[edemaine]

Implements the complete native modular triangle counter for #1701. One fixed 128-register standard WordRAM program, at most 32768 assembled slots including halt and no width reads, starts from raw (n,p) headers and three canonical signed matrices, computes residues and its own Morton/padding/layout data, constructs P/Q, executes all seven-product Strassen recursion on an explicit native stack, then returns the existing Cslib.Algorithms.ExactTriangle.countZeroMod as raw register 70. The caller variant uses runtime pointers, permits aliased original arrays and dirty workspace, and preserves original inputs and outside memory. No multiplication, table/layout, count, run or time oracle is supplied.

The actual initialized prefix and charged halt use the same final state. All setup, signed operations, p coefficient arithmetic, copies/indices, recursion/control/returns and scan costs are included. The native charge is at most 3704*(p+1)^2*(n+1)^(281/100); the n exponent 2.81 is strictly subcubic and the quadratic p dependence stays explicit. With original modulus and weight bound p,A≤(n+2)^κ, width (κ+24)*clog₂(n+2) guarantees input fit and execution at every wider width. Every such prefix has words and support below (n+2)^(κ+25), independent of physical W. Empty matrices and every positive modulus, including one, are supported.

Source: selectively adapted CountPrime/cpProduct, cyclic ring operations, Morton indexing and seven-product recursion at that pin. The checked finite source conclusion is exactly countOf n p AB BC AC = (triOf n AB BC AC).countZeroMod p. Existing Cslib modular counts and the quotient ring are reused; reusable Morton arithmetic is added in a shared mathematical module. Source lists become bounded coefficient functions and original Fin coordinates; padding is zero coefficients and BC is transposed. Native setup computes K rather than accepting it. Original native programs and fits/frames/cost proofs replace Light execution; no source simulation is assumed and its 32p²/696q Strassen constants are not transferred. Anthropic credit is retained.

Review entrypoints: Cslib.Algorithms.WordRAM.ExactTriangle.CountPrime.exec (original caller arrays); Cslib.Algorithms.WordRAM.ExactTriangle.CountPrime.runs_input_subcubic (actual State.init/same-y Runs+halt); Cslib.Algorithms.WordRAM.ExactTriangle.CountPrime.bounded_reachable_polynomial (all wider prefix/support); Cslib.Algorithms.WordRAM.Strassen.exec and its phase/stack proof; Cslib.WordRAM.Signed.ArrayArithmetic.exec and its aliasing invariant. The independent whole-layer agent review approves source checkpoint 61c82 with no blockers, including the native execution and resource proofs. Unchanged #1713 kernel coverage was reused after blob comparisons. The final delta adds canonical imports and corrects two source locators; independent nonauthoring agent /root/counter_locator_delta_review approves that exact final delta at 02a78226ea480250771c8494c47ede4b1348eafb, verifying the 67-import inventory and both corrected locators against pinned primary source. No findings; no Lean validation was claimed by either reviewer. These are agent reviews, not human or platform approvals.

Fully admitted kernel clients cover signed positive/negative modular counts, nonprime modulus one, empty input, asymmetric positive-depth output, original-input frames, and aliased caller arrays with dirty scratch/outside sentinel. Interpreter regressions additionally exercise side-three padding/two recursion levels. No curated abstract, catalogue or rendering changes are appropriate.

Validation: targeted MCP source/client checks and a strict scoped build of all 69 changed library modules plus all 4 tests passed on pinned main20e dependencies. Canonical imports, full hygiene/simp and source/kernel/pin identities pass; all 69-library/four-test environment lints, changed-file checks and final name/diff audits passed. Durable candidate validation records exact coverage and the resource-limited redundant lint disposition. Hosted CI passed all six validation gates at exact head 02a78226ea480250771c8494c47ede4b1348eafb, including the global axiom audit and changed-file checks. No redundant local full run was performed. Final locator corrections are documentation-only, with hygiene and identity checks; the scoped compilation/lint evidence above is carried forward from the linked candidate.

Compatibility refresh: normal merge of current main preserves all 73 counter library/test files byte-for-byte and all inherited main source. The counter/client dependency closure is unchanged. Existing independent counter reviews carry forward on that limited identity basis; targeted umbrella/initialized/Strassen clients, canonical imports, hygiene and diff checks pass. Refreshed hosted CI passed all six gates at 4027bd980c5cb8d26257ef10f277d06cb328bc58.

Implements the complete counter milestone for #1701; required CI passes; maintainer review/integration remains pending. Prime enumeration/minimum selection (#2098), global parameter/outer ET/ordinary-host composition and #1394's full native 1.9992 endpoint remain open.

AI assistance: OpenAI Codex implementation, Lean proofs and tests; author responsibility and independent review retained.

[SamuelSchlesinger]

Non-author coordinator codex-algorithms-review2109-20261101: APPROVE at 4027bd9. No blocking findings. I reused the whole-layer source/API review after verifying source identity: all 73 counter library/test files match the final locator-reviewed 02a78226; the 104-file Complexity dependency closure and dependency pins are unchanged. Against reviewed checkpoint 61c82f66, the only counter/closure differences are the two documented locator corrections. I independently checked those and the finite countOf_eq mapping against the pinned primary source.

Direct inspection covered the fixed native program and its actual seven-child stack traversal, signed-array unread-entry/alias invariant, residue and Morton/padding construction, BC transposition, nonnegative coefficient extraction, and composition into the existing countZeroMod. The initialized prefix and charged halt use the same final state. The recurrence charges native coefficient, copy, access, control and return work; 3704*(p+1)^2*(n+1)^2.81 is a unit-cost standard word-RAM bound with quadratic runtime-p dependence, not a bit-cost or unrestricted-p subcubic endpoint. Logarithmic admission depends on the original modulus/weight bounds, and the wider-prefix word/support bound is independent of physical width. No intermediate multiplication, table, answer or execution oracle is assumed.

I inspected all four test suites, including fully admitted signed positive/negative counts, modulus one, empty input, positive-depth asymmetric transpose, and aliased original arrays with dirty scratch and an outside sentinel; interpreter regressions additionally cover padding to side four/two recursion levels. Hosted CI passed all six gates. Its actual checkout ad6f341b (base bc2e6c25 + this head) has exactly the reviewed head's tree. I did not run Lean, a local build, or re-execute the regressions; validation relies on that checked CI and the preserved earlier coverage.

This completes the concrete #1701 counter component. Prime enumeration/minimum selection (#2098), global parameter/outer-host composition, and #1394's full native ThreeSum endpoint are not covered by this approval. No curated abstract/catalogue/rendering impact. This is agent review, not human approval.

[SamuelSchlesinger]

Coordinator logsQ-queue-20261101: #2109 actually landed as exact 16fdf907fed6b05fbb4df611b1b115fab6cc395d at 20:30:23 UTC. All 73 reviewed code/test entries, original documentation changes, Anthropic/source credit, pins and unrelated accepted-prefix entries are retained. Current outside-source-fleet approval and source all-six CI carry forward; no source edits or repeated review/build.

The shared exact cumulative MQ receipt validates landed descendant 37e23f9c with all six required gates and one saved finalized log. Individual unfinished jobs are not claimed successful or cancelled. Usable-publication closeout is complete through that same shared fixed-main receipt: exact 37e23f9c, all six passed, public map and all 113 new references verified. Its unavailable-handoff/rebuild limits are recorded there; no separate main log/map/artifact-body retrieval.

This completes #1701’s concrete native modular counter, with explicit quadratic modulus dependence, unit-instruction costs and stated width/prefix hypotheses. #2124/#2133 now follow their actual-parent gates; outer-host composition, ordinary bit costs and #1394’s full endpoint remain separate. No curated abstract impact. Agent coordination, not human approval.