Selected packing: all 21,886 cross-call 0,1,7 to 0,0,8 cycles fail timing

research/selected-crosscall-rank8-cycle/README.md

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+# Selected cross-call cycles cannot coalesce idle ranks 0,1,7 into 0,0,8
+
+**Complete exclusion for one fixed-map rank transition; no new supplier or κ.**
+
+On the selected PR1094 owner map, 21,886 simultaneous directed three-role
+cycles have the proposed remainder change. Every one violates a strict
+source-event window. This remains true if active-pair and per-call family
+restrictions are relaxed. It does not exclude other remainder changes,
+longer paths, changed call orders, or a global packing improvement.
+
+## Domain and exact obstruction
+
+Keep the selected scalar word, all helper widths, 144 calls, call order,
+actual source-event windows and occupied-prefix hosting model fixed. Three
+existing whole-helper roles rotate among three distinct occupied bins
+A→B→C→A. At least two invocation times must be represented. The old free-rank
+multiset is `{0,1,7}` and the new one must be `{0,0,8}`. Anchor A at the unique
+old-slack-7 bin; both directed orientations are included, cyclic rotations
+counted once. “Slack 7” means seven unused coordinates, not an empty bin.
+
+For old slacks `(a,b,c)` and outgoing widths `(x,y,z)`, the new slacks are
+`(a+x-z, b+y-x, c+z-y)`. The source map supports exactly two type patterns
+with the required target, where a type is `(own-bin slack, outgoing width)`:
+
+| A,B,C types | Cycles | Constant forbidden landing |
+|---|---:|---|
+| `(7,8), (0,8), (1,7)` | 17,567 | C→A: event 181 is outside `(255,430)` |
+| `(7,8), (1,7), (0,7)` | 4,319 | A→B: event 417 is outside `(-1,208)` |
+
+There is exactly one role of type `(7,8)`: `(stage,replica,helper)=(7,14,296)`,
+owner bin `(13,15,14)`, event position 417. There is exactly one role of
+type `(1,7)`: `(1,15,226)`, bin `(11,8,103)`, event position 181. The other
+members are the 17,567 type `(0,8)` or 4,319 type `(0,7)` roles. The fixed
+forbidden landing therefore rejects each entire row independently of the
+third role. The two fixed roles belong to different calls, so none of these
+arithmetic candidates is removed by the same-call scope restriction.
+
+The unused coordinates could reduce cost if the change were legal:
+with `p=1-a` in `(0,1)`, strict concavity gives `8^p < 1^p+7^p`.
+All local charges stay fixed, so the complete modeled moment delta would be
+`(8^p-1^p-7^p)/(14336*73^p)`. This census realizes none of that potential
+gain because the landings are illegal. It is not a new general 3-cycle method.
+
+## Evidence, independence and controls
+
+[RESULT.json](RESULT.json) includes the two supported class rows, the
+constant-leg proof objects, baseline owner recount, source hashes and complete
+supplier pricing. Two enumeration methods agree:
+
+- The primary implementation exhausts actual width/slack types, counts all
+  role multiplicities, then performs an indexed strict-window join. A
+  simultaneous family update removes all vacated families at each call
+  before inserting the incoming roles; it never substitutes sequential
+  relocation legality for a cycle.
+- A separately written role-first enumeration tries all three possible
+  placements of the target rank 8. It solves the incoming-width equation,
+  materializes every supported triple, and compares each literal event
+  position directly to its destination window. It calls neither the primary
+  transfer/classification helper nor its landing predicate. Its complete
+  candidate-ID list has SHA256
+  `65b6437819f57f90f1d2d076bc96638b1d44302ef431462056fc136d497cf1dd`.
+  All three windows pass on zero candidates. The digest is a compact receipt;
+  acceptance depends on the regenerated exact census and inequalities.
+
+Both methods share source decoding and Josie Elliston's PR1091 geometry and
+baseline audit. This is algorithmically different enumeration, not a
+code-disjoint reimplementation of the entire source geometry or independent
+human review. Windows are rebuilt from actual source events and checked
+against PLAN by the unchanged inherited auditor. All eleven inherited owner
+mutation controls run.
+
+Six local synthetic controls cover an admitted `{7,1,0}->{8,0,0}` toy cycle,
+a same-call vacated family, an unvacated-family collision, the same-call scope
+restriction, a blocked last-leg window, and an indexed/direct toy-triple
+comparison with two possible third roles. The toy gain is not a physical
+source witness. CLI tests also reject an omitted-candidate receipt and an
+integer/float count alias. Receipts use type-preserving canonical JSON.
+Deadline regressions reject an over-budget census even when every first
+landing is blocked or the role set is empty. The deadline covers setup,
+skipped branches and final return; timeout is never recorded as an exclusion.
+
+## Both supplier budgets and the packing cap
+
+The complete source profiles are unchanged. The pinned exact rational
+calculator checks strict moment acceptance at both retained endpoints and
+strict rejection at the next `10^-24` tick:
+
+| Supplier | Endpoint | Rank mass / deficit |
+|---|---|---|
+| Complex | `67018507072324140917/40000000000000000000000` | 1,041,408 / 5,120 |
+| Bit | `1733427039589844234749/10^24` | 1,808,352 / 10,272 |
+
+Bit pricing includes the inherited `10^-16` bad-residue envelope of
+`32*m^2` rank-one fallback calls per paid child. Neither this surcharge nor
+any physical bill is reduced. Complex remains the binding side. These are
+pricing checks of the pinned profile model, not supplier or full cold replays.
+
+The required `ceiling(local,73,896,9,64)` call on local profile
+`{1:2412,2:418,3:432,4:142,5:82,8:8}` gives
+`a < 0.001690054109089`, balanced planning cap `κ < 0.001687202646`.
+The fraction of remaining packing headroom realized by this domain is **0**.
+The newer [fixed-route indivisibility bound](../fixed-route-indivisible-idle-mass/README.md)
+is stronger for this unchanged-route model (`a < 0.001681977435447`,
+planning κ about 0.00167915314); it is credited, not newly replayed or claimed
+sharp here. Zero gain also realizes zero of that tighter headroom.
+
+## Reproduce and assignment
+
+Python 3.12, standard library, repository root:
+
+```sh
+python3 -I -O -B research/selected-crosscall-rank8-cycle/verify.py
+python3 -I -O -B research/selected-crosscall-rank8-cycle/test_verify.py
+python3.12 -B scripts/research_package.py --package research/selected-crosscall-rank8-cycle --check-only
+python3.12 -B scripts/research_package.py --package research/selected-crosscall-rank8-cycle
+```
+
+Expected primary status:
+
+```text
+PASS_SELECTED_CROSSCALL_RANK8_CYCLE_OBSTRUCTION candidates=21886 all_window_blocked direct_crosscheck=PASS owner_controls=11 new_kappa=NO
+```
+
+Default replay is read-only. `--write NEW_PATH` refuses an existing path;
+`--probe` runs the primary census without pricing, the direct cross-check or
+receipt validation. Test scratch directories are scoped to the package and
+removed automatically. No dependencies or native builds are needed.
+
+Track `incumbent-optimization`, card `selected-packing`, nonce
+`3474c3e21150f5db2b291dfc2989aac6`, catalogue key `2eb6f6918b10e182033b`,
+priority revision4, base `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`.
+Scope was refined to this precise cross-call transition, approved before
+implementation, recorded locally before computation, and claimed at
+https://github.com/CrocSwap/integer-mult-bounds/discussions/1332#discussioncomment-18933588.
+The prescribed baseline binding check passed. Source Git blobs and SHA256
+pins are in [SOURCES.json](SOURCES.json); detailed scope/overlap is in
+[TASK.json](TASK.json). The five-minute first-probe budget was not exhausted;
+there was no scope pivot or randomized optimizer search.
+
+## Overlap and limits
+
+This takes the cross-call handoff of
+https://github.com/CrocSwap/integer-mult-bounds/pull/1873 (same-call 3-cycles),
+closing only one rank-transition slice. It is distinct from
+https://github.com/CrocSwap/integer-mult-bounds/pull/1790 (2-swaps),
+https://github.com/CrocSwap/integer-mult-bounds/pull/1617 (complete
+neutral-then-strict 2-relocations), and
+https://github.com/CrocSwap/integer-mult-bounds/pull/1407 (longer sequential
+paths). https://github.com/CrocSwap/integer-mult-bounds/pull/1154 has a positive
+3-cycle on a different word and owner map. Fresh text-based overlap plus
+live owning heads found no matching cross-call census; no-match does not
+prove novelty.
+
+## Open next questions
+
+Can a different supported rank transition admit a
+legal cross-call 3-cycle on the original map? Enumerate the remaining
+capacity-feasible type patterns touching a slack-7 bin (for example old
+slacks involving rank3), classify exact moment differences, and only then
+join windows/families. The blocker is that 3-component transitions need not
+be ordered by majorization; the simple two-component concavity sign rule
+does not decide every case. This package supplies no such larger census.
+
+There is no global optimum claim, modified source map, native/controller
+rebuild, physical invoice, supplier adoption, full selected cold replay,
+outer assembly, Lean proof or κ change. All inherited all-size/compiler,
+realization, hosting, precision/tape, analytic and bit H1–H5 obligations remain.
+No attaining source witness exists in this domain, so no modified-map
+admission is claimed. Frozen inputs and the selected record are untouched.
+
+## Credit
+
+Rohan Arun's PR1094 supplies the selected packing, retaining Jeremy Kothe's
+mutable-leaver and Hao Yan's controller lineage. Josie Elliston's PR1091
+supplies the unchanged independent owner/event audit. The PR1790 swap
+fixture and PR1873 same-call census supply the immediate extension context;
+Arham Tahir's one-relocation work, PR1617, PR1819, PR1407 and the other cited
+predecessors keep their separate contributions. Douglas Colkitt's PR1240
+supplies the ceiling engine; PR1012 supplies the coverage law; PR1847
+supplies the stronger fixed-route context. The bit source retains the
+PR589/PR555 and earlier attribution. No predecessor files are copied or edited.
+
+Prepared by **Aaron Wang / navinor, with help from chatgpt**, including
+research, code, writing and separate read-only AI review. New work Apache-2.0;
+no independent human or formal-kernel review claimed.