Conditional κ = 0.003286849: clean native merge with mixed caller

research/p104-clean-mixed-root/NOTICE

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+New source-bound composition and portable package: Rohan Arun, with substantial OpenAI Codex assistance. Apache-2.0.
+
+Exact prior clean native merge: PR6399, Rohan Arun with substantial OpenAI Codex assistance.
+Mixed six-field root, normalization, physical binding and price adapter: PR6398, Ali Romman with substantial OpenAI Codex assistance.
+Shared-carrier input lifts: PR6375, DreamingOfClouds with Claude Opus5.5 via Claude Code.
+All predecessor credit notices are retained byte-for-byte in native-source.tar and root-source.tar.
+The P104, Gaussian/native, productive helper, BIT, compiler, precision, outer and original manuscript authors retain their attribution and source licenses.
+No new claim is made for the mixed root itself or for classical rank-one inverse identities.

research/p104-clean-mixed-root/PRICING-EDITS.json

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+{
+  "source_sha256": "b668ec87a3b6a1d5ed5e86ceac16100752dc8fb4300b7012e8b07cb477709ecf",
+  "edits": [
+    [
+      "KAPPA = Q('0.00328621476572836015146308')",
+      "KAPPA = Q('0.003286849')"
+    ],
+    [
+      "TESTED = Q('0.003286214765728360151463085')",
+      "TESTED = Q('0.003286854')"
+    ],
+    [
+      "PREVIOUS = Q('0.00328620')",
+      "PREVIOUS = Q('0.00328621476572836015146308')"
+    ],
+    [
+      "(13652, 67150)",
+      "(13652, 67132)"
+    ],
+    [
+      "'kappa_decimal': '0.00328621476572836015146308'",
+      "'kappa_decimal': '0.003286849'"
+    ],
+    [
+      "'refinement_kind': 'Same complete invoice; finer strictification and compiler parameters.'",
+      "'refinement_kind': 'Clean donor-transport merge, unchanged mixed root, complete native invoice.'"
+    ]
+  ],
+  "result_sha256": "60e9182838c0361293438153bf3232f96e28404021773b33d93ddaac657680a2"
+}

research/p104-clean-mixed-root/PROOF.md

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+# Source-bound conditional composition at κ=.003286849
+
+## Boundary compatibility
+
+The regenerated PR6399 word is compared field by field against its exact
+shipped payload. Its persistent interfaces are unchanged from PR6375:770
+arbitrary public inputs,104 live ports, the original main entrance/exit
+coframes and the identical helper input/output frames. Its normalized scalar
+endpoint is the required main shear and identity on every independent helper.
+The only added owned lifetime is fully uncomputed before its CLEAR.
+
+The mixed caller of exact PR6398 consumes this same PR6375 interface.
+Therefore the replacement is made at each of its18 full native sites without
+altering any main input, output, normalization or productive helper contract.
+This is verified afresh: the complete native phase inventory agrees with the
+exact PR6399 receipt, the literal mixed caller agrees with its pinned570-event
+payload, its independent six-field module passes and all7,488 physical
+main/idle contacts are checked against the replaced native word. Interface
+compatibility is checked from actual coframes and phases, not inferred solely
+from a shared port count or a declared source name.
+
+The native rank-one correction is the classical identity F=S+uv with
+b=vS^-1 and d=1+bu=1 in this instance. A clean cache stores bF(input)=dv(input).
+Subtracting uc/d restores S(input); subtracting dbS(input) then clears the
+cache exactly. All correction supports lie in the full frame. The constructor
+checks the entire rational error row space and799-column normalized endpoint;
+the separate integer-row checker proves the actual new cache zero. The
+original native construction and its sources retain PR6399’s credit.
+
+## Complete invoice
+
+Relative to PR6398’s pinned complete invoice, productive targets are identical.
+At each native site remove one H4 and one H1 job and add one H5 job. Thus
+
+    paid_new = paid_6398 +18(H5−H4−H1),
+    targets_new = targets_6398.
+
+Every binary child,17thin-query groups, paired/individual whole idle, central
+normalization, source helper debit and physical adapter remains present.
+The emitted event inventory and the independent caller formula both derive
+this same profile:13,652productive fields,67,132paid jobs and rank-mass
+surplus760. Strict subadditivity gives H4+H1>H5 for powers0<s<1, with equality
+at linear rank cost. This signed change is not credited as a new helper
+output. The additional508native scalar-allowance units and new lifetime are
+included in the complete ordinary-work budget.
+
+## From the profile to the whole conditional exponent
+
+Two separately implemented rational moment engines certify the strict raw
+crossing bracket(.00328685686446,.00328685686447). The chosen claim
+.003286849 and tested saving.003286854 lie strictly below that root. The
+retained derivative bound proves the crossing unique in the stated range.
+
+The actual completion uses power1920, cutoff12, floor13 and reserve10^-29,
+with its exact tail, splitting and rounding costs retained. The declared
+conservative reserve is funded by the positive exact moment margin. The
+compiler checks its shifted exits and complement capacity at theta63/64,
+logarithm power2100, gap1/1,400,000,000 and integer threshold
+H=138,100,200,000,000. The full scalar/movement/growth allowance and precise
+prime rule are retained in RESULT.json. Ordinary BIT saving.0034 exceeds the
+tested whole saving. Every one of54strict and4functional outer inequalities
+is strictly positive. These are the actual checks, not merely a raw-root
+extrapolation or a tensor-factor assumption.
+
+Consequently, conditional on the inherited native_all_columns, owned_erasure,
+compiler, precision_tape and analytic_recovery framework premises and their
+retained all-width transfer arguments, this composition supplies the whole
+bound κ=.003286849. It improves the exact pinned PR6398 claim by
+.00000063423427163984853692, about.01930percent. It does not establish an
+unconditional multiplication theorem, human/formal-kernel acceptance, a
+materialized rounded multiplier, a selected-frontier change or κ=.005.

research/p104-clean-mixed-root/README.md

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+# Conditional κ = 0.003286849
+
+This standalone composition supplies a new locally verified whole conditional
+bound, κ = 0.003286849, improving pinned PR6398’s
+0.00328621476572836015146308 by about 0.01930 percent. It combines the exact
+clean native merge from PR6399 with the exact six-field mixed caller from
+PR6398. Neither predecessor mechanism is claimed as new here. The selected
+repository frontier is unchanged; independent scientific review remains open.
+
+## Complete construction
+
+PR6399, head `a928a7aa5ab5b21b7cf841d6d960ab2e7efd1041`, supplies the native
+word SHA256 `09afbc6fbf5fe7a3b9bdeb7401f0d9437ac52c628b81f3378e31dc11afbbcf6d`.
+It merges one rank-4 and rank-1 query into rank5, uses an already-paid donor
+for the intermediate export, and repairs the remaining rank-one endpoint
+error with one provably zero-restored scratch lifetime. Helper productive
+frames and the complete main interface remain those of exact PR6375.
+
+PR6398, head `dee2663ba0918be86993fd9d63c8d64b020f4c83`, supplies the mixed
+root and its complete-field normalization. Its four binary children have
+sizes7,2,2,7; their projector ranks are2,3,3,2. Both extra whole idles are
+retained. The six root outputs have stage supports ABCD,AB,CD,empty,B,C and
+all contain the central transform. The570-event caller is unchanged.
+
+The new signed native saving H4+H1−H5 is applied at all18 native calls.
+Every helper debit, thin query, whole idle, normalizer, route and ordinary
+operation is paid. The complete invoice has:
+
+- 13,652 productive fields and67,132 paid recursive jobs, with rank-mass
+  surplus760;18 full calls,17 thin queries per port and3,120 whole idle jobs.
+- 770 independent public inputs,29 owned roles,44 lifetimes, peak13;
+  799 arbitrary input/scratch columns and638,401 exact coefficient positions.
+- 2,940 native maps with signed Pauli action and absolute phases,
+  208 main adapters and1,124 helper normalizers;7,488 mixed caller contacts.
+- Native scalar allowance130,178, local route allowance5,382,000 and complete
+  raw scalar upper248,152,864, below the charged10^9 budget.
+
+Two rational engines enclose the raw crossing in
+(0.00328685686446,0.00328685686447). The smaller whole claim uses tested
+saving0.003286854, strictification power1920, cutoff12, floor13, reserve10^-29
+and the exact charged tail. Compiler theta63/64, logarithm power2100 and
+H=138,100,200,000,000 are explicit. The retained ordinary BIT admission is
+0.0034. All54 strict and4 functional outer predicates are positive.
+Full profiles, parameters and exact margins are in [RESULT.json](RESULT.json).
+
+## Reproduce
+
+Python3.12, standard library only. From the repository root, set TMPDIR to
+writable temporary storage outside the checkout for read-only execution:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-clean-mixed-root
+python3.12 -B scripts/check_research_commit.py --package research/p104-clean-mixed-root --check-source-history --check-modes
+```
+
+The registered hook runs complete normal and assertion-disabled replays.
+Each command rebuilds every scientific native word field, authenticates every
+retained source member, checks chronology/ownership, the separate integer
+new-scratch-zero rows, all transpose columns, every native map and phase,
+the separate root module and full caller, all physical contacts, both moment
+engines, completion/compiler/precision and every outer predicate. Corrupted
+source bytes, missing uncomputation and missing caller operations reject.
+Ordinary replay writes only temporary files and leaves the package unchanged.
+
+Sources are stored in two small authenticated runtime archives to keep this
+PR standalone while its predecessors remain pending. They contain16 exact
+files needed for native regeneration, caller execution, pricing and notices.
+[SOURCES.json](SOURCES.json) binds their original Git paths at the two exact
+heads. [RETAINED-INPUTS.json](RETAINED-INPUTS.json) authenticates every archive
+member before import. The retained old native checker archive is a pinned
+main-branch input. [PRICING-EDITS.json](PRICING-EDITS.json) lists every change
+to the source price adapter; the mixed root itself is not modified.
+
+## Proof and limitations
+
+[PROOF.md](PROOF.md) states the source-bound composition and full conditional
+claim. The assumptions native_all_columns, owned_erasure, compiler,
+precision_tape and analytic_recovery remain inherited and open. The new
+scratch is exactly zero before erasure; this does not discharge inherited
+owned-erasure obligations. Separate same-author arithmetic checks do not
+establish independent human or proof-kernel acceptance. No uniform rounded
+multiplier is materialized, no practical speedup is asserted and κ=.005 has
+not been attained. The ordinary BIT saving0.0034 would itself need improvement
+for a whole bound beyond.005.
+
+This new PR leaves PR6399 and PR6398 unchanged. The canonical base is
+7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority8. Exact predecessor history
+is retained for source-byte checks without importing their pending package
+trees into this diff. Bounded live overlap checks are not novelty certification.
+
+## Open next questions
+
+1. Independently reproduce and review the clean-native/mixed-caller binding.
+   Start from the two archived pins, complete word regeneration, physical
+   contacts and exact paid/target deltas. Human/kernel review remains open.
+2. Find a substantially cheaper native word or genuinely different caller
+   interface toward.005, with a stronger BIT backend as needed. First emit
+   an arbitrary-input word and account for every productive debit and query;
+   favorable local or formal prices alone are insufficient.
+
+Structured scope and questions are in TASK.json.
+
+## Credit
+
+Rohan Arun with substantial OpenAI Codex assistance supplied this standalone
+composition, price rebinding and complete checks. PR6399 supplies the clean
+native merge; Ali Romman with substantial OpenAI Codex assistance supplies
+PR6398’s root, normalization, physical binding and compiler adapter.
+DreamingOfClouds with Claude Opus5.5 supplies PR6375’s input lifts. The retained
+P104, Gaussian/native/helper, BIT, compiler/precision and analytic authors
+keep their full notices in both source archives. New work is Apache-2.0.