Assessment164: coordinate adoption and primary-proof review

9 October2026. Dedicated literature assessment70. Canonical base 5d1b115116f4c49a8b731fa1c99c9cab2d9cd446; shared conditional lease 4c1e90578d53887ad54085e9ffd73cd368089c25.

The maintained argument proves width-ready atomic registration in O_r(n): old logical row masks survive per-width basis changes while one shared cross-width reader is repaired. This closes coordinate adoption under an explicit charged interface. It leaves ordinary-input width dispatch and first-record bootstrap open. The native endpoint remains reader42; no root admission or novelty claim.

Primary proof1: minimal linear realization

G. David Forney Jr., Minimal Realizations of Linear Systems: The “Shortest Basis” Approach, arXiv0910.4336v3,24August2010,21pages. Primary PDF. SHA256 60f9514f840065e7ebe04447fc59a50e1bf2c2b755b0a4e1b064291f1a7f3fc7. Read the complete paper, including the appendix; extracted copy remains private.

SectionsIII-IV derive state and transition quotients and characterize shortest bases by predictable spans and subsystem bases. Active generators count minimal state and transition dimensions. SectionV treats time-invariant polynomial systems; VI gives dual observer realizations. VII separates realization theory from construction algorithms, and the appendix treats complete uncontrollable systems. Finite trajectories avoid the infinite-support hypotheses.

Application: the exact cut is after input bit t but before width-t observation. The future quotient then has dimension rho_t. This semantic event expansion grants no additional input symbols or preparation time. The paper supplies the minimality mechanism, while the repository’s original prefix-repair proof supplies the charged operation and the new note handles immutable masks.

Primary proof2: incremental persistent preparation

Robert Hood and Robert Melville, Real Time Queue Operations in Pure LISP, Cornell TR80-433,July1980,8PDFpages including cover and blank final page. Repository record. Primary PDF. SHA256 f2e94253671f72484ce3798ab631fadefb3bb784ed030079097132303ffb15a9. Read all body pages and appendix by OCR, with visual inspection of the appendix; PDF and page images remain private. This is the technical-report edition.

The recopy invariant retains an old readable front while incrementally reversing and assembling lists. Starting with front length n and rear n+1, at most2n+1 copy steps are serviced two per update, before deletions exhaust the old front. The copy counter reconciles deletions and the fresh rear accepts insertions. Queries remain readable during preparation. The fixed record and primitive list operations provide the implementation mechanism; allocation cost and the native old-top embedding remain separate model obligations.

Application: a readable old reader is useful but may carry obsolete mask coordinates. Our transport invariant resolves that mismatch. The queue proof’s front reserve has no automatic counterpart for a repair released at a word’s last symbol, so it does not establish the producer deadline.

Contract comparison and consequences

The maintained proof gives a directly dependent combination, rather than restating either primary theorem. Per-width Fourier-support transport preserves surviving masks, vector-output prefix repair preserves all other widths, and both fit one width-ready transaction. Minimal internal states may change while external syndromes and old logical masks stay compatible. The hereditary future-rank gate is invariant under the chosen invertible output coordinates.

The next candidate is checked contiguous width blocks without headers. Later records know their active width early; the first record does not. A two-lane speculative raw/bootstrap design avoids proposing one worker per stored width, but current-key closure, depth-profile installation and fresh-width extension are not yet paid by a complete native invariant. Section7 records these exact obligations. The failed route is inferring deadlines from a real-time FIFO or total linear work. No general native nonrecognition follows.

Evidence and disposition

The independent finite experiment checks707 accepted transactions among903 proposals at capacities1 and2 through width7;861 repair gates match full recompilation, including154 future-rank rejections. Ten nonidentity transports, 55 retained versions,671632 current-row queries,51934 retained-row queries, 193548 union queries and179578 syndrome queries pass. Literal row sets are the semantic oracle. Python object identity is only a suffix-sharing audit, not an allowed native observation. This is not a native clock simulation.

Imported results: the two established primary mechanisms above. Written new argument: their exact FPRD comparison and the combined adoption/repair proof. Conditional transfer: O_r(n) registration with handles ready at word start. Conjectural construction: unbounded checked width blocks. Failed route: late job release justified only by amortized credit or FIFO operations.

Seven surfaces: primary custody stays private; original argument and checker are in GitLab; root CLAIMS.yaml is unchanged; failure ledger and frontier are updated; reader42 remains the public theorem; Site publication is deliberately not advanced for this supporting interface. Prior publication receipt is retained without asserting a new source-parity check. Prior SAT/scaffold, independent-join, affine and causal controls remain intact.

Validation: full make verify: 1490 passed,1 skipped,5 failed in230.83s; four existing custody-provenance failures and unavailable-lake frontier verifier. Later make targets not reached. Python syntax, JSON/cadence, local link paths, unchanged root CLAIMS.yaml and git diff --check passed. No frontend build or deployment was performed.

Scheduled69->70 once; dedicated review70 complete with two full primary arguments. Next71 research and dedicated75. Mathematical110, window0 and reassessment110 unchanged. Next decisive test: implement the first-width bootstrap and paid depth-profile handoff under ordinary syntax, or produce a specific failed scheduling contract. No new endpoint is counted for this supporting combination or for publication work.