Change the representation.
Look for algebraic structure, symmetry, a better parameterization, or a new active constraint before spending more compute.
Independent research / October 2026 / Devin J. Wright
Discovery
needs witnesses.
A public laboratory for exact mathematics, quantum information, and AI verification. Every significant claim has a status, a source trail, and a question worth checking independently.
2026Research archive
September → October
September → October
10+Research programs
Mathematics to agent safety
Mathematics to agent safety
4Agent verification
tasks open
tasks open
OpenCorrections welcome
Evidence status visible
Evidence status visible
NEW / AI SAFETY · 28 OCT 2026
Explore review dossier
Theorem-and-evidence series + SourceBound
September oversight theory, corrected proof status and independent finite checks, with SourceBound evaluated as a separate implementation. Peer review open.
RESEARCH ARCHIVE / EIGHT-DOSSIER EXPANSION · 28 OCT 2026
Open eight dossiers
Eight additional lines of inquiry.
Werner finite-copy margins, periodic forest-gauge geometry, ETH interpolation, Busy Beaver returns, selection-aware pivoting, interpretability audits, causal-cut methods, and exact contest records. Each dossier distinguishes mathematical statements, imported premises, finite evidence, and open review gates.
01 / SELECTED FINDINGS
A few results, in depth.
Begin with the strongest finite construction, the largest conditional quantum transfer, and the theory underlying our approach to trustworthy AI.
01 / DISCRETE & CONTINUOUS OPTIMIZATION↗
Erdős minimum overlap
A 131,072-cell exact rational upper-bound witness. Full signed-shift verification was replayed internally; external reproduction remains open.
FINITE CONSTRUCTION / EXACT AUDIT→
02 / QUANTUM INFORMATION↗
Werner-state bounds
Complete 4–20 Werner bounds in three evidence columns, with separate 21–24 refinements and the 1–100 registry.
CONDITIONAL CERTIFICATES→
03 / FORMAL AI SYSTEMS↗
Agent safety under abstraction
What a safety monitor can know, when enforcement is sufficient, and how provenance changes the boundary.
MANUSCRIPT / EXTERNAL REVIEW OPEN→
How to read research status · Full classification ↗
Exact finite certificate
An arithmetic checker supports a particular finite construction under specified conditions.
Conditional deduction
Exact downstream steps depend on explicitly identified source inequalities or assumptions.
Manuscript / candidate
A proposed proof or model awaits independent examination of its complete argument.
Machine-checked proof
An explicit proof is checked by a proof kernel against stated premises; no global headline theorem has this status yet.
EVIDENCE NOTE / ERDŐS #36Independently review this ↗
A bound, with its provenance.
Our exact 131,072-cell construction is a mathematical upper-bound witness, with an internally replayed six-prime integer certificate. The Arena's accepted leaderboard snapshot, one documented oversized rejected submission, and an older archived 131,072-cell v3 construction are separate evidence records. External referee acceptance is still open.
| Research / source | Upper bound | Evidence status |
|---|---|---|
| AlphaEvolve (2025) | 0.380924 | Published reference |
| TTT-Discover (2026) | 0.380876 | Published reference |
| Together AI (2026) | 0.380871 | Published reference |
| SimpleTES (2026) | 0.380868 | Historically listed; separate 4096-cell normalization warning below |
| Atris (2026) | 0.380858550316428560… | Independently replayed exact finite witness |
| NIGHTFALL / accepted Arena entry | 0.3808564043546676 | Leaderboard snapshot; submission dimensions / hash unverified |
| NIGHTFALL / exact internal witness | 0.380856370118029325246… | 131,072 cells; internally replayed rational certificate; external review open |
LOWER REFERENCE / CONDITIONAL
Price (2026) reports c > 0.38055470: independently reproduced finite interval arithmetic, with specialist review of the complete reduction outstanding. That conditional bracket has width about 0.000301670118. Wetch reports c > 0.380627425, backed by local fresh-copy verification. A NIGHTFALL October 27 dual tightening, replayed with exact rational checks on October 28, conditionally gives c > 0.38062747462668. Its original upstream analytic and Arb integrations remain inherited; pending fresh independent replay, the resulting conditional gap is 0.000228895491. The same eight fixed dual rows have a rigorously proved method ceiling below 0.380627474626686.
IDENTITY / SEPARATE ARTIFACTS
Exact witness SHA-256: a574c280f8839503c90076507a27f4c819455fb2512fae6a43b6a17f6a784b8e, N=131,072, exact maximizing lag −17,280. A distinct 131,072-cell attempt (score 0.380856370118029394982…) was rejected for exceeding the Arena's 100,000-value limit. The accepted entry in the October 27 leaderboard snapshot (0.3808564043546676) still lacks a recovered cell count, original file hash, and independent exact score (provenance issue #6 ↗). A distinct 4096-cell value near 0.380856 has a reported grid-width normalization error, giving a corrected objective near 0.38094895; this is unrelated to the 131,072-cell NIGHTFALL witness.
Source comparisons: Optimization constants ↗ · MathWorld / Price ↗ · Wetch lower-bound manuscript and certificates ↗ · Hill Sampling (0.38090; beats AlphaEvolve, yet trails TTT-Discover) ↗ · NIGHTFALL receipt ↗ · Witness-by-witness evidence status ↗ · Distinct 4096-cell normalization correction ↗ · Exact conditional lower audit ↗ · Full binary release pending ↗
02 / RESEARCH INDEX
The work, indexed.
Filter by discipline. Each entry opens a source file or an evidence dossier in the public GitHub archive.
01
Erdős minimum overlap
Exact rational upper-bound witness; 131,072 cells and all signed correlations. The platform's rejected oversized submission is recorded separately.
Exact finite witness · review requested 02Werner-state undistillability
Seventeen 4–20 copy comparisons: best qutrit, theorem-only and all dimension; 21–24 refinements.
Exact conditional ledger · independent review open 03Finite-field phase retrieval
Uniform fourth-power sensing and lattice decoding. The original manuscript awaits independent proof analysis.
Manuscript proof · audit pending 04Affine source rigidity
September prime-zeta source-collision theorem and local shifted-series expansion; analytically distinct from global critical-line claims.
Mathematical manuscript 05Involution shadow codes
Sharp finite-group translation-code distance and view-allocation formulas; direct independent small-group checker published.
Exact finite checks · manuscript 06Agent safety under abstraction
Information sufficiency, enforcement collateral, provenance automata, history, and system composition.
Theorem manuscript · review open 07Counterfactual authorization gap
Capabilities induced by combining grants; reference-class escape and complexity of auditing.
Original LaTeX published · review open 08Three ceilings on oversight
Information, computation, and trusted evidence as relative limits on oversight guarantees.
Revised scope · review open 09SourceBound
Restricted evidence-to-triple admission boundary with browser checks, synthetic fixtures, and adversarial mutation tests.
Reproducible prototype · held-out study open 10Proof After Scarcity
Proof-dependency graphs, provenance-preserving verification policy, and negative stress tests.
Public metadata freeze · graph prereg pending 11Sidon finite constructions
A thirty-point (4,5) configuration with maximum Sidon subset size 17, supported by finite exact checking.
Finite certificate · scoped 12SAT tensor-network encoding
Exact degree-three Boolean graph compiler; asymptotic complexity transfer depends on an external published theorem.
Exact reduction · conditional runtime 13AI safety theorem-and-evidence series
September oversight theorems and corrected evidence with a separate SourceBound natural-web evaluation track.
Research synthesis · external review requested
03 / OPEN VALIDATION INVITATIONS
Help us find
Help us find
what survives.
Independent verification agents reconstruct, falsify, and formalize claims. The decisive output is executable evidence: a reproduced certificate, a counterexample, or a kernel-checked proof.
Four bounded agent assignments.
One transparent evidence standard.
One transparent evidence standard.
Each verification task has a precise claim, frozen dependencies, a falsification target, and an executable deliverable. The agent protocol requires independent implementations and publishes failure receipts. Full binary evidence packets still need a public mirror; view certificate hashes and access status and explicitly flag any missing primary input.
AUDIT / 01
Erdős overlap certificate
Verify continuous-shift reduction, rational feasibility, every lag, and convention agreement.
Read scope & tests↗ AUDIT / 02Werner source dependencies
Recheck rational duals, separability, and the imported four- and five-copy bounds.
Read scope & tests↗ AUDIT / 03Finite-field retrieval
Attack the uniform probability estimate, lattice decoding argument, and algorithmic cost.
Read scope & tests↗ AUDIT / 04Agent safety & authority
Check exact theorem quantifiers, Horn closure reductions, and security-model boundaries.
Read scope & tests↗
Agent checks require independent methods, frozen input hashes, and reproducible source code. Negative results and counterexamples are first-class findings. Four public verification issues are active; machine-checkable evidence determines scope-specific status.
Reviewer guide ↗
04 / HOW CLAIMS ADVANCE
The verification contract.
The research process is explicit, evidence-dependent, and designed to survive changes in models, collaborators, and techniques.
Write the attack first.
Separate candidate construction from its checker. Audit arithmetic, numerical margins, missing hypotheses, and hidden source dependencies.
Make evidence portable.
Keep inputs, exact checks, hashes, proof obligations, failure cases, and credit beside each claim. Preserve a complete revision trail.
A convincing argument is one that another researcher can try to disprove using the same evidence, without relying on our interpretation.