Raise conditional κ to 0.00312192127 with retained native copies

research/p104-retained-native-copy/LOCAL-EDITS.json

@@ -0,0 +1,10 @@
+[
+  [
+    "8 <= owned <= 9",
+    "8 <= owned <= 22"
+  ],
+  [
+    "0 < peak <= 2",
+    "0 < peak <= 12"
+  ]
+]

research/p104-retained-native-copy/NOTICE

@@ -0,0 +1,61 @@
+Paid intermediate meetings and collective helper splits.
+Ali Romman, with substantial OpenAI Codex assistance. Apache-2.0.
+No subagents. All checks are author-side calculations.
+
+The complete PR5718 notice follows unchanged.
+
+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.
+
+Two-boundary main-assisted helper split and early cleanup: flyingviper with substantial
+OpenAI Codex assistance, including independent AI review agents. Apache-2.0.
+
+Retained native-copy construction
+Prepared by Ali Romman with substantial OpenAI Codex assistance. No subagents.
+The paid-meeting source is PR5751 by Ali Romman with OpenAI Codex assistance.
+The dimension-four span [265,194,164,75] is from Joel Pulikkan / GamingPuzzled
+PR5739, with Claude Opus 5.5 assistance. The R22 block edits are not included.
+The retained-copy mechanism, exact constructor, source-specific verification,
+new price and proof are the contribution of this package. Apache-2.0.

research/p104-retained-native-copy/PLAN.json

@@ -0,0 +1,120 @@
+{
+  "source_canonical_sha256": "c3b338bd5b48d916f332a64470a86d2ee5534d8839c9d80b23a7e89bed9742f5",
+  "appended_frames": [
+    [
+      265,
+      194,
+      164,
+      75
+    ],
+    [
+      11,
+      21,
+      51,
+      469
+    ]
+  ],
+  "steps": [
+    {
+      "anchor": 1090,
+      "changed_nodes": [
+        2002,
+        3753,
+        3756,
+        3794,
+        3817
+      ],
+      "source_sha256": "8c6fbcb70e545c1af0dc0b61408b9113f613ced4fa971739e4be66a34b75d960",
+      "output_sha256": "80d2dc6dcb01650ab481f0f54093eb98fea9aa63aee71bcc55ab627d8fdb72f8"
+    },
+    {
+      "anchor": 1091,
+      "changed_nodes": [
+        1988,
+        3743,
+        3777,
+        3779,
+        3782
+      ],
+      "source_sha256": "80d2dc6dcb01650ab481f0f54093eb98fea9aa63aee71bcc55ab627d8fdb72f8",
+      "output_sha256": "103ed3cc9fdea6c4a814eaad7dd1948ab0db93276bab5bff23fdc0c784af154c"
+    },
+    {
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+      "output_sha256": "7bf889ef2a80c21052e4ea952ae4eebb724622a13d25a65efbc6f90681e7185a"
+    },
+    {
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+      "changed_nodes": [
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+        3794,
+        3840,
+        3843
+      ],
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+      "output_sha256": "de1a355529c63cb4bd390c1593be6f99ddd4f2c84838ccb6ea7adce1d1597758"
+    },
+    {
+      "anchor": 260,
+      "changed_nodes": [
+        1990,
+        1994,
+        1996,
+        3783
+      ],
+      "source_sha256": "de1a355529c63cb4bd390c1593be6f99ddd4f2c84838ccb6ea7adce1d1597758",
+      "output_sha256": "d575b9cd85b2692e60167dbcf905f5a3a843c33d4072acd7b5dee27958cf4362"
+    },
+    {
+      "anchor": 394,
+      "changed_nodes": [
+        1982,
+        1986,
+        1988,
+        3814
+      ],
+      "source_sha256": "d575b9cd85b2692e60167dbcf905f5a3a843c33d4072acd7b5dee27958cf4362",
+      "output_sha256": "3bcc97cc552116b889fb417e900203022dea2bacca2c91c3a567ea2b5f4aed07"
+    },
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+      "changed_nodes": [
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+        2009,
+        2010,
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+      "source_sha256": "3bcc97cc552116b889fb417e900203022dea2bacca2c91c3a567ea2b5f4aed07",
+      "output_sha256": "c9cb46f134a10586f3a6785893aae5a138676f18cdaf26cde46e031554a6794c"
+    },
+    {
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+      "changed_nodes": [
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+        2021,
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+      "output_sha256": "3766e9a0fcf4e6ab8990c8c02ed35ed8073aa657f9cfbdc9269ed35eff18b124"
+    },
+    {
+      "anchor": 549,
+      "changed_nodes": [
+        1962,
+        3106
+      ],
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+      "output_sha256": "75f429fc0c8b206f4439bfbda4b621fc62ea892e6e3008c17409f2d3ee0981bb"
+    }
+  ]
+}

research/p104-retained-native-copy/PRICING-EDITS.json

@@ -0,0 +1,14 @@
+[
+  [
+    "Q('.00311301600'), Q('.003113016005')",
+    "Q('.00312192127'), Q('.003121921275')"
+  ],
+  [
+    "PREVIOUS = Q('.00311024570')",
+    "PREVIOUS = Q('.00311301600')"
+  ],
+  [
+    "'kappa_decimal':'0.00311301600','previous_pr5718'",
+    "'kappa_decimal':'0.00312192127','previous_pr5751'"
+  ]
+]

research/p104-retained-native-copy/PROOF.md

@@ -0,0 +1,188 @@
+# Retained native copies
+
+## Source and claim
+
+The source is PR5751 at `8483f9a679d06c1e270141dbc686a7e76e7a7522`.
+Its package is `research/p104-paid-meeting-splits`. The source claim is
+conditional kappa 0.00311301600. This package claims conditional kappa
+0.00312192127 under the same five framework assumptions.
+
+The complete source export is retained and authenticated before import.
+PLAN.json binds the source word and each of the nine changes by canonical SHA256.
+A canonical hash uses sorted JSON keys and compact separators.
+
+All scalar rows below refer to decoded values. A native frame specifies the
+physical encoding of each value. The public endpoint is
+
+```text
+T = I + sum e_(r+112) e_r^T, over the 104 live ports r.
+```
+
+Every helper input is arbitrary. Owned input columns are erased by INIT and
+must be zero at exit. COPY does not turn a public helper into a free zero.
+
+## Changed contact contract
+
+The source requires a scalar operation to use fields in the same native frame.
+The new construction can supply its source operand from a retained converted copy.
+It does not assume that an earlier value remains available.
+
+A chart node is the interval between successive MOVE, INIT or CLEAR operations
+on one field. A scalar update does not change that field's chart node.
+The constructor assigns a fixed new frame to each selected node.
+Each main input and output keeps its source frame.
+
+A source version is the interval after one write or native MOVE and before the
+next such operation on that field. The constructor groups scalar reads by the
+actual source role and version. For each group, it compares the source frame
+with the frames of its consumers.
+
+If the frames differ, the fixed plan has one other consumer frame B. Let A
+be the source frame. Each accepted cache has B strictly contained in A.
+The constructor emits these operations before its first changed use:
+
+```text
+INIT  cache at A
+COPY  cache = source at A
+MOVE  cache from A to B, as a paid owned query
+```
+
+It then uses cache for every source operand in B. It emits CLEAR after the
+last such use. The source value has no write between these uses. The cache
+also has no scalar write between COPY and CLEAR. Thus every redirected read
+has exactly the decoded value of the original read.
+
+The native MOVE changes the physical encoding and preserves the decoded value.
+Its rank is dim(A)-dim(B). The verifier checks its exact native map and phase.
+All changed public queries remain strictly forward and nested. All changed
+owned queries remain strictly reverse and nested. A MOVE whose two frames
+become identical is removed; it is the identity operator.
+
+Induction over the scalar program proves the same decoded endpoint T. Each
+inserted COPY reads a current value, and each CLEAR occurs after all uses.
+Changing a helper boundary changes its native Gaussian target, so its new rank
+must replace the old productive credit. The main endpoint and its adapters
+remain fixed. The exact forward replay and a separate dense transpose replay
+check every public and dirty owned input column.
+
+## Fixed construction
+
+The first four changes retain a dimension-four copy of a dimension-eight value.
+Each copy serves one existing owned path and four helper corrections.
+The next four changes retain intermediate copies for those paths. The last
+change serves the remaining helper 705 contact. The table identifies the plan;
+WITNESS.json gives each exact role, version, event interval and use list.
+
+| Step | New frame | Added cache lifetimes | Removed identity transports |
+|---|---:|---:|---:|
+| 1 | 1090 | 1 | 0 |
+| 2 | 1091 | 1 | 0 |
+| 3 | 240 | 1 | 0 |
+| 4 | 243 | 1 | 0 |
+| 5 | 260 | 2 | 3 |
+| 6 | 394 | 2 | 3 |
+| 7 | 431 | 2 | 3 |
+| 8 | 470 | 2 | 3 |
+| 9 | 549 | 1 | 1 |
+
+Frame 1090 has basis `[265,194,164,75]`. This basis is credited to Joel Pulikkan /
+GamingPuzzled in PR5739. Frame 1091 has basis `[11,21,51,469]`. Its span is the
+sum of the relevant source subspaces. The R22 block edits are not used here.
+The other frame definitions are unchanged source data.
+
+There are thirteen new paid conversions and thirteen removed identity
+transports. The final word has 25,882 instructions, 767 public inputs and
+22 owned labels. It has 24 owned lifetimes and peak 12 live owned fields.
+The scalar replay checks all 789 input columns. The transpose checks the same
+622,521 endpoint coefficients by a separate arithmetic implementation.
+
+## Strict signed-moment gain
+
+Let H_r = r^t for 0<t<1. P counts paid children and T counts productive targets.
+The exact local changes are
+
+```text
+Delta P = 12H1 + 4H3 + 4H4 - 16H5 + H6 - 5H7,
+Delta T = 4H3 + 12H4 + H7 - 17H8.
+```
+
+Both call counts stay fixed. Paid and productive rank mass each fall by 69.
+After cancellation, the signed gain is
+
+```text
+Delta(T-P) = 8H4 + 16H5 + 6H7 - 12H1 - H6 - 17H8.
+```
+
+Form two sorted lists:
+
+```text
+x = [4 repeated 8 times, 5 repeated 16 times, 7 repeated 6 times],
+y = [1 repeated 12 times, 6, 8 repeated 17 times].
+```
+
+Both lists have 30 entries and sum 154. Every ascending prefix sum of x is at
+least the corresponding prefix sum of y. Their differences are
+
+```text
+3,6,9,12,15,18,21,24,28,32,36,40,39,36,33,
+30,27,24,21,18,15,12,9,6,5,4,3,2,1,0.
+```
+
+Thus y majorizes x. Strict concavity of r^t gives
+sum x_i^t > sum y_i^t for every 0<t<1. This proves the signed-moment gain
+throughout that interval. It does not by itself prove compiler closure.
+
+The final local paid profile is
+`{1:2231,2:454,3:496,4:96,5:159,6:7,7:10}`.
+The helper profile is
+`{1:25,2:5,3:4,4:103,5:6,7:7,8:21,9:388}`.
+The unchanged complete caller makes 18 forward local calls. It also retains
+15 query shears and 3,120 whole idle jobs. The complete bill has 66,834 paid
+calls,13,390 targets and rank surplus760. No idle or thin query is omitted.
+
+## Complete conditional price
+
+Two rational interval engines check the complete power sums. The declared
+saving is 0.00312192127; the tested saving is 0.003121921275. Both are below the
+certified raw crossing (0.00312192130450, 0.00312192130451). A derivative bound proves a unique
+raw crossing on [0,0.0034].
+
+The completion parameters remain cutoff 16, floor 17, tail offset 1/7,
+power 1024, reserve 10^-12, decay 125/128 and tail block 128. The verifier checks
+all three strict tail ratios, both decay blocks, completion, splitting,
+rounding, complement capacity and the finite compiler threshold. It checks
+all 54 strict and four functional outer inequalities. Admitted BIT 0.0034
+remains above the tested saving.
+
+The new finite envelope changes two source caps:22 owned labels and peak 12
+live owned fields. The public and operation caps stay fixed. All789 labels
+fit the retained1,000-slot allowance. Every new lifetime has INIT, COPY,
+a paid native MOVE, its actual reads and CLEAR.
+
+The scalar allowance is 224,294 units. The local route allowance is 5,291,000
+units. Their sum is below 10^7. The complete ordinary bound is 184,647,552,
+below 10^9. The source growth bound 2^(16*26000) still covers the scalar word.
+The paid native rank mass is 5,918, and the verifier records the corresponding
+tensor norm bound. These are declared bounds, not measured attained norms.
+
+## Verification boundary
+
+The tests check the exact source bytes, nine fixed transformations, all scalar
+columns, ownership, native maps and absolute phases. They also check the full
+physical caller, complete paid and target inventories, compiler and outer price.
+Controls remove a paid cache query, change its copied value, clear a live cache,
+omit CLEAR, omit storage, retain an old target credit and falsify the invoice.
+Each control must fail in normal and optimized Python.
+
+The search used finite common-frame graph cuts and actual source versions.
+It also added subspaces from sums of neighboring native subspaces. Nine accepted
+steps passed exact scalar replay. The last bounded scan found no additional gain.
+This is not a global optimum or an exclusion of other retained-copy graphs.
+The optimizer is not required for replay; the fixed plan supplies every choice.
+
+The five assumptions native_all_columns, owned_erasure, compiler, precision_tape
+and analytic_recovery remain. The large uniform word and rounded multiplier
+are not materialized. Author checks do not establish independent acceptance.
+The selected frontier is unchanged.
+
+Prepared by Ali Romman with substantial OpenAI Codex assistance. Apache-2.0.