Restart the encoded forward and inverse balanced CRT endpoints on one 79-role inventory with paid reentry and retained history

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research/encoded-crt-restart/OVERLAP.md

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+# Focused overlap and expansion decision
+
+Pinned canonical main: `e54523517d0f03e58352e647c403a5af3e525a57`.
+Live PR queries on 2026-11-12: `"CRT" "reuse"`, `"CRT" "restart"`,
+and `"79" "roles"`. The canonical research-tree metadata was also checked
+for restart, reentry, historical-storage and owner packages. These bounded
+queries are not an exhaustive novelty proof; the decisive evidence is the
+exact predecessor's explicit missing interface.
+
+| Predecessor | Established | Distinct remaining seam |
+|---|---|---|
+| #5505; canonical `crt-persistent-numerical-owner/owner.py` | Stable 63-role owner and numerical call reentry | Guards, topology and source staging at the whole endpoint boundary |
+| #7152, `66adbede4bd4ab603ba3e0a7f6708403905b753c` | Repeated compiled-geometry numerical/ROM state traversals on 127 roles | Different provider closure, encoded frontend and 79-role inventory |
+| #7154, `cc35ecedce6f208d5056fab6d17c58555affc73c` | Encoded numerical node schedule; 78 roles in one read-only iterator | Whole-source changing-state writer and whole-call restart |
+| #7351, `d2ed3959c30528b0b85fc6d815d4ad4f94f6be86` | Complete encoded forward address-state endpoint, 79 roles | Persistent restart after full topology retirement |
+| #7352, `8c0e55c9ba25ff2c8199b01539a4d56ae71a1473` | Encoded reverse and fresh two-sided composition | PROOF section 5 and Open next question 2 explicitly leave same-inventory restart open and charge 158 histories |
+
+Decision: continue one narrowly scoped adapter. It can change the concrete
+retained-inventory interface while preserving all scientific predecessors.
+The optimistic budget is constant marker/ownership traffic plus the entire
+old invocation bill, not a speculative new recurrence. Stop on a required
+new physical role, a hidden historical-capacity scan, nonblank successful
+old tails, changed numerical source, or a failure of the rolewise envelope.
+No added payload, prime-selection or compact-macro implementation is bundled.
+
+The new theorem retains a supplied-clean-history premise at initial entry.
+It does not rename arbitrary dirty acquisition as successful reentry. The
+negative dirty-tail experiment is a scope control, not an impossibility
+theorem about algorithms with encoded frontiers or paid cleaning passes.

research/encoded-crt-restart/PR-DESCRIPTION.md

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+## Result and why it matters
+
+Close the exact persistent-restart obligation in CrocSwap/integer-mult-bounds#7352.
+The unchanged encoded forward and inverse address-state endpoints can run any
+finite successful sequence on the same 79 physical histories. The predecessor
+charged 158 histories for a fresh forward/inverse pair. Every original
+invocation cost remains charged.
+
+For current width sums A_i, time is T_initial + sum_i O(A_i^4). With initial
+private history K0 and maxima Amax,dmax, retained local backing is at most
+K0 + 3 Amax dmax + 74 Amax + 23 dmax + 223, plus source and protected-prefix
+histories. The proof bounds each physical role's historical maximum.
+
+## Exact change and novelty
+
+A fixed constructor facade rearms the existing eight guards, seven topology
+ports and staging port, and returns the already retained 63-role numerical
+bank. Ten pinned scientific files remain byte-for-byte unchanged. Initial
+fresh acquisition plus validation costs 1264 raw Port actions (316 for supplied
+clean inventory); each call adds exactly 80 rearm and 316 finish actions.
+
+Credit CrocSwap/integer-mult-bounds#5505 for numerical-bank reentry,
+CrocSwap/integer-mult-bounds#7154 for encoded geometry, and
+CrocSwap/integer-mult-bounds#7152 for the different compiled 127-role pipeline.
+CrocSwap/integer-mult-bounds#7351 and #7352 already provide the CRT maps.
+This contribution is their exact whole-call restart and repeated-history bill.
+
+Base: `e54523517d0f03e58352e647c403a5af3e525a57`.
+Immediate exact heads: #7351 `d2ed3959c30528b0b85fc6d815d4ad4f94f6be86`;
+#7352 `8c0e55c9ba25ff2c8199b01539a4d56ae71a1473`.
+All runtime inputs are committed exports with Git-blob/SHA256 authentication;
+replay requires neither pending Git history nor network access.
+
+## Verification
+
+```sh
+python3 -I -W error -B research/encoded-crt-restart/verify.py
+python3 -I -O -W error -B research/encoded-crt-restart/verify.py
+```
+
+Expected: `PASS_ENCODED_CRT_PERSISTENT_RESTART calls=174 nodes=270 roles=79 controls=14`.
+The actual encoded run loop drives every call. A defining-congruence observer
+checks current-node output, complete tails, identities, meters and costs.
+New Port/Word/Arena constructors are forbidden after acquisition. The changed
+geometry sequence grows, shrinks and regrows on translated origins behind
+opaque prefixes. Fourteen controls target lifecycle, direction, aliasing,
+hidden acquisition, historical accounting and inadmissible dirty tails.
+
+Separate root proof/source review and an independent modular-inverse CRT oracle
+pass 32 further calls and 96 nodes. See REVIEW.md and independent/ for exact
+hashes, source bindings and reproduction. Finite tests corroborate the written
+induction; no formal-kernel or independent human acceptance is claimed.
+
+## Limits and kappa status
+
+**No new kappa; the selected 0.00363005817 remains conditional on all five
+foundational assumptions.** Initial whole-tail blankness is explicit for
+supplied inventory. Two local observations do not validate arbitrary dirty
+tails; successful complete retirement establishes future entry inductively.
+Linear-use calls grant no stale-handle authority and no failure rollback.
+
+Source acquisition/re-encoding, payload routing, exceptional-key adaptation,
+binary lowering and the full outer caller remain separate paid obligations.
+Open next questions and complete source-model costs are in the package.
+
+## Credit and assistance
+
+Prepared for **@CubeJerry / Jerry Chen**, with substantial **OpenAI assistance**.
+Credit the exact published predecessors, JoyboyBrian's numerical/owner work,
+Ali Romman's source interface, Cinna Davis's balanced CRT, Hiroki KUMAZAKI,
+ToikY, commdata2338 and all retained notices. Separate AI review does not imply
+independent human or formal-kernel acceptance. No selected or frozen file changes.

research/encoded-crt-restart/PR-TITLE.txt

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+Restart the encoded forward and inverse balanced CRT endpoints on one 79-role inventory with paid reentry and retained history