Conditional κ = 0.00304117 (+6.0e-7 over #5544)

research/p104-full-frame-contact/PROOF.md

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+# One full-frame contact in the productive P104 caller
+
+This package changes one contact in the exact word of
+[PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544), at
+`e2a6cce2f9db5a2c5f9714f4b9e5292dd3a10581`. The new conditional endpoint is
+`kappa = 304117/100000000 = .00304117`. The gain over PR5544 is
+`3/5000000 = .00000060`. The selected record stays unchanged.
+
+The five source assumptions remain: native all-column implementation,
+owned erasure, the uniform compiler, precision and tape costs, and analytic
+recovery. The ideal operator proof and the complete conditional price are
+given below. The enormous uniform word and the rounded integer multiplier
+are not materialized.
+
+## Exact source change
+
+Let `A=span(30,70,429)`, `B=span(13,19,70,416)`, and `D=F_2^9`.
+These are source frames 739, 240 and 127, with `A < B < D` and dimensions
+3, 4 and 9. The zero-based source events are:
+
+| Event | Source instruction |
+| --- | --- |
+| 16798 | Move register 345 from A to B |
+| 16799 | `341 -= 345`, in B |
+| 16800 | `341 *= -1`, in B |
+| 17061 | Move register 341 from B to D |
+| 17067 | Move register 345 from B to D |
+
+Register 341 is already in B at event 16798. It has no other read or write
+before event 17061. Register 345 has no other read or write between events
+16798 and 17067. The constructor checks the complete intervening event lists,
+including source operands. Other registers can retain their original order.
+
+Replace event 16798 by moves `341: B -> D` and `345: A -> D`. Run events
+16799 and 16800 in D. Remove events 17061 and 17067. Keep all other events
+byte-equivalent as JSON records. The scalar coefficients, scalar order,
+public boundaries, independent inputs and owned lifetimes stay the same.
+The word has 25,310 events, one fewer than the source.
+
+## Uniform operator identity
+
+Use the source chart Phi_V at frame V. Put
+`T_VU = Phi_V Phi_U^(-1)`. On logical values x and y, the old two-register
+fragment ends with
+
+```text
+register 341: Phi_D (y - x)
+register 345: Phi_D y.
+```
+
+The new fragment first places both values in chart D, then performs the same
+subtraction and sign. It has exactly these outputs. Equivalently, a common
+linear transport on both operands commutes with a scalar ADD and SCALE.
+The checked read intervals permit this equality inside the complete word.
+The next reads of each register use D in both words.
+
+For every positive digit-column count, replace each chart by its prescribed
+tensor power. The common-chart identity is still valid. Scalar coefficients
+remain outside tensor powers. No sum of operators is tensor-powered.
+The source native compiler lowers every candidate MOVE and helper boundary.
+Its separate Gaussian interpreter checks signed Pauli images and absolute
+phase. In particular, the new `A -> D` child has rank six, with its actual
+monomial adapters. It is not an uncharged change of coordinates.
+
+The sparse rational interpreter checks all 743 endpoint rows. The independent
+reverse interpreter uses dense integer columns and binary denominators. Both
+cover all 552,049 public and owned coefficients. All 735 public inputs remain
+arbitrary. The eight owned lifetimes still start and return at the declared
+zero states, with peak occupancy one.
+
+## Complete cost and transfer
+
+The old fragment pays H1 + 2H5. The replacement pays H5 + H6. Thus
+
+```text
+local paid delta:    -H1 - H5 + H6
+complete paid delta: -18H1 - 18H5 + 18H6
+target delta:        zero at every rank.
+```
+
+For `0 < t < 1`, strict subadditivity gives `6^t < 1 + 5^t`. Therefore the
+complete signed recursive moment is strictly smaller at every such power.
+Rank mass is unchanged. The standard signed-invoice comparator gives the
+same conclusion for the actual complete histograms. This comparison uses
+all helper targets and all thin and idle jobs, not a local cost alone.
+
+The new local profile is
+
+```text
+{1:2428, 2:557, 3:389, 4:112, 5:107, 6:17, 7:13, 9:1}.
+```
+
+All 527 helper targets keep their source ranks
+`{4:51, 5:36, 7:24, 8:122, 9:294}`. The 104-port caller, both orientations,
+its 18 forward source invocations, 15 thin queries, 15 whole idles and
+32 main banks are unchanged. The source's signed exchanges and central-square
+translations still supply all backward interfaces. The full bill has 69,912
+paid calls and 12,814 productive fields, with rank surplus 760. The unused
+helper 711 keeps both its paid H9 and its productive H9.
+
+`pricing.py` adapts the pinned PR5544 price engine. Its only mathematical
+changes are the new paid-call count, claimed and tested endpoints, and the
+comparison endpoint. It recomputes both complete histograms by two counts,
+the raw crossing with rational intervals, and a second independent moment
+enclosure. The tested saving is `.003041171`. Cutoff 17, floor 18, tail offset
+1/5, reserve `10^-10`, power 1024 and logarithm power 1000 remain fixed.
+All completion, splitting, capacity, compiler-grid, BIT-stock and 58 outer
+predicates must pass. `RESULT.json` records their exact rational values.
+The fixed-invoice crossing and its remaining headroom are reported there;
+no global optimum or exclusion of other words is claimed.
+
+The new crossing is in `(.00304117181649, .00304117181650)`. Its increase
+over the source crossing is in `(.00000059374018, .00000059374020)`.
+The claimed endpoint is below the new crossing by between
+`.00000000181649` and `.00000000181650`. The strict compiler gap is
+`1/7000000000`; its independently checked integer height is
+`H=337848000000000`, with test exponent 48264. The previous grid point fails.
+The stated endpoint gain `.00000060` also reflects the different safety
+margins below the two crossings; it is not the exact raw-root difference.
+
+This mixed-target caller is outside the historical fixed-rank packing model
+in `research/complex-local-word-ceiling/ceiling.py`. It retains independent
+productive helpers and targets of unequal ranks, rather than one target rank
+and the old hosted coverage law. The replacement bound is the exact crossing
+of this complete fixed invoice. The endpoint attains between
+99.9999402697% and 99.9999402701% of that crossing.
+
+For this invoice the crossing is unique for `0 < kappa < 1`. To see this,
+put `t=1-kappa` and divide its signed moment by `6^t`. The signed coefficients
+at ranks 1 through 6 are negative; those at ranks 7 through 9 are positive.
+Each of these normalized terms increases with t, except the constant rank-six
+term. The other terms are 416 copies of `((r+1)/6)^t-(r/6)^t` for
+`r=16,24,...,64`, 208 copies at r=72, and `208*(145/6)^t`.
+They also increase for `t >= 0`: the derivative of each difference is positive
+because `x^t*log(x)` increases for `x > 1`. The full normalized moment is
+strictly increasing. Its values at t=0 and t=1 have opposite signs, since
+the count difference is -57,098 and the rank surplus is 760. Thus the upper
+crossing endpoint bounds the saving allowed by this fixed invoice. It does
+not bound a changed word, caller, target contract or invoice.
+
+The local scalar program is unchanged. There is one fewer native call and
+no new owned field. Native ranks stay at most nine locally; complete maximum
+target and child ranks stay 145 and 72. The source's finite bound of fewer
+than 26,000 events, scalar growth factor below `2^16` per event and total
+local Gaussian rank 5,894 still applies. These bounds fund the reordered
+prefix as well as the old prefix. All caller routes, private COPY paths,
+returns, normalizers and matching remain in the complete ordinary allowance.
+No precision or machine-operation cost is set to zero.
+
+## Controls and limits
+
+The checker rejects a one-operand retiming, a changed subtraction sign, an
+intervening source read and an omitted paid charge. It also reruns the source
+caller controls, exact phase control and adverse compiler/outer controls.
+The dependency hashes are checked before the source modules are imported.
+
+These are author-side exact checks. They are not independent human review or
+a proof-kernel verification. The source interpreters and mathematical
+framework remain credited dependencies. No merge or selected-frontier update
+is part of this contribution.
+
+Credit Ali Romman's PR5544 for the productive caller; Gareth Davidson's
+PR2305, David Arias's PR2152 and Cinna Davis's PR2219 for the composed word.
+The P104 shared-chart and dual-ADD retiming packages already use the standard
+two-operand identity. The new result is this literal contact and its complete
+conditional endpoint. Retain Jacob Alan Sussman's productive recursion,
+Cinna Davis's controller, zxv's compiler and outer machinery, Cao Yifan's
+pricing lineage, and all geometry, native, COPY and analytic source notices.
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.

research/p104-full-frame-contact/README.md

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+# Conditional kappa .00304117 from one P104 contact
+
+This contribution increases complete conditional kappa from **.00304057 in
+[PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544)** to
+**.00304117**, a gain of **.00000060**. It changes the recursive paid profile.
+The selected record remains .003027288235 and is not edited.
+
+The change moves the subtraction on registers 341 and 345, and its sign,
+from a four-dimensional frame to the full nine-dimensional frame. It replaces
+H1 + H5 by H6 in each of 18 local calls. All scalar coefficients, public
+boundaries, independent outputs and owned lifetimes remain unchanged.
+The full bill has **69,912 paid calls and 12,814 productive fields**.
+
+Read [the proof](PROOF.md), [the five-site constructor](construct.py),
+[the full receipt](RESULT.json), [the emitted word](WORD.json.gz), and
+[the exact source pins](SOURCES.json). The raw crossing and remaining headroom
+are recorded in the receipt. No global optimum is claimed.
+
+This is a focused successor to the released PR5544 at
+`e2a6cce2f9db5a2c5f9714f4b9e5292dd3a10581`. Its original commit remains the
+parent. The predecessor package is unchanged and is required for replay.
+The research started at canonical main
+`32890bc5de034ab8fc93ac88ead7279a6a416d04`, priority revision 7.
+
+## Replay and evidence
+
+Python 3.12 and the standard library suffice:
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-full-frame-contact
+```
+
+The scientific marker is `PASS_P104_CONTACT_COMPLETE_KAPPA_00304117`.
+The normal and optimized commands reconstruct the source, apply the literal
+change, check all 552,049 public/owned coefficients by two interpreters, check
+all native maps and target phases, replay the complete physical caller and
+compute both full histograms. Two rational moment engines, all compiler and
+stock bounds, and all 54 strict plus four functional outer predicates run.
+Controls reject a one-sided move, wrong sign, undeclared source read and
+omitted cost. Saved compressed words are compared by decompressed JSON.
+
+[VALIDATION.md](VALIDATION.md) records the checks actually run and their limits.
+The standard signed-invoice preflight is also recorded there. The first
+search was a bounded common-contact descent on the exact source; the final
+constructor contains only the one verified replacement, not that search.
+
+The five native all-column, owned-erasure, compiler, precision/tape and
+analytic-recovery assumptions of PR5544 remain. The enormous uniform word and
+complete rounded multiplier are not materialized. No independent human or
+proof-kernel acceptance is claimed. The source libraries are inherited,
+although their candidate checks run again.
+
+## Open next questions
+
+Independent review should check the five edited sites, source-read intervals,
+all-width chart identity and complete cost join. Start with the literal
+constructor and the before/after invoices. Human or proof-kernel acceptance
+is still absent. A later cost improvement must change a paid path or target
+contract and pass the same full checks; more digits of this crossing are not
+another structural gain. See [TASK.json](TASK.json) for the structured handoff.
+
+## Credit
+
+Ali Romman's [PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544)
+supplies the productive caller, two scalar interpreters and full price engine.
+Gareth Davidson (@bitplane) supplied
+[PR2305](https://github.com/CrocSwap/integer-mult-bounds/pull/2305), which joins
+David Arias's (@DavidAriasC)
+[PR2152](https://github.com/CrocSwap/integer-mult-bounds/pull/2152) coalesced word
+and Cinna Davis's (@1337isnot1337)
+[PR2219](https://github.com/CrocSwap/integer-mult-bounds/pull/2219) private reuse.
+The retained [shared-chart retiming](../p104-shared-chart-retiming/README.md)
+and [dual-ADD retiming](../p104-dual-add-retiming/README.md) already give the
+two-operand transport method. This package claims the new source contact and
+its complete conditional endpoint, not that general identity.
+
+Retain Jacob Alan Sussman, Cinna Davis, zxv, Cao Yifan and all geometry,
+scalar, native, COPY, compiler, precision and analytic authors in the
+[predecessor proof](../p104-productive-controller/PROOF.md) and
+[native notices](../p104-native-channel/notices).
+Prepared by Ali Romman with substantial OpenAI Codex assistance; no subagents.
+New work is Apache-2.0.