Bind admitted R437 q127 root Count to initial NODE consumers

research/r437-admitted-count-consumer/DIAGNOSTIC.json

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+{
+  "command": [
+    "python3.12",
+    "-I",
+    "-B",
+    "research/r437-admitted-count-consumer/verify.py",
+    "--diagnostic",
+    "--write"
+  ],
+  "external_process_group_timeout_seconds": 90,
+  "interruption_location": "original cardinality.multiply_atom_power -> radix_power -> Word Unsigned.divmod -> shift_add_bit -> rewind",
+  "returncode": -2,
+  "scientific_status": "INCOMPLETE_FULL_PREFIX; no final fibre/cleanup pass",
+  "seconds": 90.505,
+  "source_commit": "5fc3091bf853b9f19a155e03ce0750a2104dc135",
+  "stdout": "{\"phase\": \"certified source and actual NODE prefix bound\", \"seconds\": 5.779}\n{\"phase\": \"actual root Count encoded\", \"seconds\": 18.286}\n",
+  "timed_out": true,
+  "timeout": 90
+}

research/r437-admitted-count-consumer/PROOF.md

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+# Admitted original root to the first actual Count consumers
+
+The source-bound original R437 checked_entry accepts certified q=2^127−1,
+e=n=64,w=2,h=0,L=255,I=8 and actual compiled Q=520213. Its compatible root
+stock is K=9475*A, where A=28416*|GL64(F_q)|*q^4096. D(64)=1, so no sharp-stock
+change is required. No new proof of 9475, primality, ordinal ordering or complete
+directory reserve is claimed.
+
+The original entry validates source/Specifications/handle and all parameters
+before invoking a continuation. That continuation constructs actual source
+Word/Ring arenas with exactly those widths, root Program with unit2 and no STEP,
+and the full exact 1,040,413-bit binary Count K. The context carries the same q,
+dimension and live codebook object. Full directory.Context construction is not
+claimed: its high-count producer is not needed by this NODE prefix and remains
+a separate charged construction obligation.
+
+The AST projection preserves every literal original Machine.node statement
+through `fibre=Count.product(self.count("leading"),self.count("gap"))`. It changes
+only the fresh_rows quotient dependency to the credited opt-in #4794 adapter,
+then appends an explicit adapter return of that original owned local Count.
+The next original `total=...` statement and all later operations are excluded.
+No original input validation, incoming coefficient call, save, 9475 guard or
+Count.product is bypassed within the retained prefix. Actual Machine methods
+count/tape/save_count/commit are bound to the runtime, not reimplemented.
+
+The retained quotient divides K by A, yielding unused 9475. Original node ingress
+validates its positive binary roles and incoming root Program. The original
+9475 guard accepts, then before=gap=1 gives saved leading 9475 and initial fibre
+9475. Observation independently decodes only completed Count bytes, outside
+runtime execution. Word.inspect is disabled throughout the NODE projection.
+The returned local fibre is explicitly closed by the adapter consumer BEFORE
+checking live sets and newly allocated backing; this is boundary ownership,
+not a claim that original NODE frees it at this point. Source temporaries must
+already be erased independently of final fixture disposal. Borrowed role and
+Program bytes/heads, a dirty Count 173 and dirty Word 37 remain unchanged. Entry
+rejection controls must never invoke this encoded continuation.
+
+The original next operation would construct total=128 and execute
+multiply_atom_power(fibre,total,ring,q). Its Counter has 128 iterations. Each
+radix_power on q² yields twice, so the original segment requires 256 Word.divmod
+calls and 256 Count.multiply_small(q) calls. It produces 9475*q^256 with 32,526 bits
+before suffix multiplication. That segment is NOT completed by this package.
+The preserved full-prefix diagnostic reached this function and was externally
+interrupted after 90.505 seconds. No measured output or cleanup pass is inferred
+from the interrupted process; OS process termination is not source cleanup.
+
+The q^4096 batch divisor has 520,192 bits; a host remainder can occupy that width
+and has q^4096 possible values. Count.divide_small's Python shift/add/compare
+operations on this state are not unit-time bit operations. The finite source
+execution proves the parameter/representation/consumer join, not its uniform
+binary-TM tariff. Its full input encoding, runtime and disposal action counters
+are reported separately from the new adapter's square-and-multiply operand
+widths and schoolbook bit-product diagnostic. Ordinal codebook construction,
+actual compiler, full Context, payload, allocator and fixed-control costs remain
+open. In particular a low number of Count calls is not a physical improvement.
+
+Credit David Arias's #2753 Count/caller; Chris R / Clear1nsight #4176 entry and
+compiler; #4794 batching; Nick Petalas #4854 shared-radix alternative; codyw912
+#4734 ordinal adapter; ToikY #4025; and the pinned stock/source lineage. #4927's
+directory/reserve audit is independent and does not supply these missing
+payload/cost hypotheses. New boundary and checks: JoyboyBrian, substantial
+OpenAI Codex assistance, Apache-2.0.

research/r437-admitted-count-consumer/README.md

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+# Admitted R437 root to initial binary Count consumers
+
+This package binds the original certified q=2^127−1 root entry to an actual
+1,040,413-bit binary Count, #4794's opt-in batched quotient, the literal
+Machine.node ingress and 9475 stock guard, and the original saved-leading and
+initial fibre Count products. It stops before original exponent expansion.
+The outputs at this boundary are unused=leading=initial fibre=9475; the bounded
+actual-q127 replay passed in 56.311 seconds.
+The completed package does not claim the final expanded fibre, complete NODE,
+full directory.Context, materialized payload or supplier admission.
+
+## Increment and exact boundary
+
+#4757 established admitted host parameters with a stock-only adapter; #4794
+executed local structural contexts at q3; Nick Petalas's merged #4854
+(2877e4920338d9a2e56aa960bdb5663f8f96b2d8) proves a shared-radix quotient with
+unchanged Count operation sequence. This task uses the original checked_entry
+at e=n=64,w=2,h=0, exact L255/I8/Q520213, and actual encoded binary ports. The
+original stock and sharp stock coincide at this n; no sharp-entry override is
+used. #4927 is a separate complete-directory/reserve Discussion audit, whose
+serialization and absorption result is not repeated or assumed here.
+
+`bridge.py` AST-selects all original NODE statements through
+`fibre=Count.product(leading,gap)`, substitutes only the credited opt-in quotient,
+and appends a return transferring that local Count. The original count/tape/
+save/commit methods, actual root incoming callback, normalization and stock
+checks execute. `PROOF.md` states the exact composition. The verifier closes the
+returned local Count before checking temporary cleanup. Later fixture teardown
+is recorded separately and cannot make a failed source cleanup check pass.
+The supplied context is a structural view tied to the admitted field, dimension,
+codebook and encoded Ring; its expensive full Context constructor is unrun.
+
+## Measured scope change
+
+A full pre-payload NODE diagnostic encoded the actual root Count by 18.286 s and
+reached original multiply_atom_power. The external 90 s bound interrupted an
+actual Word.divmod at 90.505 s. No complete-fibre result, source cleanup pass or
+runtime upper bound follows from that interrupted run. The child process was
+terminated and its private temporary directory removed.
+
+The exact diagnostic harness is preserved in commit
+5fc3091bf853b9f19a155e03ce0750a2104dc135, before the scope cut. In a checkout of
+that commit, reproduce with an external 90-second process-group timeout around
+`python3.12 -I -B research/r437-admitted-count-consumer/verify.py --diagnostic --write`.
+It is intentionally not a registered repeated workload. `DIAGNOSTIC.json`
+retains its phase/time/stack boundary and command; all scientific pass claims
+refer to the narrower current verifier.
+
+The excluded original segment performs 128 radix traversals of q²: 256 Word
+long divisions and 256 Count multiplications, ultimately producing a 32,526-bit
+fibre before suffix multiplication. This is a concrete remaining cost boundary,
+not evidence that the full path is impossible. No tiny fixture replaces q127.
+
+## Verification and complete cost limits
+
+The accepted continuation binds actual source identity and all widths, encodes
+full root stock and root Program, and uses the original source arithmetic and
+Count consumer statements. Runtime Word.inspect is disabled. Host observations
+only decode completed outputs; they do not drive execution. Wrong precision,
+reset root index, wrong Q, incompatible rows, nonroot history and stale source
+identity reject before the continuation. Dirty Count/Word spectators, borrowed
+metadata/Program heads and bytes, owned numeric live sets, and all new record
+backing are checked before final fixture disposal.
+
+`RESULT.json` reports actual source record/index/residue actions separately for
+the NODE prefix and full construction/execution/disposal, as well as visited
+record cells (3,122,293). The initial NODE boundary executes 22,373,579 record
+reads / 5,723,680 writes / 20,811,850 moves, plus the separately reported index
+and residue actions. The compiled divisor construction records 13 host
+products and 90,200,420,437 schoolbook bit-products, not a measured physical
+execution bill. Full source compilation and host fixture/stock/oracle arithmetic
+are outside these lane counters. The batch divisor has 520,192 bits and a host
+remainder can have the same width. The retained adapter records its explicit
+square-and-multiply operand sizes and schoolbook bit-product diagnostic; this
+is not a proven total binary-TM instruction count. Full codebook/Context setup,
+large-divisor physical arithmetic, fixed finite-control compilation, backing
+allocation and payload remain charged obligations. A large host integer is not
+an atomic constant-cost physical instruction; no speed or space improvement is
+claimed.
+
+Run `python3.12 -I -B research/r437-admitted-count-consumer/verify.py`, also with
+`-O`. Both deterministic replays are registered with 120-second bounds. The
+receipt uses typed JSON equality. Hosted CI is not asserted.
+`SOURCES.json` authenticates 403 live inputs at canonical base
+b91956876e5b4122fd89179f1b57557ff8378f15. A SHA-bound historical selected record
+is projected only for the unchanged historical loader. No frozen source or
+selected frontier changes. `TASK.json` retains revision 7 and complete reported
+overlap coverage 317 PRs / 4064 Discussion records / 6636 local notes; keyword absence is not novelty.
+
+Credit David Arias, Chris R / Clear1nsight, Nick Petalas, ToikY, codyw912 and the
+pinned compiler/caller/stock lineage. New composition and checks: JoyboyBrian,
+substantial OpenAI Codex assistance, Apache-2.0. Scoped source argument and
+author-checked finite execution, not formal-kernel verification.
+
+## Open next questions
+
+1. Complete and charge the original 256-divide exponent segment at admitted
+   precision, keeping original Count outputs and restoration contracts.
+2. Price a binary implementation of the large quotient divisor alongside full
+   codebook and Context construction, rather than treating Python arithmetic as
+   an atomic operation.
+3. Join this initial Count boundary to actual complete directory, gather and
+   payload consumers before claiming a complete caller or uniform supplier.

research/r437-admitted-count-consumer/RESULT.json

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+{
+  "batch_constant": {
+    "bits": 520192,
+    "sha256": "750f89ba4ed2f9b59c25d497275b3f666ef874f5f06a8b555b4fb8c35b2082b5"
+  },
+  "construction": {
+    "multiplications": 13,
+    "operand_bit_pairs": [
+      [
+        127,
+        127
+      ],
+      [
+        254,
+        254
+      ],
+      [
+        508,
+        508
+      ],
+      [
+        1016,
+        1016
+      ],
+      [
+        2032,
+        2032
+      ],
+      [
+        4064,
+        4064
+      ],
+      [
+        8128,
+        8128
+      ],
+      [
+        16256,
+        16256
+      ],
+      [
+        32512,
+        32512
+      ],
+      [
+        65024,
+        65024
+      ],
+      [
+        130048,
+        130048
+      ],
+      [
+        260096,
+        260096
+      ],
+      [
+        1,
+        520192
+      ]
+    ],
+    "schoolbook_bit_products": 90200420437,
+    "stored_divisor_bits": 520192
+  },
+  "controls": [
+    {
+      "continuation_called": false,
+      "error": "actual canonical residue width",
+      "name": "wrong precision"
+    },
+    {
+      "continuation_called": false,
+      "error": "actual canonical root-index width",
+      "name": "reset root index"
+    },
+    {
+      "continuation_called": false,
+      "error": "actual complete codebook width",
+      "name": "wrong code width"
+    },
+    {
+      "continuation_called": false,
+      "error": "compatible original-root stock divisor",
+      "name": "incompatible rows"
+    },
+    {
+      "continuation_called": false,
+      "error": "executable original-root entry; descendant path certificate required",
+      "name": "nonroot history"
+    },
+    {
+      "continuation_called": false,
+      "error": "fresh source codebook identity",
+      "name": "stale actual source"
+    }
+  ],
+  "encoded_result": {
+    "borrowed_preserved": true,
+    "full_construct_execute_dispose": {
+      "index": {
+        "moves": 3582,
+        "reads": 3579,
+        "writes": 787
+      },
+      "record": {
+        "moves": 33298292,
+        "reads": 35900416,
+        "writes": 9885986
+      },
+      "residue": {
+        "moves": 8239386,
+        "reads": 8783351,
+        "writes": 1787125
+      }
+    },
+    "node_invoice": {
+      "index": {
+        "moves": 3274,
+        "reads": 3269,
+        "writes": 701
+      },
+      "record": {
+        "moves": 20811850,
+        "reads": 22373579,
+        "writes": 5723680
+      },
+      "residue": {
+        "moves": 8230636,
+        "reads": 8774107,
+        "writes": 1784814
+      }
+    },
+    "numerical_restored": true,
+    "outputs": {
+      "leading": {
+        "bits": 14,
+        "sha256": "b184d29a1c103b5269165d679d2460bdc54ed484d57a4716800bfba78ae036ff"
+      },
+      "pre_expansion_fibre": {
+        "bits": 14,
+        "sha256": "b184d29a1c103b5269165d679d2460bdc54ed484d57a4716800bfba78ae036ff"
+      },
+      "unused": {
+        "bits": 14,
+        "sha256": "b184d29a1c103b5269165d679d2460bdc54ed484d57a4716800bfba78ae036ff"
+      }
+    },
+    "record_backing_erased": true,
+    "visited_record_cells": 3122293
+  },
+  "full_directory_context_constructed": false,
+  "input_rows": {
+    "bits": 1040413,
+    "sha256": "f6bf5a75756bf8267103578f24f2b5934e122da6d96e68100fc2b28853da7a01"
+  },
+  "live_inputs": 403,
+  "node_boundary": {
+    "adapter_return": true,
+    "ast_sha256": "8deb56502ea15ec160ac1ab332218372c042ac734e8b0b3b967284dbec93202b",
+    "boundary": "literal NODE through fibre=Count.product(leading,gap); adapter returns owned local fibre before total/multiply_atom_power",
+    "statements": 17
+  },
+  "production_payload_executed": false,
+  "remaining_original_expansion": {
+    "count_multiply_small": 256,
+    "final_fibre_bits": 32526,
+    "word_divisions": 256
+  },
+  "root_entry": {
+    "common": false,
+    "compatible_rows": {
+      "big_endian_sha256": "f6bf5a75756bf8267103578f24f2b5934e122da6d96e68100fc2b28853da7a01",
+      "bit_length": 1040413
+    },
+    "domain": {
+      "I": 8,
+      "L": 255,
+      "Q": 520213,
+      "e": 64,
+      "h": 0,
+      "n": 64,
+      "w": 2
+    },
+    "entry_certificate_modular_square_subtract_steps": 125,
+    "guard_before_continuation": true,
+    "guard_implementation": "host finite arithmetic; exact source/parameter guard, physical encoded guard tariff open",
+    "mode": "numerical",
+    "numerical_admitted": true,
+    "production_payload_execution": false,
+    "q": "170141183460469231731687303715884105727",
+    "rank": 2,
+    "request": 1676,
+    "request_key": [
+      "MOVE",
+      0,
+      0,
+      22397
+    ],
+    "row_multiplier": {
+      "big_endian_sha256": "4bf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a",
+      "bit_length": 1
+    },
+    "source_identity": "bcea2a31e9001699148b6f1ff8524a0c6c4524d70ef47add027651da31389a73",
+    "stock_certificate_scope": "original root"
+  },
+  "scope": "Original admitted root to literal NODE ingress/quotient/stock/saved leading/initial fibre product; original fibre expansion, full Context, physical big-int tariff and payload remain open.",
+  "status": "PASS_R437_ADMITTED_INITIAL_COUNT_CONSUMER"
+}