Mister-Meeseeks · Oct 28, 2026 · Oct 27, 2026
diff --git a/research/g20-independent-review/README.md b/research/g20-independent-review/README.md
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+# Independent review of the G20 BIT chain PR5679 / PR5708
+
+**Review result; no new bound claimed.** This is a non-author review of
+[PR5679](https://github.com/CrocSwap/integer-mult-bounds/pull/5679) (ordinary BIT
+component .003507410738409) and
+[PR5708](https://github.com/CrocSwap/integer-mult-bounds/pull/5708) (.003507719059749),
+answering the revision-8 request to review this chain before another G20 search.
+Four new checkers, written from scratch, import no code from either package or its
+predecessors. **No discrepancy was found.** One structural finding reduces what an
+admission of PR5708 must depend on.
+
+## What is checked independently
+
+| Claim | Checker | PR5679 | PR5708 |
+|---|---|---|---|
+| Every used frame: exact rank(B)=dim, rank(A)=8−dim, A·Bᵀ=0 | `audit_local.py` | 636 frames | 636 frames |
+| Every query: nesting by **subspace inclusion** (rank of stacked bases), rank = dim difference in 1..7, R_s·R_t = I−2(P_hi−P_lo) | `audit_local.py` | 2,367 kinds | 2,367 kinds |
+| Local word legality: common-frame ADD, free moves only on zero payloads, ERASE/INIT only on owned wires | `audit_local.py` | 21,807 events | 14,794 events |
+| GF(2) endpoint on all 685 columns | `audit_local.py` | pass | pass |
+| **Operator endpoint with exact 8×8 rational matrices** per input symbol, no moduli or probe points | `audit_local.py` | pass | pass |
+| Global GF(2) replay: identity on 11,022 originals, 48 owned registers return zero | `audit_global.py` | 443,238 events | 317,004 events |
+| Paid histogram recounted from QUERY events equals INVOICE (56,223 queries) | `audit_global.py` | pass | pass |
+| All 18 calls equal the local word under one consistent injective wire map | `audit_global.py` | pass | pass |
+| Target owners are all originals once; histogram equals INVOICE; rank-8 targets in 8-dim frames; split targets 1→508 and 508→0 have rank 4 | `audit_global.py` | pass | pass |
+| Raw crossing, tested margin, α/γ/δ tails, H0/H1 cutoffs, rank-mass tails (stdlib Decimal, 60 digits) | `audit_admission.py` | .0035074107384692 | .0035077190598115 |
+| PR5679→PR5708 delta: paid +36H1−72H2+36H3, targets unchanged | `verify.py` | — | pass |
+| Twelve negative controls (wrong rank, dropped or duplicated ADD, wrong ADD frame, free move of a payload, erased original, wrong exit frame, global rank change, dropped global ADD, lost target debit, understated invoice); a legal over-payment is accepted and visible in the bill | `controls.py` | — | pass |
+
+The local endpoint check is exact over Q. PR5782's modulus guard (odd moduli coprime
+to 12) is not rederived here.
+
+## Finding: the predecessor chain need not be admitted first
+
+PR5708 seeds its five finite ordinary levels with PR5679's value as the completed
+backend. PR5679 seeds from PR5665's value, and so on. Read literally, admitting PR5708
+would require admitting each predecessor value. `chain_levels.py` reruns the same
+recursion `a=(1−ρ)C1+ρ·backend` (ρ=1/100, strict 10⁻¹⁵ grid) from other seeds:
+
+- seeded with the **selected admitted ordinary backend .0034363538396**, six levels
+  reach exactly .003507719059749;
+- seeded with .0034, six levels also reach it;
+- `audit_admission.py` shows that the uniform tail guards hold on
+  [.0034363538396, .00351] (γ ≤ 0.96106 < 31/32, δ ≤ 0.92956 < 19/20).
+
+The same holds for PR5679's value. If the PR4814 levels accept any completed ordinary
+backend of this type as a seed, PR5708's component can be admitted from the selected
+backend directly. Maintainers should confirm this reading.
+
+## Not covered
+
+- The five framework assumptions, including the native contract over the source-admissible
+  prime domain, ROW/spectator, owned erasure, compiler, precision and fixed tape.
+- Inputs used as given: FRAMES.json, the controller, the local endpoint specification, the
+  paid ranks of WHOLE_IDLE (7 per stage) and THIN (1) controller queries, and the ranks of the
+  3,552 MAIN-bank targets. These are unchanged since the G20 baseline and are not part of the
+  PR5679/PR5708 delta. The controller's formal MAIN polynomial was not replicated.
+- The finite fee, stock and compiler schema, apart from recomputing H0/H1.
+- Converting the ordinary component into admitted BIT and its use in the nine outer rows.
+- Later ADD-only successors (PR5807, PR5828/5835).
+
+## Reproduce
+
+```sh
+python3 scripts/research_package.py --package research/g20-independent-review --check-only
+python3.12 scripts/research_package.py --package research/g20-independent-review
+```
+
+Python 3.12 and the standard library are enough. The expected final token is
+`PASS_G20_INDEPENDENT_REVIEW_5679_5708`. A full run takes about 90 seconds,
+mostly for the controls. [RESULT.json](RESULT.json) records every compared value.
+
+## Open next questions
+
+- **Can the ordinary levels be reseeded from the selected backend under PR4814?**
+  This would separate PR5708's admission from its unadmitted predecessors. First step:
+  check the PR4814 level statement for any requirement on the seed backend.
+  Blocked by: a maintainer reading of the framework.
+- **Do the 3,552 MAIN-bank target ranks follow from the controller?** This is the
+  largest input still taken as given. First step: derive 7·(stages)+1 from
+  CONTROLLER.json thick stages for each bank. Blocked by: nothing.
+
+## Credit
+
+Review and checkers by Matarener, with substantial Anthropic Claude assistance.
+All G20 constructions, packages and credit belong to their authors: Ali Romman,
+Dugongue, ai-nanachi and the retained lineage named in those packages. Apache-2.0.
diff --git a/research/g20-independent-review/RESULT.json b/research/g20-independent-review/RESULT.json
@@ -0,0 +1,284 @@
+{
+ "PR5679": {
+  "admission": {
+   "H0": 748357344491618305,
+   "H1": "524959317249823813072659373926",
+   "admitted": "3507410738409/1000000000000000",
+   "delta": "0.9293639043",
+   "gamma": "0.9608454716",
+   "guards": {
+    "package_backend": {
+     "C_min": "3505778525569/1000000000000000",
+     "delta": "0.929376399660",
+     "gamma": "0.960858423971"
+    },
+    "selected_admitted_BIT": {
+     "C_min": "17/5000",
+     "delta": "0.929654969123",
+     "gamma": "0.961148623594"
+    },
+    "selected_admitted_ordinary": {
+     "C_min": "8590884599/2500000000000",
+     "delta": "0.929559221281",
+     "gamma": "0.961048875756"
+    }
+   },
+   "one_minus_alpha": "3.953371E-14",
+   "package": "g20-helper-split",
+   "raw_root": "0.00350741073846921418",
+   "tested": "350741073843/100000000000000",
+   "v": 2048
+  },
+  "chain_levels": {
+   "admitted": "3507410738409/1000000000000000",
+   "package": "g20-helper-split",
+   "seeds": {
+    "package_backend": {
+     "levels": 5,
+     "seed": "3505778525569/1000000000000000"
+    },
+    "selected_admitted_BIT": {
+     "levels": 6,
+     "seed": "17/5000"
+    },
+    "selected_admitted_ordinary": {
+     "levels": 6,
+     "seed": "8590884599/2500000000000"
+    }
+   }
+  },
+  "global": {
+   "calls": 18,
+   "events": 443238,
+   "label": "PR5679",
+   "ops": {
+    "ADD": 375474,
+    "OWNED_CLEAR": 3489,
+    "OWNED_ZERO_HEADER": 180,
+    "PAID_PORT_ROUTE": 7548,
+    "QUERY": 56223,
+    "WHOLE_ZERO_FRAME": 324
+   },
+   "paid": {
+    "1": 24687,
+    "14": 444,
+    "2": 24156,
+    "21": 444,
+    "28": 444,
+    "3": 1008,
+    "35": 444,
+    "4": 1026,
+    "42": 444,
+    "49": 444,
+    "5": 1836,
+    "56": 444,
+    "6": 180,
+    "63": 222
+   },
+   "rank_surplus": 753,
+   "target_kinds": {
+    "frame508_to_zero:4": 18,
+    "full8_to_frame508:4": 18,
+    "main:127": 222,
+    "main:15": 444,
+    "main:22": 444,
+    "main:29": 444,
+    "main:36": 444,
+    "main:43": 444,
+    "main:50": 444,
+    "main:57": 444,
+    "main:64": 222,
+    "native:8": 7434
+   },
+   "targets": {
+    "127": 222,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
+    "4": 36,
+    "43": 444,
+    "50": 444,
+    "57": 444,
+    "64": 222,
+    "8": 7434
+   }
+  },
+  "local": {
+   "distinct_queries": 2367,
+   "endpoint": "exact rational operator endpoint on all 685 columns",
+   "frames_used": 636,
+   "label": "PR5679",
+   "ops": {
+    "ADD": 18837,
+    "ERASE": 96,
+    "INIT": 10,
+    "Q": 2846,
+    "ZERO_Q": 18
+   },
+   "owned": 48,
+   "paid": {
+    "1": 1279,
+    "2": 1342,
+    "3": 56,
+    "4": 57,
+    "5": 102,
+    "6": 10
+   },
+   "records": 21807,
+   "width": 685
+  }
+ },
+ "PR5708": {
+  "admission": {
+   "H0": 748422004163100673,
+   "H1": "525050825750085681680519744370",
+   "admitted": "3507719059749/1000000000000000",
+   "delta": "0.9293640686",
+   "gamma": "0.9608590866",
+   "guards": {
+    "package_backend": {
+     "C_min": "3507410738409/1000000000000000",
+     "delta": "0.929372101855",
+     "gamma": "0.960867398500"
+    },
+    "selected_admitted_BIT": {
+     "C_min": "17/5000",
+     "delta": "0.929654969123",
+     "gamma": "0.961162084658"
+    },
+    "selected_admitted_ordinary": {
+     "C_min": "8590884599/2500000000000",
+     "delta": "0.929559221281",
+     "gamma": "0.961062333613"
+    }
+   },
+   "one_minus_alpha": "4.187778E-14",
+   "package": "g20-conjugation-admission",
+   "raw_root": "0.00350771905981154294",
+   "tested": "350771905977/100000000000000",
+   "v": 2048
+  },
+  "chain_levels": {
+   "admitted": "3507719059749/1000000000000000",
+   "package": "g20-conjugation-admission",
+   "seeds": {
+    "package_backend": {
+     "levels": 5,
+     "seed": "3507410738409/1000000000000000"
+    },
+    "selected_admitted_BIT": {
+     "levels": 6,
+     "seed": "17/5000"
+    },
+    "selected_admitted_ordinary": {
+     "levels": 6,
+     "seed": "8590884599/2500000000000"
+    }
+   }
+  },
+  "global": {
+   "calls": 18,
+   "events": 317004,
+   "label": "PR5708",
+   "ops": {
+    "ADD": 249240,
+    "OWNED_CLEAR": 3489,
+    "OWNED_ZERO_HEADER": 180,
+    "PAID_PORT_ROUTE": 7548,
+    "QUERY": 56223,
+    "WHOLE_ZERO_FRAME": 324
+   },
+   "paid": {
+    "1": 24723,
+    "14": 444,
+    "2": 24084,
+    "21": 444,
+    "28": 444,
+    "3": 1044,
+    "35": 444,
+    "4": 1026,
+    "42": 444,
+    "49": 444,
+    "5": 1836,
+    "56": 444,
+    "6": 180,
+    "63": 222
+   },
+   "rank_surplus": 753,
+   "target_kinds": {
+    "frame508_to_zero:4": 18,
+    "full8_to_frame508:4": 18,
+    "main:127": 222,
+    "main:15": 444,
+    "main:22": 444,
+    "main:29": 444,
+    "main:36": 444,
+    "main:43": 444,
+    "main:50": 444,
+    "main:57": 444,
+    "main:64": 222,
+    "native:8": 7434
+   },
+   "targets": {
+    "127": 222,
+    "15": 444,
+    "22": 444,
+    "29": 444,
+    "36": 444,
+    "4": 36,
+    "43": 444,
+    "50": 444,
+    "57": 444,
+    "64": 222,
+    "8": 7434
+   }
+  },
+  "local": {
+   "distinct_queries": 2367,
+   "endpoint": "exact rational operator endpoint on all 685 columns",
+   "frames_used": 636,
+   "label": "PR5708",
+   "ops": {
+    "ADD": 11824,
+    "ERASE": 96,
+    "INIT": 10,
+    "Q": 2846,
+    "ZERO_Q": 18
+   },
+   "owned": 48,
+   "paid": {
+    "1": 1281,
+    "2": 1338,
+    "3": 58,
+    "4": 57,
+    "5": 102,
+    "6": 10
+   },
+   "records": 14794,
+   "width": 685
+  }
+ },
+ "controls_PR5708": [
+  "local wrong_query_rank",
+  "local drop_one_ADD",
+  "local duplicate_one_ADD",
+  "local ADD_wrong_frame",
+  "local free_move_made_paid->ZERO_Q_on_payload",
+  "local paid_query_made_free",
+  "local erase_an_original",
+  "local changed_final_frame",
+  "global global_query_rank_lowered",
+  "global global_drop_ADD",
+  "global invoice_lost_target_debit",
+  "global invoice_paid_understated"
+ ],
+ "delta_PR5679_to_PR5708": {
+  "paid": {
+   "1": 36,
+   "2": -72,
+   "3": 36
+  },
+  "targets_equal": true
+ }
+}