Selected conditional κ: 0.003027288235 = 605457647/200000000000, Chris R / Clear1nsight's PR5413 complete neutral caller, with the provider audit in PR5407 and independent companion PR5414. It uses Dillon Amburgey's PR5402 coupled provider and Ali Romman's PR5398 direct controller. Cao Yifan's native construction, Cinna Davis's helpers/controllers, zxv's compiler/precision work, Jacob Alan Sussman's mixed-target recursion and the earlier lineage remain credited.
Selected record · Proof review · Promotion and scope · Integration receipt · Contributors.
Replay: make frontier5413-verify. The provider's five engines, primary eight
engines and independent companion screen run serially in a closed source export
under a sampled 1 GiB descendant-memory limit and per-package timeouts.
Source-bound PR4610/#5241 and earlier foundation coverage is reused, not rerun.
The local macOS replay uses an explicit RLIMIT_AS compatibility adapter;
it is not presented as an unmodified Linux run.
Exactly the five preceding assumptions remain: native/all-column realization, owned erasure, compiler closure, precision/fixed-tape execution, and analytic recovery. No complete Lean or independent human multiplication proof is claimed; the enormous uniform word is not materialized. Hosted CI status is separate from the successful local replay and recorded in the integration receipt.
The preceding selected checkpoint is 0.0030217758. Its review remains part of the inherited foundation. The gain is about 0.182424%; the final +5×10⁻¹² over #5398/#5400 is compiler/outer headroom. Equal additional paid/target H8 jobs preserve the raw signed moment. Frozen submission and review files retain their pre-promotion wording; this status and the integration receipt supersede that publication status without rewriting the evidence.
The remaining sections form a historical snapshot; their “current” wording is local to their checkpoint, not the selected record above.
Historical selected conditional κ: 0.001672660197076918, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555.
Review and attribution · Integration/CI receipt · Selected record.
Cold replay: make frontier1094-verify. This local review explicitly reuses the published, source-bound complete #1042 construction/bit evidence and freshly checks #1094. Exact native, hosting and arithmetic evidence remains conditional on the listed compiler/realization/precision/analytic interfaces. Linux CI is separate.
#1048 remains open; no negative theorem from that proposal is accepted. The PR1048 correction map separates retained arithmetic repairs from pending transport-census review and the remaining domain-completeness questions. Other historical deferrals, including #946, remain unchanged.
Reviews since the #1094 selection. These rounds retain scoped constructions, negative results, audits and tooling with individual credit, without changing the selected κ. The table records frozen prose review checkpoints, not live queue counts; later rounds can revisit older PRs. Use the PR ledger for the current disposition of a specific contribution. The last prose review in this table is the nineteenth reconciliation. Recorded intake continues through the twenty-sixth reconciliation; rounds 2000 through 2600 are archive and tooling intake, not a selected-frontier update. Round 2200's heading says "final unbatched remainder"; rounds 2300 through 2600 are recorded after it. Pending obligations in every round stay separate from incorporated research and supplier admission.
| Review | Frozen PR selection | Disposition |
|---|---|---|
| efficient100 | #697–#814 | 83 merged; 17 follow-ups |
| efficient200 | #815–#1095 | 76 merged; 24 follow-ups |
| efficient300 | #1100–#1208 | 69 merged; 31 follow-ups |
| efficient400 | #1209–#1343 | 85 merged; 15 follow-ups |
| efficient500 | #803, #1344–#1466 | 89 merged; 11 follow-ups |
| efficient600 | #797, #1026, #1468–#1600 | 78 merged; 15 follow-ups |
| efficient700 | #1601–#1726 | 79 merged; 21 pending |
| efficient800 | #1729–#1862 | 85 merged; 15 pending |
| efficient900 | #1863–#1951 | 56 merged; 12 pending |
| efficient1000 | #1952–#2027 | 44 merged; 2 pending |
| efficient1100 | #620–#2135 | 79 merged; 21 pending |
| efficient1200 | #654–#2257 | 78 merged; 22 pending |
| efficient1300 | #1175–#2377 | 76 merged; 24 pending |
| efficient1400 | #1155–#2490 | 78 merged; 22 pending |
| efficient1500 | #1758–#2591 | 76 merged; 24 pending |
| efficient1600 | #2592–#2715 | 83 merged; 17 pending |
| efficient1700 | #2478, #2716–#2828 | 66 merged; 34 pending |
| efficient1800 | 42 new/revised submissions; 58 earlier follow-ups | 42 merged; 58 pending |
| efficient1900 | 44 new; four revised; 52 earlier follow-ups | 63 merged; 1 closed as superseded; 36 pending. |
Below this point every section is a historical snapshot. Inside them, “current,” “selected,” “latest” and “next” refer to that snapshot's own checkpoint. The authoritative record is selected-result.json, and live research priorities are in autoresearch.md.
Selected conditional κ: 0.001672188119205421, Jeremy Kothe's #1042 on the mutable-leaver/slot chain, Rohan Arun's #987 slot search and Hao Yan's T16 controller. The bit side remains #589 on #555.
Review and individual credit · Publication/CI receipt · Selected record · PR ledger.
Cold replay: make frontier1042-verify. Complete local finite construction and both exact moment engines pass, with source-bound retained ancestry reuse recorded. All-size/compiler, realization, hosting, precision/tape, analytic and bit-interface assumptions remain. Linux CI is separate; no complete Lean multiplication theorem is claimed.
The forty-PR batch integrates constructions, parallel audits, circuit candidates, scoped negative results and verification tooling with individual attribution. #946 remains deferred, corroborated by #994's exact source-pin inventory.
Selected conditional κ: 0.001661960547713947, Jonathan Capalbo's #942 T37
composition of the #890/#869/#870/#858 lineage, with unchanged #589 on #555.
Review and credit ·
Publication/CI receipt ·
Selected record · PR ledger.
Cold replay: make frontier942-verify.
Seventeen of eighteen frozen PRs complete scoped review; #946 stays open pending source-pin migration for its broad encoding patch. Circuit candidates, scoped negative results, continuum owner bounds and exact-verifier tooling are integrated as research with separate attribution. The new circuit counts are not combined or installed as the selected bit supplier. The T37 all-replica bound applies only to its fixed family and outer grid recipe.
Local full T37 execution passes with explicit checked ancestry reuse. Linux CI is tracked separately. All-size/compiler, realization, hosting, precision/tape, analytic and bit-interface assumptions remain; no full Lean multiplication proof.
Selected conditional κ: 0.001661957774647029, PR890 on PR869/870 and
Hao Yan's PR858 T16 mechanism, with PR589 on PR555.
Review ·
Integration/publication/CI receipt ·
Selected record · PR ledger.
Cold replay: make frontier890-verify.
The frozen eighteen-PR round includes frontier constructions, complete-receipt and proof-pointer fixes, parallel replay, exact local bounds and independent finite audits. Source coverage, individual credit and review corrections are recorded separately. All-size/compiler, realization, hosting, precision/tape and analytic assumptions remain; no full Lean multiplication proof is claimed. The Linux integration job status is separate from the completed local replay.
The batch through #932 reviews eighteen circuit, precision and verification contributions without changing κ. It includes faster isolated tests, X4 scalar savings, R439 compensation candidates and independent outer/layout/provenance evidence. Full supplier adoption of the new bit circuits remains open; their finite boundary checks are not a new selected witness.
Selected conditional κ: 0.001661634653669567, #799 with #589 on #555.
See the review,
integration receipt,
selected record and PR ledger.
Public cold replay: make frontier799-verify.
The explicit X4 construction passes native scalar/frame/phase checks, physical owner admission, the full invoice, two independent moment engines and all 47 outer constraints. Composition is bound to rebuilt SW4 ancestry and PR589. Local reuse and Linux CI are reported separately; inherited realization and analytic hypotheses remain. No full Lean multiplication theorem is claimed.
This round completes #795/#777 reviews and the six individual #681 component reviews, integrates five verification-tooling packages, and narrows #806's hash-tracing claim to what its diagnostic actually establishes. Historical CI payloads remain unavailable. The ledger records exact-head publication status.
The #741 checkpoint remains
reproducible with make frontier741-verify. Original component sources remain
unchanged; scripts/verify_supplier_consolidation.py --component-tests provides
the historical selected-record closure without changing the current selection.
Selected conditional κ: 0.001635527380375392, #626 on #622/#623 with #543.
See the review, integration receipt,
selected record and PR ledger.
Public cold replay: make frontier626-verify.
The previously queued #626 Linux run completed successfully on 2026-10-13. The preserved evidence and offline checker bind that run to its tested sources, six replay stages and exact assembly. Three generated provenance digests differ from the committed assembly; the linked reconciliation records their scope and the unavailable payloads.
The frozen round covers #618–#626. Eight scoped reviews complete; #620 remains partial pending portable research replays and validation of its solver/barrier claims. Earlier open reviews retain their ledger status. Inherited uniform, physical and analytic assumptions remain; no full Lean multiplication proof. Local replay and remote Linux CI statuses are recorded separately.
The selected conditional saving is κ=0.001635183729255778, #617 with #543,
building on #601/#604/#615. See the review,
integration receipt,
selected record and PR ledger.
The public replay is make frontier617-verify.
The frozen round covers #600–#617. Parallel allocations, replay reports, formalization and research retain attribution. #611's older branch diff and #605/#612 Linux harness and precursor reviews remain open. Scoped finite and Lean checks do not discharge the inherited uniform and analytic assumptions. Remote Linux CI is reported separately from local execution.
The selected conditional saving is κ=0.0016127213726553, Jeremy Kothe's
#596 on #591/#592 with eumemic's #543 bit supplier. See the
review,
integration receipt,
selected record and
PR ledger. The public replay is make frontier596-verify.
#593/#599 add scoped Lean proofs; #589 adds bit headroom; #595/#598 add research. #594's independent replay contribution is incorporated, while its older branch differences await reconciliation. All inherited all-size/realization/hosting/ precision/tape/analytic conditions remain; this is not a full formal proof of multiplication. Remote Linux CI status is recorded separately from local checks.
The selected reviewed conditional witness is κ=400569730495803/250000000000000000=0.001602278921983212, from Jeremy Kothe's #588 with eumemic's #543 bit supplier. The preceding #535/#510 checkpoint is preserved.
See the selected record,
review and assumptions,
execution receipts, and
per-PR dispositions.
The public make frontier588-verify command cold-rebuilt both finite suppliers
and their exact composition. All-size/compiler/common-label/mutable-basis,
pooled-cell hosting, normalized residual, precision/tape and analytic
interfaces remain conditional. Linux CI is tracked separately; no full Lean
multiplication theorem is claimed.
The frozen round covers 43 construction, research and tooling PRs through #588. Separate Lean proposals and later arrivals stay in the next queue. Parallel and superseded mechanisms, exact diagnostics and negative results retain attribution in the contributor record. The research integration index preserves earlier non-frontier contributions. Larger pending claims remain proposals until reviewed.
Earlier “selected” statements below are historical snapshots.
The selected conditional witness is κ=330942774629799/500000000000000000 =0.000661885549259598, from Dugongue's #186, on chafreaky's #181 and eumemic's #168. It is approximately 2^-10.56113: 43.60% above the preceding published checkpoint and 40.18% above the recycled-bit review checkpoint.
See the round-eight review,
selected record,
construction,
bank scheduling supplement,
and integration validation.
Reproduce with make entrance-bank-verify.
Published on main on 2026-10-09; the receipt identifies the tested branch/head.
The retained analytic, uniform-recursion and fixed-tape interfaces remain
assumptions. Finite replay and scoped formal contributions do not formalize
the multiplication theorem. #185's reviewed leaf bootstrap does not further
raise this witness, whose complex supplier already binds.
The assembly-domain audit distinguishes the
enforced b<1/32 range from the balance kappa<a/(1+a) and the independent
retained Gaussian condition kappa<1/4. Its larger-supplier examples are
arithmetic diagnostics, not new witnesses or an enlarged theorem domain.
The preceding reviewed recycled-bit composition was κ=0.000472154791; its round-seven review retains the evidence.
Earlier local experiments and rounds-three-through-five reviews are now preserved as dated historical records. Their old frontier and pending-work statements do not supersede this page; the retired shared-aggregate search remains retired.
Everything below is historical and retains its checkpoint-specific scope.
The selected conditional witness is κ=4609169/10000000000=0.0004609169,
from icekylinx's PR #144.
This is about 9.03 times the preceding main saving, approximately 2^-11.0832.
It is above 2^-12 and below 2^-11.
The construction builds on icekylinx's compiler lineage, an664's #128 completed-core sharing, eumemic's #117 producer, Zhihao Chen's #97 physical ledger and Swapnil Jain's underlying frozen word. See the review and attribution, validation receipt, selected result record, and reproduction guide.
The retained upstream analytic, semantic and fixed-tape interfaces remain assumed. The finite controls and written audit do not formally verify the full multiplication theorem. The review distinguishes local checks from head-pinned Linux CI evidence; no independent human peer review is claimed.
Everything below is historical. Its “current” and “selected” statements refer to the corresponding checkpoint.
The selected conditional witness is κ=25508460085039/500000000000000000 =5.1016920170078e-5 > 2^-15, from Avi Eisenberg's #62 pair assembly, eumemic's #57 compiler, and Alejandro Zarzuelo Urdiales's #61 parameter refinement. It is 23.71% above the previous #49 release, and remains below 2^-14. See the review and contribution ledger, independent arithmetic, and selected certificate.
The original #109 framework and inherited all-size analytic/fixed-tape interfaces remain assumed. Scoped Lean checks do not prove the full algorithm. Submissions after #62 are not included in this review checkpoint.
Everything below is historical; its numerical “current” and “latest” statements refer to the corresponding checkpoint.
The selected conditional witness is κ=4123863984/10^14=4.123863984e-5 > 2^-15,
from PR #49 at f95d2910e027495983b53cae1693cf535abf2569. It improves the
previous PR #39 release by 6.10%, retaining its analytic and fixed-tape contracts.
See the follow-up review,
integration record,
exact certificate, and
contributor record.
PR #45 (Gaussian parity and finite tensor execution) and PR #26 (historical arithmetic and algebraic contracts) are incorporated as scoped formal verification. Their Lean builds and axiom audits do not prove the complete multiplication theorem. The original #109 framework remains assumed; no independent human peer review is claimed.
The preserved research index collects the earlier compression and topology searches, with scoped exclusions and reproduction commands.
The previous PR #39 release and tested 2^-30 checkpoint at 1a74950 remain
preserved. Everything below is historical: “latest” and “current” refer to the
checkpoint, not the selected community follow-up witness.
Updated October 8, 2026. Author: Douglas Colkitt.
The latest included conditional witness is kappa=2^-30. Its note, certificate, and independent patch are described in the review guide. The previous 2^-31 construction and all older witnesses remain unchanged.
The bit circuit uses F3 scalar arithmetic and rational frames on five-subset labels at h=29. Its complete counts are
m_b=24389, W_b=589493540769997500,
s_b=14377157287342062574725,
a_b=467/10^11.
The complex circuit is retained at a_c=5/10^9. Parameters are
epsilon=1999/10000, c=1, beta=1/100, zeta=1/1000,
delta=1/10^6, C1=4961/1000,
lambda=1-4669/10^12, lambda'=1-4668/10^12,
kappa=2^-30.
The exact minimum assembly margin is
2332833/2500000000000000 > 2^-30. The bound remains conditional on the
pinned upstream theorem and the retained written extensions. Finite checks
and manuscript compilation are not independent mathematical verification.
Zhihao Chen's earlier PR #7 contains the same ternary motif with a different producer and stronger claimed bound. Further pending contributions claim larger improvements. See the contribution-review index for attribution, dependency order and the distinction between a submitted claim and a reviewed result. This checkpoint asserts neither priority nor a strongest-known algorithm.
Everything below records the preceding integration. Numerical uses of “current,” “latest,” or “retained” in that historical record refer to 2^-31; the parameters above supersede them for this checkpoint.
| State | Exponent saving kappa | Artifacts |
|---|---|---|
| Earlier published baseline | 2^-59 |
paired note, patch |
| Published compact-control checkpoint | 83/10^12 > 2^-34 |
note, certificate, patch |
| Integrated follow-up, pending publication | 2^-31 |
note, certificate, patch |
The latest witness increases kappa by approximately 5.61 times over the exact
preceding witness; the dyadic comparison 2^-34 to 2^-31 is eightfold.
These compare exponent savings, not practical runtime. All earlier certificates,
patches and the pinned upstream source remain unchanged.
The complex-network construction uses weighted
rectangles for disjoint triples, shared sums for intersection-two triples,
and binary phase frames valid in both signed directions. Transparent computation
restores arbitrary auxiliary inputs. A matching shares the complete first/third
auxiliary banks. At h_c=26, it has
m_c = 17576, W_c = 7082222160000,
s_c = 124477130005280000,
a_c = 1-sigma = 5/10^9.
The bit network remains h_b=50, m_b=125000, with
a_b=1-tau=296/10^11. Thus the complex interface now has the larger saving.
The bit interface is the bottleneck.
The retained compact-control construction moves compact dirty fields instead
of spaced windows, at cost O(V*((f log p)^tau+1)). It reserves two front
fields and one back field from existing address coordinates, preserves complete
ranges in every recursive child, restores arbitrary values, and charges
exceptional-address repair at every node. All three movement/layout/guard
proof sources are embedded verbatim in the new patch.
The certificate uses
epsilon = 199/1000, c = 1,
beta = 1/100, zeta = 1/1000, delta = 1/10000,
C1 = 4961/1000,
lambda = 1-293/10^11,
lambda' = 1-29/10^10,
kappa = 2^-31.
The internal, leaf and reservation exponents are
chi = tau+(1-beta)*max(sigma-tau,0) = tau,
leaf = sigma+beta*(1-sigma),
reserve = max(1-c,0) = 0.
All required comparisons are strict. The seven assembly margins have minimum
G = g3 = 5771/10^13 = 5.771e-10 > 2^-31.
The explicit new scalar-operation count fits the generalized guard's node
charge E=64*(W_c+m_c+1)^3. The guard still has
C1=5-4*beta+zeta, and epsilon*C1=987239/1000000<1.
Reserved-axis processing costs O(V log p) for c=1.
The old quadratic restriction from K^tau is absent. With the retained
certified bit exponent and Gaussian assembly inequality, the current scoped
ceiling is kappa<a_b/5=5.92e-10<2^-30. This is not an all-network limitation.
The new complex saving provides numerical headroom for 2^-30 if a stronger
bit construction is supplied; that is not another established witness.
The integration review guide identifies each new obligation and its tests. General arguments are supplied in:
- compressed complex construction;
- movement and deterministic repair;
- reservations, row splitting and recurrence;
- generalized guard.
The new certificate records all four source hashes. The combined patch applies directly to the pinned original and includes the full retained refinements. It updates every complex constant, the exponent ordering, scalar guard charge, final parameters and derived powers. It preserves the legacy wide-slot lemma for the appendix and retains the corrected local exceptional-stream sum.
Finite tests check exact signed scalar maps with independent dirty variables, rectangle partitions, binary residual bases, phase identities, matching, parameter inequalities and source integration. They do not simulate the entire multiplication machine or replace independent proof review. The retained compact-control arguments have the same review dependencies as before.
Completion checks passed: 176 tests, 18 patch-application checks, exact certificate/patch regeneration, and both note and manuscript builds.
Reproduce with make verify and make complex-note. See the
reproduction instructions for applying the patch and
building a manuscript preview without changing the pinned source.
The complex construction is integrated. The next improvement should target the bit finite network, especially methods transferable from the new circuit compression or a new topology. More complex-network tuning alone cannot cross the present bit/Gaussian ceiling. Independent review remains valuable for both the new phase-frame transfer and the retained compact-control tape proof.
The previous joint-frame obstruction remains scoped to its fixed-boundary, grouped-gate model. Older research pages retain their chronology; use this page when interpreting superseded targets and barriers.