Transfer Semigroups and Memory
Probabilistic refinement, fractional operators, and exact hidden-state elimination
Paper VI · Komorebi P.
| Read | Pages |
|---|---|
| Traditional manuscript | 152 |
| Visual guide | 44 |
| Lean and evidence guide | 64 |
| Total | 260 |
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Accepted publication and scientific scope
The accepted release is 1.0.0, dated October 20, 2026; its mathematical body edition remains October 9. This freeze preserves its manuscripts, figures, scientific source, history, licenses and evidence. All 184 numbered records, 140 proof bodies, 739 original scientific source files and three original archives remain unchanged.
The inherited formal contract covers 33 scoped results, 341 theorem targets, 47 production modules and 782 namespace declarations. Its compiler and axiom evidence is the September 6 0.5.0-checked-fifth-block release. The broader 142 theorem-like records and 140 written proofs do not enlarge this finite contract. Full-paper Lean formalization is incomplete.
The accepted closeout's eleven bounded records retain their own input sets, units and dates. They include overlapping dispatcher checks and are not an independent theorem count. Floating residuals are not interval certificates. Finite-state, common-gap, fixed-partition and other stated assumptions remain in force. Classical conditional expectation, martingale convergence and stable subordination retain their ordinary classical scope; no arbitrary-martingale L2 convergence is asserted.
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Use a separate working copy and external output directories for other reproduction commands. The pinned runtime, dependency binaries, TeX/Python tools and declared fonts remain external prerequisites. The corrected builders and font instructions from the accepted release are unchanged.
Research, history and open use
Three research questions remain open: transfer-semigroup realization on completed state spaces, uniform refinement control, and latent-packet closure for stable infinite systems.
The dated original ledger and closeout JSON refer to IX as the next incomplete paper and X as a source-recovery hold. Those workflow pointers are historical: IX and X subsequently closed within their selected scopes. The current sequential freeze continues with VII. Original audit lineage and its disclosed historical whole-file reconstruction limits remain intact; this freeze does not reconstruct a missing historical assembled file or repeat a semantic proof audit.
Original software and machine-readable material use MIT. Original writing, figures and editable writing sources use CC BY 4.0. The unchanged grants and third-party/font exceptions are in LICENSE.md, LICENSE_STATUS.json and LICENSES/.
This distribution is frozen as of October 20, 2026, America/Chicago. Actual verification timestamps retain UTC dates. No fresh Lean execution, finite experiment, control suite, TeX rebuild or whole-paper proof audit is claimed. No public website or repository is published by this task.