Certify current-provider A2 transfer and unchanged owner-cone allowance

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research/staged544-a2-cone-composition/PROOF.md

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+# Eight-site A2 transfer and owner-cone composition
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Exact statement
+
+The two current PR3945 words at `91f81d131252db704f945891da1ea54e29d46b8b`
+admit all eight fixed contractions in ToikY PR4019
+`f408e09df300b575235f7f77f81948071397e16d`, including the A1858 contraction
+credited to PR3998 `389268a6b5e0373a3125d5c6fcd6995f4ea324f5`.
+This is a new source-specific applicability certificate; the identities and
+selected sites are inherited. Native operators, role identities, cut, entrance
+and terminal frames remain fixed. No register or dirty buffer is allocated.
+
+The complete profile remains `{1:2482,2:712,3:218,4:109,5:20,8:8}`:
+3,549 recursive children and rank mass 5,160. The helper inventory remains
+`{5:28,6:18,7:53,8:96,9:213}` across 408 roles. Relative to the already credited
+PR3998 contraction, the additional saving is seven forward and five projected
+inverse-cleanup ADD records. Against the raw current provider, it is eight and
+six. These rational scalar counts are not a physical/native or runtime tariff.
+
+Moreover, each contracted site's two-gate frame itinerary is forced at fixed
+neighbor boundaries. Composing all eight changes with the precise PR4016
+`08c8990f7022b94cf63207229465fb8fa0e8fc75` forced-intersection terminal-cone
+domain leaves its finite outcome unchanged after remapping B indices. Five
+survivors remove H1 locally but require at least H1 more owner idle cost under
+the credited packing dual. Therefore the composition has no positive complete
+optimistic allowance at the source endpoint. This is not a universal graph,
+terminal or scalar-frame obstruction, nor a supplier or kappa admission.
+
+## Local equality, gathering and cleanup
+
+The sites are the original zero-based triples A(1858,1859,1860),
+B(4,53,54), B(7,49,50), and restore(20,21,36), (22,23,38),
+(26,27,51), (30,31,62), (32,33,73). Every gate and replacement is retained in
+RESULT.json. The exact PR4019 proof is retained at frozen/sep/PROOF.md.
+
+For distinct x,y,z, let S(a) act by y+=a*z, T(b) by x+=b*y and U(c)
+by x+=c*z. In chronological order,
+`[S(a),T(b),U(-ab)]=[T(b),S(a)]` and
+`[U(ab),T(b),S(a)]=[S(a),T(b)]` over the rationals. Both identities hold
+on arbitrary dirty inputs, with no zero-input assumption. Both the primary
+rational matrix check and ToikY's separate coordinate-column implementation
+recompute each identity on the new source words.
+
+All intervening unselected events avoid every register in the selected support,
+including reads. They commute with the selected triple. All eight supports are
+pairwise disjoint. No prelude, target/centre, section or native event boundary
+is crossed. Gather at the first selected position and substitute the two gates;
+all other events survive in their original order. B native positions are remapped
+to exactly the same surviving event cuts, and all native operator descriptors
+and ordered frames stay identical. Every other top-level field compares equal.
+
+The non-target subsystem is autonomous because the current words satisfy the
+inherited target-read hygiene. Full operator equality implies equality of its
+non-target block and inverse. Literal cleanup is regenerated from that projection,
+with unchanged protected-buffer renaming. Thus the composition preserves every
+arbitrary dirty buffer, no buffer-to-live leakage and all endpoints. The five
+new restore contractions each save one cleanup ADD; the two B contractions
+remove target-writing ADDs and save no cleanup ADD. The credited old A site
+saves one further forward and cleanup ADD.
+
+## Why there is exactly one compatible local frame itinerary
+
+Fix the frame just before the first selected use and the first unchanged
+successor frame for each of the three touched registers. Include every climb
+through that successor in the local invoice. Intervening events are disjoint,
+so they impose no additional use of those registers. The source's required
+checks and native entrance anchors remain fixed; the local relaxation already
+includes their successor frames.
+
+The replacement has two gates whose supports share one register. Write their
+common frames as F1 and F2; monotonic containment along the shared register
+requires F1 contained in F2. The lower bound for F1 is the span of its two input
+frames. Its upper bound is the intersection of **all three** fixed successor
+frames: the third successor caps F2 and therefore also F1. This backward cap is
+necessary; using only the first gate's two successors would retain dead ends.
+On each of the eight sites this lower bound equals that upper bound. Thus F1
+is forced. After that assignment, the second gate's lower bound is the span of
+its current input frames; its upper bound is the intersection of its two
+successors. Those bounds also coincide. The forced pair is the original common
+frame, up to equivalent basis order. Both implementations verify these set
+identities and every local charge on both providers.
+
+Each support is disjoint from every other selected support, so the eight local
+problems compose without a shared frame variable or omitted successor charge.
+There is one complete flag for the fixed composite graph. Its profile agrees
+rank by rank with the source, hence at every exponent, not just numerically at
+one endpoint. This does not rule out optional changes outside the local bounds.
+
+## Changed graph and the owner-aware cone
+
+The exact forced-cone algorithm and tariff proof are retained from PR4016 in
+frozen/cone/verify.py, tariff.py and PROOF.md. Their algorithms are reused,
+not advertised as independent implementations. For every protected terminal
+hyperplane, shrink its last scalar frame by intersection; propagate necessary
+intersections to scalar predecessors. Reaching an incompatible immutable
+entrance/native exit or a fixed check rejects. The successful assignment is
+the greatest feasible one below the original scalar frames. It does not search
+additional optional frame shrinks, arbitrary rotations or coupled terminals.
+
+Both original and combined current words yield the same 13,285 hyperplanes:
+2,688 fail start containment; 10,023 reach an incompatible entrance/native;
+552 reach a fixed check; 17 are the separately credited direct-refund class;
+five have a changed scalar cone. The five helpers are 282, 293, 298, 309 and 373.
+The entire candidate records agree except B event indices are reduced by two,
+accounting for the two deleted B records before all five events. Each witness
+has exactly one changed SCALE frame and terminal, local delta -H1, and width
+5 to 4. All ten literal combined witnesses are reconstructed, invoiced and
+checked with arbitrary-dirty forward/dual semantics and cleanup boundaries.
+
+At the source endpoint k=1730663236534549309146/10^24, write h(r)=r^(1-k).
+The PR4016/3988 packing dual has pi4-pi5=h(1)=1. Its feasibility is rechecked
+for all 2,551 capacity 8/16/32/48, width 4..9 patterns: 12 exact equalities and
+2,539 strict rational interval bounds. The retained incumbent aggregate attains
+the dual across 725,760 bins. Hence even fractional repacking after a width 5 to 4
+change increases the owner idle lower bound by H1. It cancels the local saving
+exactly. These checks reuse the credited exact tariff engine. Actual physical
+owner chronology remains inherited. Other unknown costs are not assigned zero.
+The 17 direct refunds are excluded from the changed-cone claim and remain
+credited to PR3988; this package does not newly audit their whole lifecycle.
+
+## Evidence boundaries
+
+The primary performs all 723-input ordinary, dual, reverse pullback and both
+cleanup-boundary checks for original, credited-only and combined words for both
+providers, comparing full ordinary and dual operator digests. The separate
+checker reuses ToikY's no-primary-import point-set/coordinate engine on the new
+inputs, reconstructs the word and cleanup digests, verifies all 149 complete
+register-frame boundary states and recomputes the entire profile. A new separate
+chronological timeline verifies the backward-cap singleton proof. This is
+independence of representation from the primary, not fresh independent authorship
+of the retained engines or a second full free-operator replay.
+
+Physical owner/holding/routing/control/tape costs, changed intermediate growth,
+finite precision and signed-floor errors, concrete native phases/lowering,
+uniform stock, all-size compilation, outer consumption and analytic/BIT
+obligations remain inherited or unproved. No full multiplication theorem,
+human/formal-kernel review, merger or selected-frontier change is claimed.

research/staged544-a2-cone-composition/README.md

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+# Current-provider A2 transfer with no new owner-cone allowance
+
+The exact current PR3945 providers admit ToikY PR4019's seven separated A2
+contractions together with the credited PR3998 A1858 contraction. Relative to
+that already credited contraction, this removes **seven forward and five inverse
+cleanup scalar ADDs**. Both complete paid profiles remain
+`{1:2482,2:712,3:218,4:109,5:20,8:8}`: 3,549 children and rank mass 5,160.
+There is no recursive-moment, runtime or kappa improvement.
+
+This answers PR4019's explicit later-word handoff and tests the requested
+combination with PR4016's forced scalar cones and owner dual. The eight-site
+changed graph has exactly one compatible two-gate frame assignment per site at
+fixed neighboring boundaries. Backward cap propagation proves this directly;
+first-step flags that cannot reach the second gate are excluded. Its terminal
+cone census reproduces PR4016 exactly after B-index remapping: 13,285 hyperplanes,
+five changed-cone survivors, each local -H1 canceled by at least +H1 owner idle
+cost. The owner bound allows arbitrary fractional repacking. The 17 prior direct
+refund cases are retained as a separate credited class, not re-admitted here.
+
+This is a bounded combination certificate, not a general graph search or proof
+that optional interior changes, coupled terminal edits, rotations or changed
+native interfaces cannot work. The complete favorable allowance stops further
+dependent expansion of this fixed composite.
+
+## Frozen sources and credit
+
+- PR3945 `91f81d131252db704f945891da1ea54e29d46b8b`: the two current input words,
+  native descriptors and lineage notice, by Dugongue with retained predecessors.
+- ToikY PR4019 `f408e09df300b575235f7f77f81948071397e16d`: the seven separated
+  sites, local identity/composition proof and separate point-set checker.
+- Chris R/Clear1nsight PR3998 `389268a6b5e0373a3125d5c6fcd6995f4ea324f5`:
+  A2 graph identity, credited consecutive A1858 contraction and current-source
+  source exports; dataisfire PR3734 supplies the older literal-word lineage.
+- PR4016 `08c8990f7022b94cf63207229465fb8fa0e8fc75`: exact forced-cone and
+  owner-dual algorithms; PR3988, PR3969 and PR3815/3862/3890 retain tariff,
+  owner aggregate and packing-dual credit. Jeremy Kothe, zxv, RossRichardson,
+  ErwanSecousses and hexapode retain related profile/packing credit.
+- Sagar Thakrar, roger-sato and Arham Tahir retain auditor/frame/native lineage;
+  unchanged notices are in `frozen/`. PR1865 by 1337isnot1337 retains the earlier
+  distinct nonconsecutive commuting-C3 precedent.
+
+Canonical base is `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. Fourteen exact
+package-local exports are authenticated with SHA256, length and Git blob before
+execution. `SOURCES.json` records original source paths and commits. No pending
+source history or network access is needed for execution. Only documented pure
+helpers are invoked from retained modules; their older input-specific CLI
+entrypoints are not used. In particular the old PR3734 manifest/constants
+inside retained PR4019 files are historical context, not current-word pins.
+Actual current inputs are independently hard-pinned by the second checker.
+
+## Proof and evidence
+
+`PROOF.md` gives exact scope, local gathering, projected inverse cleanup,
+unique complete frame flags and owner-aware cone composition. `RESULT.json`
+binds every site, reconstructed word/cleanup, full profile, cone candidate and
+operator digest. The native descriptor order and frames, all helper entrances
+and roles, and all other source fields remain unchanged; B positions account
+only for deletion of the two selected B records.
+
+The primary checker reuses the credited rational dirty-state auditor, PR4019
+local checker and PR4016 cone/tariff engines. It replays source, credited-only and
+combined current words on all 723 formal inputs, ordinary and dual operators,
+reverse pullback and cleanup boundaries. Ten further combined cone witnesses
+receive arbitrary-dirty forward/dual and cleanup-boundary checks.
+
+The second checker imports only ToikY's separate point-set/coordinate engine,
+recomputes all 16 local identities, reconstructs all six words, compares their
+cleanup digests and149 full-register frame states, and computes their complete
+invoices. Its new chronological timeline separately verifies all 16 unique
+complete frame flags. Fourteen inherited semantic controls plus six production
+semantic controls and two actual optimized-CLI source/owner-receipt mutations
+must reject. This is credited independent representation, not a newly independent
+full-word interpreter or human/formal-kernel acceptance.
+
+Run from the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/staged544-a2-cone-composition
+```
+
+The five registered commands verify base, extra, the 2,551-pattern owner dual,
+the separate composition checker and controls. Python 3.12 standard library;
+no optional packages. Full generation is explicit `verify.py --record`; normal
+verification is read-only. `--quick` omits full dirty semantics and is for bounded
+controls only. A passing certificate is not full supplier admission.
+
+Physical owner/holding/routing/control/tape costs, changed intermediate precision
+and signed-floor behavior, concrete native phases/lowering, uniform stock,
+all-size compilation, outer consumption and analytic/BIT obligations are inherited
+or unproved, never priced as zero. No scalar/native unit-cost equivalence or
+measured speedup is asserted.
+
+## Open next questions
+
+- Can a genuinely different graph or changed native/check boundary remove a
+  charged transition? Specify that exact boundary and a positive complete
+  owner-aware allowance before expanding a search. This eight-site composition
+  supplies neither; another adjacent census is not justified by these ties.
+- Can the current producer adopt the verified scalar saving with its concrete
+  native/precision/owner implementation? First independently replay the frozen
+  transfer and audit intermediate growth. This package preserves formal operator
+  and frame contracts but does not admit those physical obligations.
+
+New transfer/composition work by Chris R/Clear1nsight with substantial OpenAI
+Codex assistance. Apache-2.0. No merge, closure of others' work or selected-frontier
+change. Entry overlap covered all 733 open PR bodies at 10:46:04 UTC, bounded live
+handoffs and relevant predecessor claims; broader Discussion/code coverage is
+partial. `TASK.json` retains the actual narrowed task and stopping decision.