Mister-Meeseeks · Oct 20, 2026 · Oct 18, 2026
diff --git a/research/staged544-certified-endpoint/.gitattributes b/research/staged544-certified-endpoint/.gitattributes
@@ -0,0 +1,3 @@
+* text eol=lf
+*.gz binary
+vendor/** -text
diff --git a/research/staged544-certified-endpoint/CLAIM.json b/research/staged544-certified-endpoint/CLAIM.json
@@ -0,0 +1,13 @@
+{
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+  "complex_upper": "1730578437266246818740713218049857556556448073971562433313/1000000000000000000000000000000000000000000000000000000000000",
+  "endpoint_digits": 60,
+  "fresh_native_replay": false,
+  "gain": "7132180498575565564481739715624333120000000000999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "kappa": "17305784372662468187407132180498575565564480739715624333119999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+  "physical": 323069,
+  "previous": "17305784372662468187399999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000",
+  "private_zero_buffers": 91,
+  "replicas": 360,
+  "selected_frontier_changed": false
+}
diff --git a/research/staged544-certified-endpoint/FORMAL-DATA.json b/research/staged544-certified-endpoint/FORMAL-DATA.json
@@ -0,0 +1,32 @@
+{
+  "endpoint": "54080576164570213085647288064058048642389002311611326041/31250000000000000000000000000000000000000000000000000000000",
+  "log_upper": {
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+    "2": "179865613029422290983743836799018300141462635525567120523750942383419817697545129/50000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "3": "319184715248028143769686362051601686625726228704884821286100452352429568270198833/100000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "4": "290416508002850051025764461452218943475375257615108715635433883817500273198120787/100000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "5": "268102152871429075449134952421235493137915149060307994268305096568761098821293953/100000000000000000000000000000000000000000000000000000000000000000000000000000000",
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+  "weight_upper": {
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+    "4": "10050385364133079746285308201955675603189995240534294134445832020584933/10000000000000000000000000000000000000000000000000000000000000000000000",
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+    "8": "10038336696855168412899988593909345131643424182661368231754045234034801/10000000000000000000000000000000000000000000000000000000000000000000000"
+  },
+  "log_degree": 60,
+  "exp_degree": 26,
+  "root_upper": {
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+  }
+}
diff --git a/research/staged544-certified-endpoint/FRONTIER-COMPARISON.json b/research/staged544-certified-endpoint/FRONTIER-COMPARISON.json
@@ -0,0 +1,17 @@
+{
+  "origin_commit": "de2cd5c58009205210e3bf328b0ef5cadf3903af",
+  "origin_path": "research/staged544-t385/inputs/PROFILE.json",
+  "source_sha256": "1375994cc9fbfac3604960a78e82fe6ed9db2581e5ac30175543aa56441a72f4",
+  "profile": {
+    "1": 8544690,
+    "2": 2512125,
+    "3": 801108,
+    "4": 353430,
+    "5": 73920,
+    "8": 27720,
+    "48": 147532
+  },
+  "reference_replicas": 385,
+  "current_replicas": 360,
+  "exact_normalized_profile_equality": true
+}
diff --git a/research/staged544-certified-endpoint/LEAN-AXIOMS.txt b/research/staged544-certified-endpoint/LEAN-AXIOMS.txt
@@ -0,0 +1,2 @@
+'Staged544.actual_moment_lt_one' depends on axioms: [propext, Classical.choice, Quot.sound]
+'Staged544.actual_rpow_moment_lt_one' depends on axioms: [propext, Classical.choice, Quot.sound]
diff --git a/research/staged544-certified-endpoint/NOTICE b/research/staged544-certified-endpoint/NOTICE
@@ -0,0 +1,39 @@
+Dugongue, with substantial OpenAI Codex assistance. New work: Apache-2.0.
+
+Direct current predecessors:
+- ChaloupeMusic / PR3815, head 77ffbf287b6ca198b4a31e3835db3bae60718b93:
+  changed T360 clock/fill, exact fixed-inventory packing cap and complete release.
+- hexapode / PR3802, head de2cd5c58009205210e3bf328b0ef5cadf3903af:
+  first publication of the same prior endpoint via T385; PR3795 is the T488 prior.
+- dataisfire / PR3734, head fa041037a3374eaa08feeca0b26a5d6893194147:
+  staged helper 544 word, current native release and retained outer arithmetic.
+- zxv / PR3638 and PR3682: chronological T360 integration and retimed suppliers.
+- Ross Richardson / PR3605: staged-entry mechanism and source supplier.
+- roger-sato / PR3642 and PR3693: commuting-release retiming and whole-word adapter.
+- Sagar Thakrar / PR3687: arbitrary-dirty independent interpreter.
+- Arham Tahir: retained exact free-operator/frame audit lineage.
+- SovereignSteak / PR3531: positive-binomial precision precedent; dataisfire /
+  PR3361: source-bound precision integration precedent. No numerical-method priority.
+
+The original native, rank-seven, geometry, owner, hosting, COPY, prefix and outer
+contributors retain their credit: Jeremy Diviney, dcharb78, Nick Petalas,
+Marius-Paul Dumitrean, Jeremy Kothe, Mason Hale, Yiyang Lu, Tekalign, Philippe
+Van Velzen, Sagar Thakrar and all authors named in retained source notices.
+Vlado Vojdanovski supplies the outer construction; Chafik Boukhalfa's fine-prime
+padding uses Tim Trudgian's cited prime result; gauge-free/union contributors,
+eumemic's 47-row assembly and the PR589 BIT lineage remain credited.
+
+The extracted MathProof sufficient-transfer proof has Dugongue/Codex provenance.
+Mathlib supplies the sufficient real exponential/Taylor/rpow lemmas. These are
+standard methods; no claim that nobody has previously applied them is made.
+
+The vendored native receipt came from PR3734's optional source archive:
+https://raw.githubusercontent.com/CrocSwap/integer-mult-bounds/fa041037a3374eaa08feeca0b26a5d6893194147/research/staged544-producer-return/REPLAY-INPUTS.tar.gz
+Its archive and member SHA-256 hashes are documented by the retained upstream
+REPLAY-INPUTS manifest. Bounded replay authenticates the vendored receipt and
+actual words/native frames, not omitted full cache bytes. The archive is an
+explicit optional full-review source, not a hidden runtime dependency.
+
+All exact retained files keep their source-specific attribution and Apache-2.0
+notices. SOURCE-CREDITS.md under vendor/staged544-producer-return preserves
+that package's own predecessor list.
diff --git a/research/staged544-certified-endpoint/OVERLAP.md b/research/staged544-certified-endpoint/OVERLAP.md
@@ -0,0 +1,64 @@
+# Current source and overlap checkpoint
+
+The session read current-main AGENTS.md, autoresearch.md and CONTRIBUTING.md
+first, pinned `20ecf2891d80b5acf18d980b2164fb44ea7faa90`, and fetched canonical
+main again before verification. Priority revision remains 6 and the selected
+result remains `836330098538459/500000000000000000`. The first working baseline
+check passed after materializing the sparse checkout's exact selected closure;
+1,626 files were byte-checked against the fresh main tree. This was a bindings
+check, not a cold scientific replay of the selected construction.
+
+The donor explicitly required best-known κ and rejected the stale T740 work.
+That earlier draft was preserved outside this package. The relevant current
+construction is the cap-attaining staged-helper line, not a descendant of our
+unpublished T740 endpoint. The current-main original `independent-moment` card
+is retained verbatim in TASK.json; its scope change is explicit. A picker draw
+was not substituted for the donor's assigned target.
+
+Entry intake fully paginated all 539 open PR bodies and read the 100 most
+recently updated closed PR bodies. An incremental public-API refresh at
+2026-10-18 22:58 UTC paginated updates until an older-than-entry row, covered
+all 16 changed records since entry through #3846, and updated the open snapshot
+to 552 records. The repository overlap helper searched the resulting cache,
+including current closed/reopened states and local package notes. Closed-history
+coverage is partial. This is title/body coverage, not an exhaustive code-diff
+or unpublished-work search; snapshots are not atomic.
+
+Visible Discussion start/handoff pages #1163/#1166 and the relevant #2612 thread
+were read, but all Discussion comments/replies were not paginated. The helper
+reports no full Discussion cache and explicit offline freshness warnings; no
+absence-of-overlap or method-priority guarantee follows. Relevant direct PR
+comments were separately fetched: #3802 credits #3815's equal endpoint/cap;
+#3734 points to that solution of its changed-clock question; #3815 had no
+comments in that check.
+
+Exact current comparisons:
+
+| PR | Head | Relevant contribution |
+|---|---|---|
+| [#3815](https://github.com/CrocSwap/integer-mult-bounds/pull/3815) | `77ffbf287b6ca198b4a31e3835db3bae60718b93` | T360 clock/fill, exact packing ceiling and full release |
+| [#3802](https://github.com/CrocSwap/integer-mult-bounds/pull/3802) | `de2cd5c58009205210e3bf328b0ef5cadf3903af` | Earlier publication of the same prior κ at T385 |
+| [#3734](https://github.com/CrocSwap/integer-mult-bounds/pull/3734) | `fa041037a3374eaa08feeca0b26a5d6893194147` | Staged helper 544 word, current native inputs and release |
+| [#3682](https://github.com/CrocSwap/integer-mult-bounds/pull/3682) | `431e6c6023ef352c41696469de7fb614cd4ded8c` | Retimed T360 integration |
+| [#3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605) | `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb` | Staged-entry mechanism |
+| [#3642](https://github.com/CrocSwap/integer-mult-bounds/pull/3642) | `6568db75adbb61437190545f6fef1534c70e91e5` | Retiming and corrected owner-control coverage |
+| [#3531](https://github.com/CrocSwap/integer-mult-bounds/pull/3531) | `550a660a97308d3aeb3620ee1f4218f77e2c2742` | Earlier binomial/T740 precision and reuse precedent |
+
+New #3836 fixes the nine-stage bridge idle alphabet at its scoped boundary;
+#3828 develops centre-kernel theory. Neither updated body supplies a higher
+complete conditional κ. Earlier donation headlines #3184/#3190/#3198/#3200/
+#3251 are now closed and have published operator objections; their numbers
+are not treated as current admissible suppliers. No claim that all changed
+architectures or repairs are impossible is made.
+
+The new bound strictly improves #3802/#3815, the highest complete
+source-backed conditional endpoint located in this search. The mathematical
+addition is a closed finite real-power moment proof plus independently replayed
+exact arithmetic, not merely extra digits or a new physical word. A global
+unconditional best-known multiplication theorem is not established. No selected
+record, shared scientific source, maintainer decision, or other PR is changed.
+
+No public claim or PR was posted from this execution context because the donor's
+GitHub credential is available in their normal PowerShell session, not this
+sandbox. The prepared publication command uses that existing session. Routine
+publication is authorized; no additional permission step is required.
diff --git a/research/staged544-certified-endpoint/PRECEDENTS.md b/research/staged544-certified-endpoint/PRECEDENTS.md
@@ -0,0 +1,27 @@
+# Existing MathProof proof material used
+
+The registered source catalog and canonical Lean tree were read without changing
+the authoritative DAG or importing a staging copy as a competing active module.
+The catalog's canonical
+`Mathproof/Computability/IntegerKappaMomentTransfer20261015.lean` has SHA-256
+`68e89786008dd3f222632920a00eafd6fc64661e08548c5325a3daa4ba964522` and
+status `NO_LOCAL_ARTIFACT`. That is source-only provenance, not an old kernel
+receipt. This package checks its extracted sufficient argument freshly.
+
+Its `weighted_mono_weights`, `rational_upper_certificate` and
+`normalized_admission` supply the finite rational-to-real admission assembly.
+Their proof bodies are retained unchanged in CapCertificate.lean; the new
+instance is the actual current seven-rank bill. The public package imports
+only Mathlib and needs no private MathProof directory or prior compiled module.
+
+The existing `IntegerKappaProviderExchange20261015.lean` and
+`IntegerSuperiorKappa20261015.lean` were also consulted during route comparison.
+They support concavity and replica-monotonicity arguments at their abstract
+boundaries. They do not create a new physical word or beat the current attained
+packing cap. No numerical saving is attributed to an unconstructed use of them.
+
+The session reused our earlier exact commuting-retiming implementation as a
+search template on the newly pinned current word. It did not reuse a stale κ.
+The current formal analytic route adds sufficient eighth-root/Taylor inequalities
+and composes them through the existing admission theorem. Proof status is bound
+to final source bytes in VALIDATION.json; retrieval alone is never proof evidence.
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1,2 @@
		'Staged544.actual_moment_lt_one' depends on axioms: [propext, Classical.choice, Quot.sound]
		'Staged544.actual_rpow_moment_lt_one' depends on axioms: [propext, Classical.choice, Quot.sound]