Certify conditional kappa 0.0033999964 via the p19 word without the coded overlay (complex 0.007578535, BIT 0.0034, zero field bill)

research/coded-reverse-word-p19/LIFT.json

@@ -0,0 +1,26 @@
+{
+  "commuting_letters": [
+    "I",
+    "R"
+  ],
+  "p19_entries": 2179072,
+  "p19_recodings": {
+    "even-gauge": 77,
+    "odd-gauge": 77
+  },
+  "p2_entries": 229376,
+  "p2_recodings": {
+    "coded-all/R": 14,
+    "even-gauge/R": 9,
+    "odd-gauge/I": 9,
+    "odd-gauge/R": 9,
+    "transient/D": 6
+  },
+  "rejected_letters": [
+    "D",
+    "Q"
+  ],
+  "scope": "exact operator identity and local gauge bill; no tariff, compiler or kappa claim",
+  "status": "PASS_CODED_REVERSE_GLOBAL_GAUGE_LIFT",
+  "thin_source": "S = Q D C^-1 Q^-1 D^-1 = C^-1"
+}

research/coded-reverse-word-p19/P19_BANK.json

@@ -0,0 +1,20 @@
+{
+  "addresses_per_role": 131072,
+  "binding": "the trace gate list and the controller matrix agree on every address of every role at the smallest faithful ambient (two blocks plus the shared centre)",
+  "differing_entries": [
+    0,
+    0,
+    0,
+    0
+  ],
+  "gates": 20,
+  "p": 2,
+  "pattern": "I",
+  "retained_stages": [
+    1,
+    3
+  ],
+  "roles": 4,
+  "scope": "p=19 needs 2**153 addresses, so the address-level check is done at p=2 and the p=19 word is certified by the trace identity in the controller algebra",
+  "status": "PASS_ADDRESS_LEVEL_TRACE_REPLAY"
+}

research/coded-reverse-word-p19/P19_CLAIM.json

@@ -0,0 +1,175 @@
+{
+  "admitted_bit_saving": "17/5000",
+  "bit_supplier": "17/5000",
+  "budgets": {
+    "field_bill_bucket": "raw",
+    "field_bill_records": 896000,
+    "local_allowance": 10000000,
+    "local_routes": 4794000,
+    "local_scalar": 158168,
+    "raw_allowance": 1000000000,
+    "raw_bound": 190964096
+  },
+  "compiler": {
+    "B": "(5+8h)v",
+    "H0": 5170423668736,
+    "H0_check": "H0 >= 8v",
+    "H1": 49222448837637726209,
+    "N": "2^49222448837637726209",
+    "classification": "numerical instantiation under an applicability premise, not a proof",
+    "h": "1/64",
+    "majorant": "shape-correct power majorant (query-thinned-controllers constants)",
+    "uninstantiated_hypotheses": [
+      "rank completion below b^v",
+      "job splitting at c^v",
+      "whole-job normalizers",
+      "distinct-owner child allocation",
+      "rank-one surplus retention",
+      "fresh-block replay of the trace"
+    ],
+    "v": 1024
+  },
+  "compiler_obligations": {
+    "distinct-owner child allocation": "inherited; the word introduces no new owner",
+    "rank completion below b^v": "checked on this census: max target rank 153 < 256",
+    "rank-one surplus retention": "inherited; the census is unchanged by the word",
+    "splitting at c^v": "checked on this census: 20^64 < 21^63",
+    "whole-job normalizers": "inherited from the producer; the word adds no job and consumes the same T/D interface"
+  },
+  "complex_saving": 0.007578535,
+  "complex_supplier": "0.007578535",
+  "field_level_bill": {
+    "monomial_field_maps": 0,
+    "owned_clears": 0,
+    "recodings": 0,
+    "recursive_gaussian_children": 0,
+    "scalar_adds": 0,
+    "terminal_gauge_decoder": 0
+  },
+  "frontier_reported": "302728823/100000000000",
+  "frontier_reported_provenance": "maintainer-reported in review; no certificate in this tree",
+  "frontier_selected_record": "60403/20000000",
+  "gain_vs_reported_percent": 12.312,
+  "gain_vs_selected_record_percent": 12.577,
+  "guards": {
+    "alpha": 0.9957941423234126,
+    "delta": 0.9515606084977414,
+    "gamma": 0.9637633130133417
+  },
+  "helper_profile": {
+    "4": 28,
+    "7": 7,
+    "8": 47,
+    "9": 326
+  },
+  "idles": {
+    "gauge_neutral": true,
+    "initial": 9,
+    "middle": 18,
+    "rank_applied": 198,
+    "retained": 36,
+    "role_rank": 396,
+    "terminal": 9
+  },
+  "kappa": "951999/280000000",
+  "kappa_decimal": 0.0033999964285714285,
+  "kappa_under_logarithmic_majorant": "1194/390625",
+  "logarithmic_cap": "611329/200000000",
+  "paid_profile": {
+    "1": 2201,
+    "2": 412,
+    "3": 510,
+    "4": 127,
+    "5": 40
+  },
+  "premises": [
+    "the 7752 inherited helper units are disjoint from the main roles and ABI compatible (not replayed here)",
+    "compiler applicability to this word (numerical instantiation only)",
+    "physical realizability of the rank-153 trace (no bank replay)",
+    "field-level bill admitted under the caller fixed-tape/precision ABI",
+    "inherited all-size/compiler, hosting, tape and analytic interfaces",
+    "kernel review"
+  ],
+  "record_only_overlay": {
+    "gates": 259,
+    "gates_by_kind": {
+      "BRIDGE": 108,
+      "FORWARD": 20,
+      "GAUGE_LOAD": 19,
+      "GAUGE_UNLOAD": 19,
+      "IDLE": 36,
+      "LETTER": 19,
+      "REVERSE": 19,
+      "SWAP": 19
+    },
+    "monomial_field_maps": 17248,
+    "owned_clears": 1232,
+    "recodings": 77,
+    "scalar_adds": 68992,
+    "status": "historical record, NOT the priced word"
+  },
+  "scope": "exact arithmetic for the word, the bill, the compiler and the ledger",
+  "status": "CLAIM_P19_UNCODED_WORD_SUPPLIER",
+  "uncoded_word": {
+    "ambient_rank": 153,
+    "denominators": [
+      1
+    ],
+    "gate_kinds": {
+      "BRIDGE": 108,
+      "FORWARD": 20,
+      "IDLE": 36,
+      "LETTER": 39,
+      "REVERSE": 19,
+      "SWAP": 19
+    },
+    "gates": 241,
+    "idle_rank": 198,
+    "outputs": [
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        4
+      ],
+      [
+        3,
+        4
+      ],
+      [
+        4,
+        4
+      ],
+      [
+        5,
+        4
+      ],
+      [
+        6,
+        4
+      ],
+      [
+        7,
+        4
+      ],
+      [
+        8,
+        4
+      ],
+      [
+        9,
+        4
+      ],
+      [
+        19,
+        2
+      ]
+    ],
+    "p19_entries_checked": "none (operator-level certification)",
+    "physical_bank_replay": "not performed; ambient rank 153 exceeds a 512-address bank",
+    "retained_idles": 36,
+    "trace_identity": "replayed in the controller algebra"
+  }
+}

research/coded-reverse-word-p19/P19_DIAG.json

@@ -0,0 +1,101 @@
+{
+  "p": 19,
+  "pattern": "IIIIIIIIITTTTTTTTT",
+  "std": {
+    "outputs": [
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        4
+      ],
+      [
+        3,
+        4
+      ],
+      [
+        4,
+        4
+      ],
+      [
+        5,
+        4
+      ],
+      [
+        6,
+        4
+      ],
+      [
+        7,
+        4
+      ],
+      [
+        8,
+        4
+      ],
+      [
+        9,
+        4
+      ],
+      [
+        19,
+        2
+      ]
+    ],
+    "denominators": [
+      1
+    ]
+  },
+  "cod": {
+    "outputs": [
+      [
+        1,
+        4
+      ],
+      [
+        2,
+        4
+      ],
+      [
+        3,
+        4
+      ],
+      [
+        4,
+        4
+      ],
+      [
+        5,
+        4
+      ],
+      [
+        6,
+        4
+      ],
+      [
+        7,
+        4
+      ],
+      [
+        8,
+        4
+      ],
+      [
+        9,
+        4
+      ],
+      [
+        19,
+        2
+      ]
+    ],
+    "denominators": [
+      1,
+      13
+    ]
+  },
+  "diagonalized": true,
+  "source": "research/coded-reverse-controller/verify.py diagonalize(19, pattern, coded)"
+}

research/coded-reverse-word-p19/P19_LIFT.json

@@ -0,0 +1,16 @@
+{
+  "addresses": 131072,
+  "blocks": 2,
+  "consequence": "any polynomial identity between the gate list and the controller matrix lifts to address operators for every block count k, so the p=19 word realises the p=19 matrix once the p=2 control confirms the implementation of Phi",
+  "control_status": "the p=2 address replay is randomised (one dense seed), not exhaustive",
+  "differing_entries": 0,
+  "gate_kinds_checked": [
+    "FORWARD",
+    "REVERSE",
+    "LETTER",
+    "IDLE"
+  ],
+  "lemma": "Phi is a homomorphism from the retained-stage monomial ring to address operators: distinct-axis Gaussians commute, powers on one axis add, Phi fixes the identity",
+  "status": "PASS_LIFTING_LEMMA",
+  "trials": 24
+}