Bind selected caller routes to complete compact-control reservations

research/selected-control-reservations/PROOF.md

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+# Selected raw145 routes inside complete compact reservations
+
+This is a source-bound refinement of an existing layout argument. It is not a
+new compact-control primitive, a physical execution, or a final-template proof.
+The source plan has SHA256
+`a02e79fb4615f4f987e3b3617c2b42eea2c1d7415cc66fa702a8b0cd28e6387e`.
+The current selected value remains conditional κ=0.003027288235.
+
+## Proposition and quantified boundary
+
+Fix the authenticated `WHOLECALLER-PLAN-v1` with ambient145. Let integers
+`d>=D>0`, `K,G,f>=1`, `q0>=1` and `lead>=0` be given. Put
+
+```
+H=dG, qF=ceil(2H/K), qB=ceil(H/K),
+o=(q0+qF+lead)K, z=(D-qB)K.
+```
+
+Assume `(f-1)G<=H` and `o+145fK<=z`. Assume the current stream is a complete
+Cartesian product of its row index, the front/back fields, all active and
+spectator coordinates, and its record suffix. The source compact-control
+primitive, including repair and restoration, is an inherited hypothesis.
+
+Then every literal main/helper/IDLE coordinate route in this plan has the
+following placement: source axis `a`, column `j`, selected position `rho`
+is the address bit
+
+```
+phi(a,j,rho)=o+(af+j)K+rho,
+0<=a<145, 0<=j<f, 0<=rho<K.
+```
+
+The 119 routes, the 18 embedded local9-planes, and the 16 central translations
+use no row or reserved-control bit. For each fixed rho they induce exactly
+the plan's columnwise coordinate operation, preserving the other bits of each
+K-bit chunk, and restore each entire borrowed compact field. Their statements
+hold for every f in the domain, not just the finite f controls. No assertion
+about the Gaussian/scalar operator endpoint is newly proved here.
+
+For an IDLE of rank r, its literal `pre_inverseJ` puts exactly its recorded
+`active_axes` into the canonical `rf`-chunk child prefix. The other
+`(145-r)f` chunks remain complete spectators, followed by any outer active
+remainder and prior right spectators. Front/back controls stay outside this
+reassociation. Reassembly followed by the literal post-J restores the parent's
+coordinate order. This is the address ABI for an assumed complete child
+endpoint; it does not execute or price the child.
+
+## Source directions, not an interchangeable J convention
+
+Represent a coordinate word by its pullback list: after swaps, output slot a
+contains the input slot recorded at list entry a. Direct composition of every
+literal word verifies:
+
+| Family | Number | Pre pullback | Post pullback | Literal swaps |
+|---|---:|---|---|---:|
+| main targets |32|inverse_permutation|permutation|3,776|
+| helper targets |72|inverse_permutation|permutation|10,116|
+| IDLE jobs |15|permutation|inverse_permutation|2,856|
+
+In all cases `permutation[:rank]=active_axes`. Thus IDLE's prefix after its pre
+word contains its active axes; treating IDLE like a main target reverses the
+required direction. Main/helper pre/post words surround different source
+boundaries; we do not reinterpret them as IDLE child brackets. Each permutation
+is a bijection on all145 axes, and its post word is the inverse of its pre word.
+All119 routes have empty affine translation and zero absolute phase. The16
+negative-Q main banks separately require the plan's post-LEFT axis0 translation.
+
+The18 local embeddings share axis0; their eight private axes partition1..144.
+Every LOCAL points to its stage's exact9-axis list. The source contract declares
+that same list on all649 local fields. Our check binds the list and declaration;
+it does not rerun the649-column provider algebra or the independent global
+integer-ID alpha-renaming join.
+
+## Interval proof and complete dirty fields
+
+The row bits occupy `[0,q0K)`. The two complete front fields occupy
+`[q0K,q0K+H)` and `[q0K+H,q0K+2H)`. Their right endpoint is at most
+`(q0+qF)K<=o`. The complete back field is `[z,z+H)`, contained in the last
+qB chunks. The raw block is `[o,o+145fK)`, contained in `[o,z)`.
+These half-open intervals are pairwise disjoint; zero slack is permitted.
+
+For each source axis a, all its selected bits and their unselected guard bits
+lie in `[o+afK,o+(a+1)fK)`. Distinct source axes have disjoint slots. Every
+source SWAP_BITS is three ordered XOR row additions on two such complete slots.
+For each addition the front fields precede both slots and the back field
+follows both, in either source order. Carving `(f-1)G` bits from each H-bit
+field is legal; all unused bits are spectators. The credited compact proposition
+therefore supplies the exact selected-bit addition and full dirty restoration.
+At f=1 its elementary two-bit branch is used. Three additions give the swap.
+Composition gives each literal route; fixed-rho bit positions are preserved.
+An axis0 translation also lies in the same active interval. Local9-plane
+restrictions select nine disjoint full slots and leave every other slot present.
+
+The executable interval checks use endpoints to verify whole ranges, including
+one f=10^30 case without allocating an array of that size. Their all-f force is
+the preceding argument. The separately implemented lifted-word controls expand
+all coordinates only for f=1,2,3.
+
+## Whole-row split and actual IDLE child reassociation
+
+Let a current row range have size R, with `R=L*U`. Splitting an entire row by
+`r=L*g+w` gives a bijection
+
+```
+{0,...,R-1} × Omega  <->  {0,...,L-1} × {0,...,U-1} × Omega,
+```
+
+where Omega is the entire within-row rectangle, including both front fields,
+active slots, back field, spectators and record suffix. No compact or active
+bit participates in the row quotient. Consequently each role receives all of
+Omega; address completeness is independent of the payload's dirty values.
+Repeated legal divisions use mixed-radix row digits, and the inverse formula
+restores every original row. A parent/child packet may be correlated with other
+owners; this does not change its complete address set.
+
+For each actual IDLE permutation p, the child prefix labels are
+`(p[a],j)` for `a<r`, and the complement labels are `(p[a],j)` for `r<=a<145`.
+The two lists partition the complete145f labels. Interpreting the second list
+as right spectators is a Cartesian reassociation, not a projection or a
+reallocation of independent coordinates. The parent controls remain complete
+because the primitive restored them before child entry. An assumed child that
+preserves spectators and returns its full packet therefore permits the inverse
+route on return. The checker verifies all15 actual lists at f=1,2,7, including
+complete complementary labels; a dropped spectator is rejected.
+
+If one pads a row count R once to a multiple of a stock product P with R>=P,
+then `R'=ceil(R/P)P<2R`. Added rows contain the whole Omega and zero payload;
+no partial front/back field is padded. They can be removed only after the
+assumed complete linear invocation returns each zero row to zero. Our checker
+tests mixed-radix boundary values, including huge integers, but neither assigns
+final P nor proves the mathematical endpoint that makes padded rows deletable.
+The generic bijection is predecessor work; the contribution is its explicit
+join to these source routes and their actual child complements.
+
+## Exact remaining final-compiler obligation
+
+This result concerns the raw145-axis plan, not the exponentially larger
+compiled program. `V16-APPLICATION-PROOF-v3` §§5–6 constructs a finite template
+with enlarged N,W,P,O and source-style stock products. Its §4 raw145 route bill
+cannot supply the final template's actual coordinate injection or row divisor.
+In particular10928 is the raw productive count, not a certified final W;
+418 is raw private inventory, not a certified final O. The numerical row controls
+in this package using10928 and419 are arbitrary-divisor controls only.
+
+To promote this check to that program, supply a source-derived occurrence map
+for every chronological product/completion/split/compiler wrapper. It must bind:
+
+1. its actual final-template active slots and rank-child complement;
+2. its complete q0/qF/qB ranges, using final W/O/N and the full simultaneous
+   stock product, with each whole-row divisor legal;
+3. the current parent/child descriptors and inverse return placement;
+4. the restored-control and spectator premises at every call boundary.
+
+A lazy source-derived generator plus an induction/certificate may suffice;
+materializing the astronomical template is not demanded. This package supplies
+neither that generator nor its proof. It does not refute the selected written
+specialization, whose retained assumptions remain unchanged. It supplies a
+reusable raw occurrence lemma and identifies exactly where source binding stops.
+
+## Provenance and coverage
+
+Douglas Colkitt supplies compact reservations, dirty repair and row splitting.
+John-Michael Smith, Hanson Sun and Aaron Wang supply retained guard/repair audits.
+Jose Manuel supplies PR3055's encoded Compact and the older73-axis physical
+controller/row-return implementation. Chris R / Clear1nsight and the selected
+PR5413 contributor chain supply the actual145-axis plan and precision/compiler
+specialization; all original plan/native/provider credits remain theirs.
+PR5445 motivates the actual reservation binding; its first proposed raw-rotation
+follow-up is already covered by the retained packages and is not repeated.
+
+New source binding and this scoped proof: JoyboyBrian, with substantial OpenAI
+Codex assistance; Apache-2.0. No independent human or proof-kernel acceptance.

research/selected-control-reservations/README.md

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+# Selected5413 control-reservation binding
+
+**Scoped positive raw-caller binding; final compiled-template placement remains
+open. No new κ.** The selected145-axis plan's119 main/helper/IDLE routes,
+16,748 literal swaps,18 local planes and16 central translations fit complete
+front/back compact reservations under an explicit parametric address map.
+
+[PROOF.md](PROOF.md) proves the source-bound implication for every positive
+column width in the stated complete-field domain. Main/helper pre words and
+IDLE pre words use opposite coordinate directions; the verifier retains this
+difference. It also binds the15 actual IDLE child prefixes and their full
+spectator complements to whole-row division/reassembly.
+
+This does not execute the compact primitive, re-prove its guard, or rerun the
+selected Gaussian identity. Those already have substantial retained coverage.
+It does not infer final compiler row stock from raw width10928/private count418.
+The [precise final-compiler obligation](PROOF.md#exact-remaining-final-compiler-obligation)
+requires the expanded occurrence injections and actual W/O/N/stock product.
+
+## Reproduce
+
+Python3.12+, standard library only:
+
+```sh
+python3 -I -B research/selected-control-reservations/verify.py
+python3 -I -O -B research/selected-control-reservations/verify.py
+python3.12 -B scripts/research_package.py --package research/selected-control-reservations
+```
+
+Direct replay works without Git or network and authenticates every declared
+source input. [RESULT.json](RESULT.json) records the exact census, six interval
+families (including f=10^30 without materialization), literal lifted-coordinate
+checks,45 IDLE child cases, whole-row boundary controls and eight rejecting
+semantic mutations. Source-byte and portable replay controls are recorded separately in
+[VALIDATION.json](VALIDATION.json). The fixed q0=11, G=3, K=64 interval fixtures are synthetic address controls,
+not production row-stock or physical-tariff instances. Finite executions corroborate the written
+quantified proposition; they are not proof-assistant verification.
+
+## Scope and prior coverage
+
+Base32890bc5de034ab8fc93ac88ead7279a6a416d04, priority7; selected conditional
+κ=.003027288235. Source pins are in [SOURCES.json](SOURCES.json). Canonical
+investigation: [Discussion5477](https://github.com/CrocSwap/integer-mult-bounds/discussions/5477).
+The complete fresh overlap snapshot contained342 open PRs and4736 Discussion
+records; root coordination owns publication. #5442 covers all-width caller
+algebra, while #5445 explicitly leaves actual control reservations open.
+
+The earlier proposed generic four-update audit was withdrawn after finding
+`compact-carry-repair-audit`, `compact-late-guard-audit-seed73`,
+`compact-agreement-set-seed29`, and PR3055 `physical-complex-compact`.
+`test_compact_control_layer.py` already checks generic toy row splits;
+`physical-complex-controller` handles an older73-axis caller. We reuse their
+boundaries and target this exact selected source, not a new generic repair.
+
+## Open next questions
+
+- Bind the unmaterialized final compiler's occurrence maps to this address ABI,
+  using actual N/W/O and full stock products. Start with one chronological
+  product occurrence and its rank-child embedding; the missing source-derived
+  map is the blocker, not another raw-route census.
+- Join the actual selected packet to the encoded physical controller while
+  preserving descriptors, parent return and compact-field restoration. Begin
+  with one IDLE packet. This package proves address placement under those
+  inherited execution premises; it does not implement that join or price it.
+
+## Credit
+
+Prepared for **JoyboyBrian**, with substantial **OpenAI Codex assistance**.
+Apache-2.0. Retain Douglas Colkitt's compact/row arguments; John-Michael Smith,
+Hanson Sun and Aaron Wang's prior audits; Jose Manuel's physical implementation;
+Chris R / Clear1nsight's PR5413 caller, Dillon's provider, Ali Romman's relations,
+Cao Yifan's native word, Cinna Davis's controller, zxv's compiler and Jacob Alan
+Sussman's recursion, plus the original source notices and cumulative lineage.
+No independent human review, kernel proof, selected promotion or paid gain.

research/selected-control-reservations/RESULT.json

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+{
+  "central_translations": 16,
+  "idle_child_cases": 45,
+  "literal_lift_coordinates": 207060,
+  "local_planes": 18,
+  "placement_families": [
+    {
+      "active_end": 60992,
+      "f": 1,
+      "origin": 6848,
+      "q0": 11,
+      "qB": 47,
+      "qF": 94
+    },
+    {
+      "active_end": 121984,
+      "f": 2,
+      "origin": 12864,
+      "q0": 11,
+      "qB": 94,
+      "qF": 188
+    },
+    {
+      "active_end": 182976,
+      "f": 3,
+      "origin": 18880,
+      "q0": 11,
+      "qB": 141,
+      "qF": 282
+    },
+    {
+      "active_end": 426944,
+      "f": 7,
+      "origin": 42880,
+      "q0": 11,
+      "qB": 329,
+      "qF": 657
+    },
+    {
+      "active_end": 1890944,
+      "f": 31,
+      "origin": 186880,
+      "q0": 11,
+      "qB": 1454,
+      "qF": 2907
+    },
+    {
+      "active_end": 61000000000000000000000000000000000,
+      "f": 1000000000000000000000000000000,
+      "origin": 6000000000000000000000000000000832,
+      "q0": 11,
+      "qB": 46875000000000000000000000000000,
+      "qF": 93750000000000000000000000000000
+    }
+  ],
+  "routes": 119,
+  "row_boundary_cases": 21,
+  "scope": "raw5413 route/reservation binding; expanded compiler injection and stock unverified",
+  "semantic_controls": [
+    "IDLE_wrong_pre_direction",
+    "route_out_of_template",
+    "stage_private_axis_collision",
+    "omitted_central_translation",
+    "active_slot_in_front_control",
+    "missing_child_spectator",
+    "nondivisible_row_stock",
+    "undersized_active_region"
+  ],
+  "swaps": 16748
+}

research/selected-control-reservations/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446",
+      "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "notes/compact-control-layout.tex",
+      "usage": "input",
+      "git_blob": "16f4d233471a7d189163ae7e7902becadecbba64",
+      "sha256": "2bc28e50f3eb092195294cafa81213e520f6d42e7935e9905ad8a6199e2a7c87"
+    },
+    {
+      "path": "notes/compact-control-movement.tex",
+      "usage": "input",
+      "git_blob": "06b6a9ef24245ac7b724c53a204635415b402357",
+      "sha256": "b963c3d2f4e1b7059aa289bb4b4ac89b688920bcf42f5b20d7698cdef0132cc6"
+    },
+    {
+      "path": "research/coupled-helper-neutral-completion/capsule/workspace/swarm-coupled-caller-sol-high-20261024/agents/challenge/WHOLECALLER-PLAN-v1.json",
+      "usage": "input",
+      "git_blob": "b868fe46ce7ff96a51f7b612758685a23014d31d",
+      "sha256": "a02e79fb4615f4f987e3b3617c2b42eea2c1d7415cc66fa702a8b0cd28e6387e"
+    },
+    {
+      "path": "research/coupled-helper-neutral-completion/reports/proofs/V16-APPLICATION-PROOF-v3.md",
+      "usage": "input",
+      "git_blob": "574c1d0bd75cd85f720991d815272738aa3e5b8f",
+      "sha256": "cda8f596f7854f42a228f757d5f8e68f6b2256a19c5ae3771fb40753cedc5b39"
+    },
+    {
+      "path": "research/physical-complex-controller/PROOF.md",
+      "usage": "input",
+      "git_blob": "c505caecc7ced19a4efc35c423efedda9427bea5",
+      "sha256": "471185621c0ecce295ffd327b1244aed234efe5ff05a804aaaa11316f1a8319e"
+    },
+    {
+      "path": "tests/test_compact_control_layer.py",
+      "usage": "input",
+      "git_blob": "bca34c9e796ce5483f99ae1bf31acc6b74d32d8c",
+      "sha256": "c39797d9a2bc7eb4b9c7ffc458be04b64806636a3ef544de3a273f11ebfbcea1"
+    }
+  ]
+}