843629479870767881322601/115792089237316195423570985008687907853269984665640564039457584007913129639936",
+      "97299554717638489828555185074159059377524063457474421814739935383940661301/57896044618658097711785492504343953926634992332820282019728792003956564819968"
+    ],
+    "D_over_E_float_interval": [
+      0.0016805907097543218,
+      0.0016805907097543218
+    ],
+    "E_enclosure": [
+      "176383069790301859470166447829668591484768381030513937824831526253600281051881392195/57896044618658097711785492504343953926634992332820282019728792003956564819968",
+      "352766139580603718940332895659337182969536762061027875649663052507200562103772340047/115792089237316195423570985008687907853269984665640564039457584007913129639936"
+    ],
+    "N_calls": 144,
+    "W": 14336,
+    "coverage_identity": "mass = 72 W + 64 N",
+    "effective_child_rank_enclosure_float": [
+      3.9159073869553946,
+      3.9159073869553946
+    ],
+    "idle_mass_per_call": 1646,
+    "live_families_float": 99.55555555555556,
+    "live_families_per_call": "896/9",
+    "local_mass_per_call": 5586,
+    "m": 73,
+    "published_portfolio_claims_reproduced": {
+      "a_star_lt_D_over_E": true,
+      "effective_child_rank_about_3_9": true,
+      "families_about_99_6": true,
+      "unpaid_about_35_6": true
+    },
+    "rank_mass": 1041408,
+    "unpaid_after_centre_float": 35.55555555555556,
+    "unpaid_after_centre_per_call": "320/9"
+  },
+  "independence": {
+    "does_not_change_selected_frontier": true,
+    "enclosure_method": "ln2 binary series + odd reduction to Mercator ln(1+x); exp Taylor on [0,1/2]; not atanh-successor chains",
+    "imports_complex_local_word_ceiling": false
+  },
+  "inputs": {
+    "ASSEMBLY.json_sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045",
+    "complex_lower": "67018507072324140917/40000000000000000000000",
+    "kappa": "836330098538459/500000000000000000",
+    "selected-result.json_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+  },
+  "levers": {
+    "baseline": {
+      "a_ceiling": "169005411/100000000000",
+      "a_ceiling_float": 0.00169005411,
+      "kappa_cap_float": 0.0016872026462333306,
+      "multiplier_float": 1.0
+    },
+    "centre_free": {
+      "a_ceiling": "473765347/100000000000",
+      "a_ceiling_float": 0.00473765347,
+      "kappa_cap_float": 0.004715313946519134,
+      "multiplier_float": 2.8032554945829515,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "14/5"
+    },
+    "centre_free_rank16": {
+      "a_ceiling": "5504212719/500000000000",
+      "a_ceiling_float": 0.011008425438,
+      "kappa_cap_float": 0.010888559542152985,
+      "multiplier_float": 6.5136526534052805,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "651/100"
+    },
+    "centre_shared": {
+      "a_ceiling": "1606486447/500000000000",
+      "a_ceiling_float": 0.003212972894,
+      "kappa_cap_float": 0.003202682761100503,
+      "multiplier_float": 1.9011065237431954,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "19/10"
+    },
+    "rank16": {
+      "a_ceiling": "1954728001/500000000000",
+      "a_ceiling_float": 0.003909456002,
+      "kappa_cap_float": 0.003894231674606531,
+      "multiplier_float": 2.313213511252607,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "231/100"
+    },
+    "rank8": {
+      "a_ceiling": "547900877/200000000000",
+      "a_ceiling_float": 0.002739504385,
+      "kappa_cap_float": 0.0027320200042185356,
+      "multiplier_float": 1.6209566124483434,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "81/50"
+    },
+    "two_unpaid": {
+      "a_ceiling": "6377984109/1000000000000",
+      "a_ceiling_float": 0.006377984109,
+      "kappa_cap_float": 0.006337563231420219,
+      "multiplier_float": 3.773834264395239,
+      "multiplier_matches_published_two_decimals": true,
+      "published_multiplier": "377/100"
+    }
+  },
+  "limitations": [
+    "Favorable lever relaxations omit realization costs; not constructions.",
+    "Does not rebuild the rank ledger from gate operations (see #1262/#1421).",
+    "Does not re-prove the no-q-adic-selector compiler premise (PR552/PR559).",
+    "Does not run make frontier1094-verify."
+  ],
+  "packing_ceiling": {
+    "a_hi": "169005411/100000000000",
+    "a_hi_float": 0.00169005411,
+    "a_lo": "1690054109/1000000000000",
+    "idle_rank_cap": 51,
+    "kappa_cap_float": 0.0016872026462333306,
+    "published_1240_a_ceiling": "1690054109089/1000000000000000"
+  },
+  "status": "PASS_SELECTED_COMPLEX_DIAGNOSIS",
+  "task_id": "independent-moment"
+}

research/selected-complex-diagnosis-seed9f90/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
+      "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "input",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "input",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    }
+  ]
+}

research/selected-complex-diagnosis-seed9f90/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 3,
+  "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea",
+  "chooser": {
+    "nonce": "9f90e3a535639d71c064e320e06118ad",
+    "track": "independent-verification",
+    "scope_key": "c6f2494b197df3bc3591",
+    "also_suggested": ["formal-interface-lemma"]
+  },
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Can one selected pricing or assembly claim be checked by a genuinely independent exact implementation?",
+    "starting_points": [
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Reconstruct the rank ledger from original operations rather than trusting its aggregate.",
+      "Implement certified moment inequalities through a different exact enclosure method."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Record the selected certificate and complex_profile rather than taking a PR headline as input.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Recompute one small part of the ledger or one certified enclosure using an independent implementation.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Code-disjoint exact certification of the selected complex revision-3 diagnosis ledger (mass, D, coverage identity, unpaid-after-centre, live families/call, effective child rank, D/E) and the six ideal lever packing ceilings cited in autoresearch.md, from ASSEMBLY.json's complex_profile, without importing research/complex-local-word-ceiling/; Mercator/binary-ln2 enclosure distinct from #1240's atanh chains; kappa checked as the 18-decimal truncation of a/(1+a).",
+  "scope_change_reason": "Preserves the card's independent-enclosure method. Operation-to-ledger reconstruction is already covered for this record (#1262 complex emitted ledger, #1421 bit projectors). Endpoint moment engines and the a<D/E lemma are covered by #1293. This session binds the portfolio diagnosis text and lever table to the selected certificate with a different enclosure.",
+  "bottleneck_link": "The donated portfolio and lever table rest on these exact arithmetic claims. Independent corroboration of unpaid-after-centre ≈35.6, families/call ≈99.6, r_eff ≈3.9 and the ×2.80/×1.90/×2.31/×3.77/×6.51 ceilings reduces the risk that coordination targets float free of the selected assembly.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after diagnosis identities, D/E intersection with PR1293, packing-ceiling containment of #1240, all six lever multipliers within ±0.005 of the published two-decimal figures, and semantic controls pass; or stop on the first failing check.",
+  "outcome": "completed",
+  "evidence": "RESULT.json: PASS_SELECTED_COMPLEX_DIAGNOSIS; D=5120; unpaid 320/9; families 896/9; r_eff≈3.9159; D/E intersects PR1293; ceiling contains 1690054109089/10^15; levers match published ×2.80/×1.90/×2.31/×1.62/×3.77/×6.51; kappa is the 18-decimal truncation of complex a/(1+a).",
+  "author": "Wentao Li",
+  "github": "VictorLiwentao",
+  "email": "wentaol4@illinois.edu",
+  "ai_assistance": "Substantial AI assistance for task selection, overlap checks, independent enclosure design, verifier implementation, and writing. No independent human review is claimed.",
+  "local_claim": {
+    "posted_to_discussions": false,
+    "expiry_utc": "2026-10-14T09:53Z",
+    "text": "CLAIM independent-moment refined to selected complex revision-3 diagnosis + lever ceilings; seed 9f90e3a535639d71c064e320e06118ad; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea."
+  },
+  "open_questions": [
+    {
+      "question": "Can the no-q-adic-selector premise (b) of the surcharge-free complex recurrence be checked from the pinned emit/controller rules rather than the PR552/PR559 review prose?",
+      "why_it_matters": "The selected kappa uses the native complex moment (surcharge false); premise (b) is still inherited.",
+      "first_step": "Code-disjoint static event-vocabulary check on the bound emit_local and hosted schedule in the frontier1094 capsule.",
+      "blocked_by": "None beyond careful reading of the pinned capsule."
+    },
+    {
+      "question": "Do the same diagnosis identities hold for each open complex claim whose local word leaves the #1240 packing model?",
+      "why_it_matters": "Portfolio triage of claims above the selected kappa needs per-word unpaid/lever numbers.",
+      "first_step": "Extract one claim's per-call local profile and idle histogram, then rerun this checker.",
+      "blocked_by": "Per-claim idle histogram extraction from each package."
+    }
+  ],
+  "predecessor_credit": [
+    "Douglas Colkitt (#1240 diagnosis and packing ceiling)",
+    "Sagar Thakrar (#1262 emitted ledger, #1334 bit levers)",
+    "Navinor (#1293 D/E diagnostic)",
+    "commdata2338 (#1421 bit projector ledger)",
+    "Rohan Arun / Jeremy Kothe (frontier1094 lineage)"
+  ]
+}

research/selected-complex-diagnosis-seed9f90/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/community-frontier1094-audit/ASSEMBLY.json",
+    "certificates/selected-result.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Read-only: full RESULT equality, D/status corruption controls, lever two-decimal matches, no receipt rewrite"
+    }
+  ],
+  "regenerate": {
+    "argv": [
+      "{python}",
+      "-I",
+      "-B",
+      "{package}/verify.py",
+      "--write"
+    ],
+    "notes": "Explicit receipt regeneration only"
+  }
+}