[SamuelSchlesinger]

#1791 gives the canonical clocked BPL matrix. This PR proves native logarithmic-space computation of its complete two-bit matrix payload from the original framed word, starting from the actual zeroed initializer. Flat identifiers split into clock and base components; the reader queries the original input using the base source, and emits the ordinary coin count exactly when the target clock is the next one.

The library proves exact output length, row-major indexing, count decoding, zero terminal rows and equality of every decoded entry with finTimeLayer of the compact coin matrix. Local native space certificates also compute the dimension and terminal reward, with the reward identified with finTimeLayerReward. The existing ordinary table and clocked table share one two-bit format and one 23-label, four-register writer. The previous ordinary instruction list and register count are definitionally preserved, along with its public execution/resource guarantees.

Stacked on #1791; advances #1444. The complete matrix payload is now initialized and natively computable. Packaging dimension/start/reward into one serialized instance, directed paired ports, the recursive estimator and its complete space realization remain open. The existing startID_budget is reused; no composed-instance theorem or bounded indegree is assumed. No selected abstract or roadmap endpoint changes are warranted.

Validation and review

All eight changed/new libraries and three regression clients pass strict pinned Lean with project options and warnings as errors, without diagnostics. Actual initialized runs emit all 1,152 bits of a 24-ID clocked system. Tests cover clock-one sources, counts one/two, off-clock and terminal zeros, exact matrix/reward decoding, and rfl preservation of the old writer. Existing input dependence, malformed IDs, exact overflow mass, acceptance and BPL-witness regressions still pass. Focused hygiene, tracked aggregate, committed-import and whitespace checks pass. Full Lean CI passed for the published revision.

Independent non-author agent polynomial_false_review approved exact source 9d493c2146a15bcf7180a6ccc197ff045287eeaf with no substantive findings; a module-heading nit and final explicit test parameters were covered before approval. Integration preserves the reviewed source/test bytes. Published revision.

AI assistance: ChatGPT worker coin_input_review authored and validated this layer; separate agents reviewed and integrated it. The proof continues the pinned paper's terminal-time construction using this project's native machines; no OAI Lean code was used.

[edemaine]

Independent agent approval by reviewer-codex-edemaine of 1cd5437. Read the complete ten-file layer over reviewed #1791, including the shared writer, actual input-reader semantics, clock arithmetic, native resource contract and regressions. No blocking findings.

The source quotient/remainder selects the correct base input query at every clock. Only consecutive-clock pairs receive the ordinary 0/1/2 count; bounded terminal rows are zero. Exact row-major decoding identifies the emitted bits with finTimeLayer, and the reward predicate pays only at the terminal clock. Fixed machine/radix/clock exponents precede inputs. The initialized writer derives length from the original frame, bounds all four registers including final counters polynomially, and obtains native logarithmic workspace with input/output excluded and unrestricted time. Local dimension/reward budgets retain their explicit short-argument/input-budget premises.

The shared two-bit format and writer preserve the ordinary table and its public execution/resource statements; the old 23-label instruction list and four-register structure remain definitionally equal. Tests discharge actual 1,152-bit initialized runs, clock-one sources, multiplicities one/two, off-clock and terminal zeros, and matrix/reward decoding. Source mapping reuses the checked terminal-time construction in pinned Lemma 2.1, pp. 7–8. Complete instance packaging, paired ports and estimator realization remain open; no curated-abstract impact.

Aggregate coverage (3,054 modules) and whitespace pass. At the single inspection title passed; Lean 41119503975, Guide and Comparator were running. Author reports strict affected-client checks; no local Lean build by this reviewer. Live head/history rechecked before posting. Agent review, not human approval.

[SamuelSchlesinger]

integrator-claude-e6cf7b0d-b (integration delegate of coordinator-claude-e6cf7b0d, at Samuel's request): parent #1791 has merged, so I am retargeting this to main, merging main into this branch to resolve conflicts, and landing it.

[SamuelSchlesinger]

integrator-claude-e6cf7b0d-b (integration delegate of coordinator-claude-e6cf7b0d): mechanical carry-forward. Retargeted to main after #1791 landed, and merged main at ff6f4040b8e2113f896a51094c4016a334b3949c. The three add/add conflicts (CompactMatrix.lean, CompactTimeLayer.lean, FairCoin/Table.lean) take this branch's side; main's copies are byte-identical to #1791's head (checked with cmp). Complexity.lean was regenerated with mk_all. Approved 1cd5437a331eaa290543615d733e728c2c384499 → ff6f4040b8e2113f896a51094c4016a334b3949c: payload +/- lines identical to the own layer over #1791; mk_all --check ok. I will queue once CI passes.