Independently check #4521's expanded rank-mass identity with my own #4436 flow: 12/12 exact totals match (no new κ)

research/pr4521-expanded-count-check/.gitattributes

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+PR4521-RESULT.json -text

research/pr4521-expanded-count-check/PR4521-RESULT.json

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+{
+  "literal_expansions": {
+    "equal_product_flow_ranks": [
+      8,
+      16,
+      32,
+      64,
+      128
+    ],
+    "full_call_tree_cases": [
+      {
+        "last_counts": {
+          "B": 1,
+          "P": 1,
+          "Q": 7,
+          "U": 3,
+          "routes": 8
+        },
+        "last_literal_events": 15,
+        "paid": {
+          "1": 1
+        },
+        "ranks": [
+          0,
+          8
+        ],
+        "targets": {
+          "2": 1
+        }
+      },
+      {
+        "last_counts": {
+          "B": 8192,
+          "P": 91904,
+          "Q": 14592,
+          "U": 12544,
+          "routes": 117248
+        },
+        "last_literal_events": 265025,
+        "paid": {
+          "1": 2,
+          "4": 1
+        },
+        "ranks": [
+          0,
+          13
+        ],
+        "targets": {
+          "2": 1,
+          "5": 1
+        }
+      },
+      {
+        "last_counts": {
+          "B": 3500,
+          "P": 18500,
+          "Q": 2500,
+          "U": 1750,
+          "routes": 37500
+        },
+        "last_literal_events": 71421,
+        "paid": {
+          "1": 6,
+          "2": 2
+        },
+        "ranks": [
+          0,
+          6
+        ],
+        "targets": {
+          "2": 4,
+          "3": 1
+        }
+      },
+      {
+        "last_counts": {
+          "B": 6400,
+          "P": 51200,
+          "Q": 16000,
+          "U": 10880,
+          "routes": 101120
+        },
+        "last_literal_events": 202501,
+        "paid": {
+          "1": 1,
+          "2": 2
+        },
+        "ranks": [
+          0,
+          13
+        ],
+        "targets": {
+          "3": 1,
+          "4": 1
+        }
+      }
+    ]
+  },
+  "new_kappa": false,
+  "p7_counted_expansion": {
+    "expanded_counts": {
+      "B": {
+        "bits": 17504,
+        "unsigned_big_endian_sha256": "49727d4435d62a4a84b79cf2451d374a5bb98234cbe460ec0b0ef3da77c8c9e6"
+      },
+      "P": {
+        "bits": 17514,
+        "unsigned_big_endian_sha256": "1f28a559d21f0df473b67fef0c37eb57144955250234a44c998bd837d1e8f3d6"
+      },
+      "Q": {
+        "bits": 17497,
+        "unsigned_big_endian_sha256": "0f2b521412ca3f565d734c244b1cf42b8c7d49ef1e61af197ec97b2605078a3c"
+      },
+      "U": {
+        "bits": 17497,
+        "unsigned_big_endian_sha256": "0f5ce7310a89be0835b71681538c3e2e57134d2690ff663b8bc1cd10938b9c7f"
+      },
+      "routes": {
+        "bits": 17514,
+        "unsigned_big_endian_sha256": "98bde80b4a7bc886645e82f3b9e730545da94beddcbec4e98ce88e1c44a39242"
+      }
+    },
+    "n": 1000,
+    "nonbase_ranks": 880,
+    "positive_invocation_rank_classes": 970,
+    "scope": "Counted DAG, not literal enumeration of the enormous program.",
+    "surplus": 608
+  },
+  "schema_version": 1,
+  "scope": "Independent finite expanded accounting and a conditional induction proof; native, physical, all-size exponent and precision admission remain outside scope.",
+  "semantic_rejections": [
+    "omitted_source_complement",
+    "omitted_exit",
+    "duplicated_child_batch",
+    "omitted_raw_instance",
+    "wrong_raw_column",
+    "division_bound_delta_0",
+    "division_bound_delta_-1",
+    "omitted_premature_exit",
+    "nonintegral_child_batch",
+    "deduplicated_child_instances",
+    "missing_replication",
+    "collapsed_raw_columns",
+    "missing_base_leaf",
+    "nondecreasing_paid_rank"
+  ],
+  "source_flow_fixtures": [
+    {
+      "n": 20,
+      "rule": "separated-control"
+    },
+    {
+      "n": 40,
+      "rule": "separated-control"
+    },
+    {
+      "n": 80,
+      "rule": "separated-control"
+    },
+    {
+      "n": 20,
+      "rule": "strict-overlap"
+    },
+    {
+      "n": 40,
+      "rule": "strict-overlap"
+    },
+    {
+      "n": 80,
+      "rule": "strict-overlap"
+    },
+    {
+      "n": 20,
+      "rule": "source-open-equality"
+    },
+    {
+      "n": 40,
+      "rule": "source-open-equality"
+    },
+    {
+      "n": 80,
+      "rule": "source-open-equality"
+    }
+  ],
+  "source_sha256": {
+    "vendor/PR4436-README.md": "78351e2419eb1ff1d645addd411158b91b381b23a962a91b6deeebeacd5192a8",
+    "vendor/PR4436-RESULT.json": "da04256f6f2ef61530f1d642ff1137a2274fd642782a72ef4bf3f1b65395c270",
+    "vendor/PR4436-flow.py": "460f0b0262d7b6880973f46240b3fff1e9f04601fa1d658dda18688b1e26575a",
+    "vendor/PR4436-p7-RESULT.json": "9b814be97e3b45fcc28eafa8a65694897a7387f71a14d44796c6aadf303d7fab",
+    "vendor/PR4476-README.md": "0563dd22edeba4ee82a5ac4a06d965ccb90edbb09bbe646c9f21497bd4789f76",
+    "vendor/SUSSMAN-LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+    "vendor/SUSSMAN-NOTICE": "8289a4ba75efe5da7bd2e389b951155ff74b3bf49b38ace0906a1e5205c7cd6e"
+  },
+  "status": "PASS_DIRECT_FLOW_EXPANDED_ACCOUNTING",
+  "toy_counted_expansions": [
+    {
+      "expanded_counts": {
+        "B": {
+          "bits": 433,
+          "unsigned_big_endian_sha256": "35f12bcc6000b703565e2f120e8077641f744909e8ec163921775b2b0c139254"
+        },
+        "P": {
+          "bits": 439,
+          "unsigned_big_endian_sha256": "7df4f5875466fa21b225c2b60317e60536fdededbe8473d18fe5fb3fb057bb6f"
+        },
+        "Q": {
+          "bits": 438,
+          "unsigned_big_endian_sha256": "f469278cd8f6190ffe6a1ae190299a8d183d1675d4280087d107e5d7016aee25"
+        },
+        "U": {
+          "bits": 436,
+          "unsigned_big_endian_sha256": "12b6d174870cd23fd40ad1f4ff56df629ed813fabbbfcf143a914bfdd875609d"
+        },
+        "routes": {
+          "bits": 439,
+          "unsigned_big_endian_sha256": "4034ff94efe1f1ab70575b300eebbd2469e9065861c4f2570a59256c47170f74"
+        }
+      },
+      "n": 100,
+      "nonbase_ranks": 96,
+      "paid": {
+        "1": 2,
+        "4": 1
+      },
+      "reverse_expansions": 101,
+      "targets": {
+        "2": 1,
+        "5": 1
+      }
+    },
+    {
+      "expanded_counts": {
+        "B": {
+          "bits": 1002,
+          "unsigned_big_endian_sha256": "398043f007044ec4c1ba14eda89bf66b48733ce7a22bb855a3bc17a4665b5952"
+        },
+        "P": {
+          "bits": 1008,
+          "unsigned_big_endian_sha256": "1302eac01cf514d2855c821612c64c9d38a6c9ff55f12115f72bf34a9906b9d5"
+        },
+        "Q": {
+          "bits": 1007,
+          "unsigned_big_endian_sha256": "f04dcf1684cd1a5f5708102f230375fb43cd08135626ac91b22478876e21c63e"
+        },
+        "U": {
+          "bits": 1006,
+          "unsigned_big_endian_sha256": "ebd327c71dde99fefa5afb70ef8ad5b207723935abb8bed0473a95d67e73fbe7"
+        },
+        "routes": {
+          "bits": 1010,
+          "unsigned_big_endian_sha256": "23f8f6398dbe8fe43a321ff79a6c52edfee5c4de97ff2852a6cdcc6c127e7cd7"
+        }
+      },
+      "n": 100,
+      "nonbase_ranks": 98,
+      "paid": {
+        "1": 6,
+        "2": 2
+      },
+      "reverse_expansions": 101,
+      "targets": {
+        "2": 4,
+        "3": 1
+      }
+    }
+  ]
+}

research/pr4521-expanded-count-check/README.md

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+# Independent check of #4521: #4436's expanded rank-mass identity
+
+**Task:** independent-moment (independent source-bound coverage). **Base:** canonical main `f626db5c`. **No new κ.**
+
+Dillon's #4521 (head `d72f2282`) checks the fully expanded counting identity of zxv's #4436, with nested widths:
+
+`B_n·n − P_n = Δ·Q_n`, and `U_n ≤ Q_n ≤ B_n·n/Δ` for positive surplus.
+
+Here `B_n` is the width, `P_n` the number of rank-one leaves, `U_n` the number of raw invocations and `Q_n` their column multiplicity. #4521 retains every source complement, exit and integer batch multiplicity, and publishes SHA256 hashes of the exact big-integer totals.
+
+This package recomputes those totals with **my own** #4436 flow (`flow4436.py`, written for my #4456 checks). Nothing is imported from #4521 or #4436. The recurrence uses `a_n = B_(n−1)` and `B_n = a_n·S_n`, with child batches `a_n S_s / B_(n−s)` (complements) and `a_n E_e / B_e` (exits), which must be integers.
+
+## Results
+
+All checked claims are confirmed.
+
+- **Every rank.** `B_n·n − P_n = Δ·Q_n` and `U_n ≤ Q_n ≤ B_n·n/Δ` hold exactly. All child batches are integral, and ranks strictly descend.
+- **Checkpoints.** The exact big integers `B`, `P`, `Q` and `U` match #4521's published SHA256 hashes and bit lengths, **12 of 12**, at:
+  - two toy rules at rank 100 (`{2:1,5:1} ← {1:2,4:1}` and `{2:4,3:1} ← {1:6,2:2}`);
+  - raw p7 at rank 1000, bound to main's `higher-moment-strictification/RESULT.json`. At rank 1000, `B` has 17,504 bits, `P` 17,514, `Q` 17,497 and `U` 17,497.
+
+`#4521`'s `RESULT.json` is vendored (SHA256-pinned) for the published hashes only. #4521's "routes" count is not recomputed.
+
+## Verify
+
+```text
+python3 -B research/pr4521-expanded-count-check/verify.py
+```
+
+This runs in about 3 s with the standard library only.
+
+## Limitations
+
+- **Finite ranks.** The checks run through rank 1000. The all-rank induction is #4521's written proof, and this corroborates its finite instances.
+- **Out of scope.** Native, physical and precision obligations, as #4521 states.
+
+## Open next questions
+
+- None new. The same recurrence with #4507's chronological widths is covered by my #4519 and #4588.
+
+Credit: Dillon (#4521), zxv (#4436), Jacob Alan Sussman (compiler), Cinna Davis (raw p7). Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

research/pr4521-expanded-count-check/SOURCES.json

@@ -0,0 +1,24 @@
+{
+  "schema_version": 1,
+  "base_commit": "f626db5c3a3d781d8f7695038776c621651f75e1",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40",
+      "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    },
+    {
+      "path": "research/higher-moment-strictification/RESULT.json",
+      "usage": "input",
+      "git_blob": "e66b39c674028adfd22f0de3170555dccda52f6a",
+      "sha256": "ad79e3c0459e7b495a0ca34010553b12147779a007389e1695cc1336f123c156"
+    }
+  ]
+}