Conditional kappa .00310915222: distributed scalar updates

research/p104-temporal-updates/NOTICE

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+Four paid interior public-basis changes.
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+No subagents.
+
+The following exact notice is retained from PR5660.
+
+New helper-subspace construction, proof and replay:
+Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+The same assistant performed the construction and author-side checks.
+
+Retained contributions:
+flyingviper: PR5605 shared relay, PR5612 delayed relay, and the PR5608/PR5613
+relay/split compositions.
+Scratch-net: PR5606 prepared-helper identities and target debit.
+Pierre-Loic Doulcet (hexapode): PR5565 commuting-contact construction, used as the exact source.
+Ali Romman: PR5602 fixed boundary relations, PR5601 three-contact frame
+change, PR5580 contact step,
+and PR5544/5545 complete P104 caller.
+Joel Pulikkan (GamingPuzzled): PR5569 priced helper handoff.
+DreamingOfClouds: PR5561 free helper endpoints and PR5568 search tools.
+thu-nmrc: PR5551 contact improvements.
+Gareth Davidson (bitplane): PR2305 source composition.
+David Arias: PR2152 coalesced P104 word.
+Cinna Davis: PR2219 private reuse and the controller lineage.
+Jacob Alan Sussman: productive mixed-target recursion.
+zxv and Cao Yifan: exact intervals, compiler and native/pricing lineage.
+GamingPuzzled: PR5472 successor handoff, a predecessor to the split concept.
+The retained source notices preserve earlier geometry, BIT and analytic credit.
+
+The elementary rank-one basis identity is not claimed as a new general
+linear-algebra theorem. The contribution is its explicit independent-target
+use on this P104 word and the complete conditional kappa improvement.
+
+New contribution: Ali Romman, with substantial OpenAI Codex assistance.
+The four-gate source-version rewrite composes zxv PR5643 and Ali Romman PR5644.
+The A2 method retains Chris R/Clear1nsight PR3998 and ToikY PR4019 credit.
+The compensated triangle method retains Cinna Davis PR4692 credit.
+No subagents were used for this contribution. Apache-2.0.
+
+Concurrent PR5650 by zxv publishes the PR5643/PR5644 composition. PR5651 by
+Ali Romman corroborates it. This package credits that released composition
+and contributes the further four-gate placement.
+
+New work: distributed scalar updates on an unobserved public field interval, the exact witness and complete conditional price. Prepared for Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. The source archive retains all predecessor notices.

research/p104-temporal-updates/PRICING-EDITS.json

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+[
+  [
+    "KAPPA, TESTED = Q('.00310871312'), Q('.003108713125')",
+    "KAPPA, TESTED = Q('155457611/50000000000'), Q('124366089/40000000000')"
+  ],
+  [
+    "PREVIOUS = Q('.00310815849')",
+    "PREVIOUS = Q('.00310871312')"
+  ],
+  [
+    "sum(paid.values()) == 66366",
+    "sum(paid.values()) == 66348"
+  ],
+  [
+    "'kappa_decimal':'.00310871312'",
+    "'kappa_decimal':'0.00310915222'"
+  ]
+]

research/p104-temporal-updates/PROOF.md

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+# Proof and complete price
+
+Prepared for Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.
+
+## 1. Sources and claim
+
+The input is PR5684 at `d0f6fa2555410a1e23fe4191424c2097ab3d5d97`.
+Its word, constructor, price and attribution are retained without edits.
+The official 16-file export of PR5678 at
+`af814f6f3c477fdd13b8f04380a33cf32004966b` retains the full checker stack,
+including its exact predecessor archives. Authentication precedes source imports.
+Every exported file has a separate Git source pin. The generated archive has
+its own fixed integrity hashes; those hashes do not claim a pre-existing
+upstream archive object. Base main is `df0137efd35e11b4445734bf612bdd4c7ebc330c`.
+
+The claim is a complete **conditional** construction at kappa .00310915222.
+It preserves the source five framework assumptions. It does not change the
+selected frontier, prove a global optimum or give a practical runtime claim.
+
+## 2. A temporal update lemma
+
+Use decoded scalar coordinates for a fixed native word. A cut `c` is immediately
+before source event `c`. Suppose field `r` is not read in `[a,b)`. Its operations
+in that interval are ADDs into `r` and changes of its native chart. In particular,
+there is no SCALE, COPY, initialization or erasure of `r` in the interval.
+
+Remove some ADDs into `r`. Let their total scalar source functional be `g`.
+Suppose actual fields `s_j`, at cuts `c_j` in `[a,b]`, satisfy
+
+`g = sum_j q_j value(s_j, c_j)`.
+
+Require `s_j != r` and an actual common frame for each replacement ADD into `r`.
+Insert those ADDs at their declared cuts. Every other field follows its original
+trajectory: no original operation reads the changed field in the interval.
+The replacement sources therefore have their original values. The difference
+in `r` is the accumulated replacement sum minus the removed sum. It is zero
+at cut `b`, before its next read. The full endpoint is unchanged.
+
+This is an exact linear-circuit identity. No old value is stored or read later
+without an operation. Each source is read at its declared physical cut.
+Native transports still use their actual charts and phases. Their decoded action
+is the identity under the retained native contract. The native replay checks the
+changed transport separately; scalar reasoning does not waive that obligation.
+
+## 3. The fixed witness
+
+All event positions below are zero-based in the pinned PR5684 word.
+Take `r=715`, `a=823` and `b=14983`. Remove event 13578,
+`ADD 715, 747, 1`, at frame 598. The exact prefix calculation proves
+
+```
+value(747,13578)
+  = value(525,823)/4 - value(712,823)
+    - value(525,14983)/4 + value(340,14983)/4.
+```
+
+The identity also has a short direct derivation. Let `A=value(525,823)`,
+`B=value(712,823)`, `V=value(747,13578)` and `C=value(340,14983)`.
+Field 712 has only one write in the interval: event 13572 adds `V`.
+The owned value is unchanged between that read and event 13578.
+Field 525 has only two writes: event 13737 subtracts four times field 712,
+and event 14654 adds field 340. Field 340 has no write from event 11202
+through cut 14983, so that last added value is `C`.
+Consequently `value(525,14983)=A-4(B+V)+C`. Rearrangement gives the identity.
+The complete prefix check independently confirms all 105 source coefficients.
+
+The first two replacement ADDs use frame 3. The last two use frame 396.
+Each source and field 715 have that frame at the stated cut. There is no read
+of715 in `[823,14983)`. Event14983 is the next read, `ADD 340,715,-4`.
+The verifier calculates every coefficient of the displayed identity over Q,
+and separately checks the no-read condition and all common frames.
+
+Remove event 13577, `MOVE 715,3,598`, and change event 14982 from
+`MOVE 715,598,396` to `MOVE 715,3,396`. The old frame dimensions are0,1,3,
+and their binary spaces form a strict chain. Thus the two old queries H1,H2
+become one H3. All other source records remain in order and unchanged.
+Four ADDs replace one ADD, so the emitted word has 25453 records.
+The complete rational replay and a separate dense transpose replay check all
+565504 endpoint coefficients. All743 public inputs remain independent;
+9 owned fields have11 lifetimes and peak occupancy2.
+
+The alternative rewrite found on field 525 has the same price. It is not added
+to this gain. A further scan of771 single visits and214 joint visit sets on
+the changed word found no additional gain in that tested domain. These discovery
+screens are not an optimality certificate and are not proof inputs.
+
+## 4. Native and ordinary costs
+
+The retained exact native engine lowers every paid request, main adapter and
+helper normalizer, including absolute phase. It checks 2917 distinct native maps.
+All original helper endpoints and the actual18-call physical caller stay fixed.
+All eight owned H7 queries remain; the removed ADD only changes one recipient.
+The original centre erasures, other reads, COPY instructions and ownership
+contracts remain in the word.
+
+The local paid profile is
+
+```
+2184 H1 +459 H2 +495 H3 +92 H4 +159 H5 +22 H6 +15 H7.
+```
+
+The unchanged local productive profile is
+
+```
+2 H1 +4 H2 +91 H4 +6 H5 +5 H7 +15 H8 +412 H9.
+```
+
+The exact local scalar allowance is220326. Native routes and adapters have a
+separate allowance 5164000. Their sum stays below the retained local budget 10^7.
+The complete raw ordinary upper bound is184647552, below 10^9. The fixed scalar
+growth and native tensor growth bounds are unchanged. Thus no new history bank,
+free query, uncharged route, COPY, CLEAR or storage lifetime is introduced.
+
+## 5. Complete moment, compiler and outer ledger
+
+The literal caller has 18 forward local calls,15 paid rank-one query shears and
+3120 whole idle jobs. It has 66348 paid calls and12958 productive fields.
+The target-minus-paid rank mass is760. The complete change from PR5684 is
+
+`Delta P = -18 H1 -18 H2 +18 H3`, `Delta T = 0`.
+
+For every `0<t<1`, `1+2^t-3^t>0`, by strict subadditivity. Hence the changed
+bill strictly improves every such signed moment. The proof does not add PR
+root decimals or use unchanged target credit after a helper removal.
+Two exact rational interval engines verify the full invoice. The unique raw
+root in the retained interval below .0034 lies in
+
+`(.00310915224562, .00310915224563)`.
+
+The declared kappa is .00310915222. The tested saving is .003109152225.
+The remaining raw headroom is between .00000000002562 and .00000000002563.
+This is a ceiling for this fixed invoice in the certified interval, not a
+ceiling for other constructions.
+
+The retained completion proof is re-evaluated with cutoff 17, floor 18,
+tail offset 1/5, tensor power 1024 and reserve 10^-12. All three tail ratios,
+splitting, rounding, complement capacity and shifted exits pass. The finite
+compiler threshold is calculated on its exact integer grid and its immediate
+predecessor fails. All54 strict outer inequalities and all 4 functional checks
+pass. The unchanged ordinary BIT input is admitted at .0034. Its full cover,
+atom and stock obligations remain charged through the retained ledger.
+
+The claim exceeds PR5684 by .00000043910, about .01412482 percent.
+This modest gain is the result supplied here. A large breakthrough is open.
+
+## 6. Limits and next checks
+
+The all-column native extension, owned-erasure contract, uniform compiler,
+precision/tape prescriptions and analytic/recovery framework remain assumptions.
+The enormous uniform word and complete rounded multiplier are not executed.
+The source receipts and new finite checks do not imply independent human or
+proof-kernel acceptance. Independent verification of the temporal identity and
+its complete bill is the next review task. A larger construction must keep the
+same distinction between an exact scalar identity and a fully paid caller.

research/p104-temporal-updates/README.md

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+# Distributed scalar updates: conditional kappa .00310915222
+
+The new construction replaces one read from owned centre 747 by four ordinary
+updates at two other contacts. The target field 715 is not read between those
+contacts. Their exact sum gives the old update before the next read.
+This removes an intermediate frame visit and replaces one H1 plus one H2
+query by one H3 query. Every public input and productive target is retained.
+
+The complete conditional saving is **kappa = .00310915222**, compared with
+**.00310871312** in [PR5684](https://github.com/CrocSwap/integer-mult-bounds/pull/5684).
+The gain is **.00000043910**, about **.01412482 percent**. This is a small gain,
+not the requested large breakthrough. It changes the scalar program and the
+complete paid bill; it does not combine the published decimals of other PRs.
+
+[PROOF.md](PROOF.md) gives the temporal identity and full cost argument.
+[WITNESS.json](WITNESS.json) fixes the cuts, sources and source event positions.
+[construct.py](construct.py) checks the identity and emits the complete word.
+[RESULT.json](RESULT.json) records exact endpoint, native, caller, compiler and
+outer evidence. [SOURCES.json](SOURCES.json) pins the complete source closure.
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-temporal-updates
+```
+
+Expected: `PASS_P104_TEMPORAL_UPDATES_KAPPA_00310915222` and
+`PASS_REGISTERED_RESEARCH_PACKAGE`. Python 3.12 and its standard library suffice.
+No optimizer, network access or Git process is used by the scientific verifier.
+The package exporter gives a separate Git-free replay.
+
+The complete invoice has 66348 paid calls and12958 productive targets.
+The whole change is `-18 H1 -18 H2 +18 H3`, with no target change.
+All eight H7 centre queries remain paid. This is not a centre-query deletion.
+The raw root lies strictly in `(.00310915224562, .00310915224563)`.
+[VALIDATION.md](VALIDATION.md) separates checks that ran from pending review.
+
+The five inherited native, owned-erasure, compiler, precision/tape and
+analytic/recovery assumptions remain. The huge uniform word and complete
+rounded multiplier are not materialized. Author checks do not establish
+independent human or proof-kernel acceptance. The selected frontier is unchanged.
+
+Credit Joel Pulikkan/GamingPuzzled with Claude assistance for PR5684,
+Ali Romman's PR5678/5660 and complete caller lineage, zxv, Cao Yifan,
+Cinna Davis, Jacob Alan Sussman and every retained source notice.
+New construction, proof and verification: Ali Romman with substantial OpenAI
+Codex assistance. No subagents. Apache-2.0.
+
+## Open next questions
+
+- Independently check the fixed temporal identity, exact native maps and complete
+  price. Start with the source event positions in WITNESS.json. There is no known
+  technical blocker; independent acceptance remains open.
+- Find a distributed update that removes a complete centre query or gives a
+  larger gain. Include every intervening target read, source dependency and
+  replacement native path. No such positive construction is supplied here.
+- Resolve one inherited framework assumption through the selected record and
+  its proof review. This finite package does not close those obligations.