Improve complete conditional κ to 0.00304153 via coupled P104 contacts

research/p104-joint-contact/PROOF.md

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+# Coupled contacts and complete conditional price
+
+The endpoint is `kappa = 304153/100000000 = .00304153`, improving Ali
+Romman's PR5545 endpoint `.00304117` by `9/25000000 = .00000036`.
+Source head: `18968423711fd902aaee1099979497d55603e1dc`.
+The selected record is unchanged. All five framework premises remain:
+native all-column implementation, owned erasure, uniform compiler,
+precision and tape costs, and analytic recovery. This proves an ideal
+operator change and a complete conditional price; the enormous uniform
+word and rounded integer multiplier are not materialized.
+
+## Literal change and all-width implication
+
+`construct.py` pins these six zero-based source events:
+
+| Event | Unchanged scalar operation | Old frame | New frame |
+| --- | --- | --- | --- |
+| 10461 | `297 += 303` | 335 | 17 |
+| 10462 | `303 -= 297/2` | 335 | 17 |
+| 13970 | `152 -= 297/2` | 335 | 17 |
+| 15479 | `198 += 319` | 915 | 207 |
+| 15639 | `205 += 198` | 915 | 207 |
+| 15640 | `198 -= 205/2` | 915 | 207 |
+
+Frame 335 has dimension two. Frame 17 is `span(145)`, dimension one.
+Frame 915 has dimension seven. Frame 207 has dimension eight and basis
+`[2,5,8,17,33,65,129,257]`. All are existing source canonical charts.
+No new coordinate transformation is granted for free.
+
+The emitter issues every nested MOVE needed to place both operands at
+the declared common frame. SCALE occurs at its operand's current frame;
+terminal public MOVEs finish at the original exits. Fifteen SCALE chart
+annotations change; every scalar coefficient and its order is retained.
+INIT/COPY/CLEAR lifetimes are unchanged. Every actual intervening source
+read and write is included in the complete replay. The word has 25,310 events.
+
+The separate [peer proof](peer/PROOF.md) and
+[role histories](peer/RECEIPT.json) bind the actual field versions. In the
+first group, role 297 coalesces two rank-one rises into rank two; role 303
+splits rank two into two rank-one rises; role 152 replaces two rank-two
+rises by ranks one and three. Their net delta is `H1 - 2H2 + H3`.
+In the second group, role 198 replaces ranks four plus one by rank five;
+role 319 exchanges the order of ranks one and two with zero profile delta;
+role 205 splits rank two into two rank-one rises. The net delta is
+`H1 - H2 - H4 + H5`.
+
+Let Phi_F be the exact canonical source chart. At field width f, a role
+stores Phi_F tensor-power f applied to its logical value. A MOVE F to G
+applies `Phi_G Phi_F^{-1}` tensor-power f, preserving that logical value.
+Same-chart ADD/COPY acts on logical values with its scalar applied once,
+outside tensor powers. SCALE commutes with transport by linearity. Thus
+the unchanged scalar/owned word and fixed endpoint charts imply exactly
+the same complete physical operator at every positive f. This is a
+compositional induction: no sum is tensor-powered and no width-one
+linear-independence claim is used.
+
+Three exact endpoint checks cover all 743 rows and 552,049 coefficients:
+sparse rational forward rows, dense integer reverse columns with binary
+denominators, and an independently written integer/dyadic peer interpreter
+that imports neither constructor nor native checker. All 735 public inputs
+remain arbitrary. All 527 productive helpers retain their targets. Eight
+owned lifetimes retain peak occupancy one and the original erasure premise.
+
+The source native compiler freshly lowers every MOVE, helper boundary and
+main adapter. Its separate Gaussian interpreter compares every signed Pauli
+image and absolute global phase: 2,979 distinct maps, 1,054 helper normalizers
+and 208 main adapters. Wrong phase is rejected. These exact base identities
+tensor to every positive f. The unchanged complete caller is freshly checked
+through its Laurent identity, 265-axis phase polynomial, 104 ports, both
+orientations and actual orthogonal routes. This algebraic check is distinct
+from materializing exponential-size all-column matrices.
+
+The added independent dense audit checks all 512 columns of each of the
+four new MOVE maps: `17 -> 720` (rank 2), `17 -> 782` (rank 3),
+`615 -> 207` (rank 5), and `775 -> 207` (rank 2). It compares
+1,048,576 exact complex entries, including
+absolute phase, column norm and support. The unchanged credited PR5548
+arithmetic engine executes the literal source charts and lowered recipes;
+the source/vendor tableau is not used for matrix equality. Phase-only
+faults invisible to signed Pauli images are rejected. The exact base
+equalities tensor factorwise, with phase i^theta lifted as i^(f theta).
+This checks the new map interfaces only, and retains the old native and
+uniform implementation premises.
+
+## Complete moment and transfer
+
+The new local paid profile is
+
+```text
+{1:2430, 2:554, 3:390, 4:111, 5:108, 6:17, 7:13, 9:1}.
+```
+
+Its delta from PR5545 is
+
+```text
+local:     +2H1 -3H2 +H3 -H4 +H5
+complete: +36H1 -54H2 +18H3 -18H4 +18H5
+target:    zero at every rank.
+```
+
+For `H_r=r^t`, `0<t<1`, strict concavity gives
+`H3-H2 < H2-H1` and `H5-H4 < H2-H1`. Summing shows the paid delta is
+strictly negative throughout this interval. Call count and rank mass are
+unchanged. This is different from repeating PR5545's `H1+H5 -> H6` edit
+and lies outside PR5548's narrow repetition ceiling.
+
+Each invocation retains helper targets `{4:51,5:36,7:24,8:122,9:294}`.
+The full bill includes 18 forward invocations, 15 genuine queries, 15 whole
+idles and 32 main banks: 69,912 paid calls, 12,814 productive fields and rank
+surplus 760. Maximum paid/target ranks remain 72/145. No helper is omitted.
+
+`pricing.py` retains PR5544/5545's funding argument. New mathematical
+parameters are claimed/tested saving and comparison endpoint; its input
+histogram comes from the freshly replayed word. Two independent full
+invoice counts and both inherited rational moment engines must agree.
+The strict raw crossing enclosure is
+
+```text
+.00304153116714 < raw crossing < .00304153116715.
+```
+
+The separate funding peer implements a third rational interval engine:
+50-term atanh logarithms with rigorous tails and 128-bit outward grids,
+followed by alternating exponential bounds of degrees 15/14. It imports
+neither retained moment engine. Its four sign enclosures and full invoice
+recount agree. The wrapper binds the audited word, source and complete
+receipt to this publication.
+
+Tested saving is `.0030415305`. Cutoff 17, floor 18, tail offset 1/5,
+power 1024, reserve `10^-10` and logarithm power 1000 fund completion,
+splitting and rounding. Compiler gap is `1/14000000000`, integer height
+`H=690116000000000`, test exponent 49,294; the preceding integer point
+fails. Ordinary/admitted BIT stock checks and all 54 strict plus four
+functional outer predicates pass. `RESULT.json` records exact rationals.
+The endpoint gain is not claimed to equal the raw-crossing difference,
+which has different safety margins. No global optimum is claimed.
+
+Scalar coefficients and counts are unchanged. The 26,000-event bound,
+per-event scalar growth below `2^16`, total local Gaussian rank 5,894 and
+owned peak one still bound reordered prefixes. Local native ranks stay
+at most nine. Routing, normalization, COPY, caller and erasure allowances
+are recomputed; no precision/tape cost is set to zero. The same five
+framework premises remain necessary.
+
+## Controls, source retention and credit
+
+The verifier rejects an old-chart contact, wrong butterfly coefficient,
+changed source event and uncharged recursive call. The peer also rejects
+missing owned CLEAR. Inherited checks reject missing central translation,
+wrong native phase, adverse completion cutoff and inadequate BIT saving.
+All 33 dependency files are authenticated before imports. The closed
+official export retains the exact PR5545 bytes and source attribution.
+
+Prepared for thu-nmrc with substantial OpenAI Codex assistance, Apache-2.0.
+These are author-side checks, not independent human/proof-kernel acceptance.
+Credit Ali Romman for PR5544/5545's caller and price; Gareth Davidson for
+PR2305; David Arias for PR2152; Cinna Davis for PR2219/controller; Jacob
+Alan Sussman for productive recursion; zxv for compiler/outer machinery;
+Cao Yifan for pricing; and all geometry, common-chart, dual-ADD, native,
+COPY, precision and analytic predecessors in the retained proofs. The
+new contribution is this coupled literal itinerary and conditional gain.

research/p104-joint-contact/README.md

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+# Conditional kappa .00304153 from coupled P104 contacts
+
+This contribution increases complete conditional kappa from **.00304117 in
+[PR5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545)** to
+**.00304153**, a gain of **.00000036**. Six ADD contacts change frame while
+every scalar coefficient and its order remain identical. The selected record
+remains .003027288235 and is not edited.
+
+The first three contacts involve registers 297, 303 and 152; the other three
+involve 198, 319 and 205. The exact source events and replacement frames are
+listed in [construct.py](construct.py). Their joint local paid delta is
+
+```text
+2 H1 - 3 H2 + H3 - H4 + H5.
+```
+
+Each of the 18 local calls uses this change. The complete bill still has
+**69,912 paid calls and 12,814 productive fields**, with rank-mass surplus
+760 and maximum child/target ranks 72/145. Its distribution changes enough
+to reduce the concave moment. All 735 independent public inputs, 743 endpoint
+rows, productive targets and eight owned lifetimes are retained; peak owned
+occupancy remains one.
+
+These are **author-checked conditional results**. The claim is tested at
+.0030415305, with raw crossing in
+(.00304153116714, .00304153116715). The five inherited premises remain:
+native all-column implementation, owned erasure, the uniform compiler,
+precision and tape costs, and analytic recovery. The enormous uniform word
+and complete rounded multiplier are not materialized. No independent human
+or proof-kernel acceptance, merge or selected-frontier update is claimed.
+
+Read [PROOF.md](PROOF.md), [the full receipt](RESULT.json),
+[the emitted word](WORD.json.gz), [the complete pricing code](pricing.py)
+and [the source pins](SOURCES.json). No global optimum is claimed.
+
+## Replay and source closure
+
+Python 3.12 and the standard library suffice. From the repository root:
+
+```sh
+python3 -B scripts/research_package.py --package research/p104-joint-contact --check-only
+python3.12 -B scripts/research_package.py --package research/p104-joint-contact
+```
+
+[VERIFY.json](VERIFY.json) registers normal and optimized execution of the
+same complete verifier, with a 540-second bound per command, plus two
+30-second independent funding checks and two 30-second dense native checks.
+The verifier
+authenticates the retained predecessor, reconstructs the literal replacement,
+checks the complete scalar and signed native endpoints, checks the physical
+caller and full invoices, and evaluates both rational moment engines,
+compiler/stock conditions and all outer predicates. The receipt and
+[VALIDATION.md](VALIDATION.md) distinguish the checks actually executed from
+the inherited premises. Metadata validation alone is not scientific replay.
+
+The separately written [funding audit](funding-peer/README.md) implements
+a third rational log/exp interval engine, without importing either source
+moment engine. It independently recounts the complete invoice and ordinary
+allowances and proves the signs at the claimed/tested savings and both raw
+crossing endpoints. [funding_review.py](funding_review.py) binds that audit
+to this publication's exact receipt, source capsule, pricing code and word.
+
+The [four-map dense audit](native-peer/README.md) reuses Chris R/Clear1nsight's
+credited PR5548 arithmetic interpreter to compare every complex entry in
+all 512 columns of each newly introduced MOVE map. It checks absolute phase,
+norm and support rank, totaling 1,048,576 entries per mode.
+[native_review.py](native_review.py) binds it to the actual published word
+and authenticated native sources and rejects two actual corrupted source
+files before import. This covers the four new interfaces, preserving the
+inherited old-map and framework premises. The conditional endpoint is unchanged.
+
+The source is Ali Romman's PR5545 at
+`18968423711fd902aaee1099979497d55603e1dc`. Its **unchanged official source
+export** is retained as
+[inputs/pr5545-source-closure.tar.gz](inputs/pr5545-source-closure.tar.gz).
+The custom verifier checks the compressed capsule, embedded export manifest
+and all 33 payload files before importing source modules. This capsule is a
+dependency: its proof and embedded attribution remain unchanged, and all
+source-specific notices continue to apply. Those 33 files are not newly
+authored contributions. No foreign-history Git pin is used. The generic
+package metadata pins canonical main
+`32890bc5de034ab8fc93ac88ead7279a6a416d04` and its revision-7 task card as
+historical provenance. The package-local capsule participates in ordinary
+package-change invalidation.
+
+## Open next questions
+
+Independent review should check the six source sites, their complete frame
+paths and source-read intervals, then replay the arbitrary-input native
+identity and both complete moment engines. This matters because the result
+still depends on the inherited framework premises. No technical source
+dependency is missing; independent scientific acceptance remains pending.
+The structured handoff is in [TASK.json](TASK.json).
+
+A later improvement must change a paid path or a productive target contract
+and fund the entire caller. Refining the digits of this fixed crossing does
+not supply a further structural gain.
+
+## Credit
+
+Ali Romman's [PR5545](https://github.com/CrocSwap/integer-mult-bounds/pull/5545)
+supplies the starting contact word; his
+[PR5544](https://github.com/CrocSwap/integer-mult-bounds/pull/5544) supplies
+the productive caller, scalar interpreters and complete pricing engine.
+Gareth Davidson (@bitplane) supplied
+[PR2305](https://github.com/CrocSwap/integer-mult-bounds/pull/2305), joining
+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 general common-chart two-operand transport identity is inherited;
+the contribution here is this coupled source-pinned itinerary and its
+complete conditional cost gain.
+
+Retain Jacob Alan Sussman's productive recursion, Cinna Davis's controller,
+zxv's compiler and outer machinery, Cao Yifan's pricing lineage, and every
+geometry, scalar, native, COPY, precision and analytic author named in the
+retained source proofs and notices. Prepared for thu-nmrc with substantial
+OpenAI Codex assistance, including parallel subagents. These are author-side
+checks. New work is Apache-2.0.