Bound retained backing across the selected complex and BIT backend stack with history-safe stock reserves

research/stratified-owned-reserves/OVERLAP.md

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+# Scope and bounded overlap review
+
+Scientific source: canonical `e54523517d0f03e58352e647c403a5af3e525a57`.
+This is the track-60/53 ownership/recursive-interface assignment, refined
+from `uniform-transfer-audit`. The other current worker studies finite
+control and source-bound contexts; this package studies physical capacity,
+backend stratification and simultaneous stock only.
+
+## Predecessor distinctions
+
+| Prior contribution | Reused or excluded result | New residual treated here |
+|---|---|---|
+| #5814 | Single-provider geometric owned-segment implication and physical bridge construction | Noncontracting cross-backend edges in a finite ordered dependency graph |
+| #5829 | Whole-high child volume V/L and complete high-field retention | Composition with ordinary wrappers and the complex caller |
+| #5404 | Coordinatewise historical backing, including rotating tape roles | Finite multibackend per-tape potential at reusable origins |
+| #6719, reviewed in #6737–#6740 | Two-site physical shape recursion and root A/R/H generation | No new shape dispatcher; its local facts remain source inputs |
+| #6879 | Old ordinary helper's reusable-origin space theorem | Exact selected .0034 backend still requires its own contract |
+| #6903 | Chronological high fields and separately quantified producer absorption | No new producer; mixed backend/stock accounting remains separate |
+| #6896 | Recursive physical capacity for the dim64 continuation inventory | Six-stage current selected dependency, rather than another bank census |
+| #2343 | Post-borrow body-dependent stock, fit cutoff and failed equality iteration | Uniform envelope over smaller sibling widths for the current stopped stock formula |
+| #4432 | #4100 stock/depth/recurrence audit | Its D is a body-depth argument; this package does not reuse its historical child-volume wording or claim a current stock discontinuity from it |
+| #4957 | Conditional completed ordinary backend API edge | Per-tape historical allocation after the API's local space data are supplied |
+| #4338 | Optional B2 arithmetic and frozen source-relative coupling | No new backend saving, factory or moment proof |
+| #7000/#7001 application | Frozen backend DAG, rho=1/250, ambient cap134, complete current inventory and simultaneous-reservation product | An explicit substitution lemma for its Sections 3 and 6, not complete dispatcher admission |
+
+The generic ownership/geometric theorem, raw lifetime counts and continuation
+bank high-water formula were deliberately excluded after source inspection.
+The new claim is the single combination in PROOF.md: a source-refined stage
+graph whose complete history and fresh stock are both billed consistently.
+
+## Live search coverage
+
+On 2026-11-10 the coordinator supplied the current PR and account snapshots,
+read the canonical discussion/claim guidance, and checked active scope.
+The worker also read the named predecessor bodies and used bounded all-state
+GitHub PR searches (six-result cap for each query):
+
+* `"stratified"`: #3998 and #5249, unrelated algebraic stratifications.
+* `"same-volume" "space"`: #3724, an arithmetic ordinary-rate audit.
+* `"stock" "monotone"`: #6488, #5881, #2353, #4432, #2343 and #6788.
+* `"backend" "historical"`: #4338, #4957, #5848, #4167, #4172 and #1075.
+
+The material stock/API matches are distinguished above. #4167/#4172 concern
+QQ16 physical-context/action coupling, not this selected backend-space
+certificate. Search result caps and indexing can omit work. No matching
+stratified-stack theorem was found in the inspected scope; that is a bounded
+overlap finding, not proof of global novelty. The coordinator's live sprint
+updates and final upstream refresh remain the publication checkpoint.

research/stratified-owned-reserves/PR-DESCRIPTION.md

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+## Change and mathematical scope
+
+The selected #7000/#7001 application freezes `.0034 -> .0038507 -> .00385248`
+ordinary backends and retains suspended complex/BIT parents. Backend entry
+can preserve or enlarge complete bit volume, so the one-provider geometric
+space argument needs an explicit composition step.
+
+This package proves that step as a per-tape finite-stage allocation lemma.
+The least certificate is `M_i=max(c_i/(1-rho_i), c_i+a_ij M_j)` over lower
+backends. It gives a complete-history bound `sum K_t+V_root sum M_root,t`
+under stated local physical contracts and reusable-origin discipline. The
+source-refined six-stage graph retains ordinary padding, radix embedding,
+all external payload factors, parent copies, private banks and erased tails.
+Sequential siblings do not add a historical-count factor; the time bill
+still sums every actual occurrence.
+
+A monotone envelope retains the full input-dependent stopped stock and the
+product of simultaneous complex/BIT reservations. An exact stock-formula
+counterexample at N=2, rho=1/250 shows why endpoint-only stock is unsafe as a
+generic argument: from `3215^250` to `3215^250+1` the new factor drops by
+`1/(L q^1244)`. This is symbolic for eligible fixed primes. q=3 is only an
+algebraic control; no selected producer or actual selected-N discontinuity
+is claimed.
+
+**No new κ.** The selected conditional κ=.00363005817 is unchanged. This is
+an enabling allocation/accounting implication for application Sections 3
+and 6, not complete dispatcher admission or discharge of owned_erasure.
+All five foundational assumptions remain.
+
+## Novelty, exact sources and reproduction
+
+Base: `e54523517d0f03e58352e647c403a5af3e525a57`. SOURCES.json binds eleven
+live inputs by Git blob and SHA256 and retains historical selected/card
+provenance. The package extends #5814's one-provider ownership theorem,
+#5829's whole-high V/L geometry and #5404's historical-tape accounting.
+#6719/#6737–#6740, #6879, #6903 and #6896 retain their distinct physical
+shape, helper, chronological-field and capacity results; none is republished
+as a new theorem. The related stock/API questions in #2343/#4432/#4957
+are explicitly distinguished in OVERLAP.md.
+
+```sh
+python3 -B scripts/research_package.py --package research/stratified-owned-reserves
+```
+
+Expected: `PASS_STRATIFIED_OWNED_RESERVES` twice,
+`PASS_STRATIFIED_BOUNDARIES`, `PASS_INDEPENDENT_STRATIFIED_SPACE` twice,
+and `PASS_REGISTERED_RESEARCH_PACKAGE`.
+CPython 3.12, standard library only.
+
+The exact finite evidence covers 512 stage graphs, 12,384 independently
+enumerated bounded paths, a 31-node restored-origin history, 60,600
+smaller-width stock comparisons and 118 complete product coordinates.
+Separate subprocess controls reject source drift, typed receipt corruption
+and omitted radix inflation, including under optimization. The written
+induction supplies the universal lemma; finite checks corroborate it.
+Executed checks and scope are recorded in VALIDATION.md and RESULT.json.
+
+A separate research worker independently reviewed the mathematical/source
+interfaces and supplied a different exact checker: complete descending paths
+with geometric terminal rewards and finite dual witnesses. Normal and
+optimized checks pass 1,068 coordinate certificates, 4,920 descending paths
+and four controls. The source/stock/history review and reviewed core hashes
+are included under independent-review; this is AI-assisted review, not human
+or formal-kernel acceptance.
+
+## Remaining obligations and credit
+
+The exact `.0034` all-history space contract, actual local coefficients,
+emitted numerical dispatcher, source width maxima, root stock fit and
+common physical precision layout remain to be supplied. No actual cell
+tariff, complete runtime, unconditional multiplication theorem, independent
+human acceptance or formal-kernel proof is asserted.
+
+Prepared for **@CubeJerry** with substantial OpenAI Codex assistance in
+derivation, source audit, implementation and checking. Credit the cited
+predecessors, Jose Manuel/jmbarrancoml's ordinary and stock interfaces, and
+the native, delayed-cover, compiler, frame and precision lineage retained
+by the selected application. New work is Apache-2.0; predecessor files and
+the selected certificate remain unchanged.

research/stratified-owned-reserves/PR-TITLE.txt

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+Bound retained backing across the selected complex and BIT backend stack with history-safe stock reserves