Safety claims need the right evidence.
A coherent theorem-and-evidence series on what an AI monitor can distinguish, compute, trust and enforce. September's mathematical results remain separate from the October SourceBound implementation and its independently specified evaluation.
September 2026MATHEMATICAL FOUNDATIONS · REVIEW PENDING
27,740REPORTED FINITE CHECKS · EXTERNAL REFEREE REVIEW OPEN
SourceBoundSEPARATE BUG-FIXED SYSTEMS TRACK · NATURAL-WEB STUDY OPEN
01 / COMMON FOUNDATION
One precise boundary.
A safety property can be decided from a fixed observation only when every pair of executions giving the same observation requires the same decision. This classical factorization result supplies a common language for agent-monitor design, without claiming novelty for the underlying mathematics.
STATIC OBSERVATION / FACTORIZATION
F = d ∘ R ⇔ ker(R) ⊆ ker(F)
R is the actual observable view; F is a specified safety label. A restricted protocol still needs the induced decision rule to be implementable in its permitted class. This qualification corrects an earlier draft.
From this foundation follow a maximal sound admission rule, explicit collateral denial from mixed-label observation classes, a weighted-set-cover model of evidence repair, and policy-specific provenance and history requirements.
02 / PUBLICATION SERIES
Six connected papers.
01
Agent Safety Under Abstraction
Observation sufficiency, maximal sound guards, minimum-cost repair, provenance, memory, and composition.
Primary manuscript dossier ↗02
Boundary-Limited Oversight
Corrected restricted-protocol converse, adaptive indistinguishability, and two-world randomized error bounds.
Proof corrections ↗03
Compositional Authorization
Counterfactual reference reach, graded composition, minimal generating sets, and explicit audit complexity boundaries.
Original authorization research ↗04
Three Ceilings on Oversight
Information, computational resources and trustworthy evidence, relative to a specified overseer and threat model.
Revised theory ↗05
Collective Sufficiency
Joint-view observation, centralized fusion, independent veto limitations. Mathematical constructions with mock evidence; real-model measurement still open.
Measurement scope ↗06
Verification Through Failure
Claim demotion, counterexamples, reproducible evidence, and the September error-ledger methodology.
Review requirements ↗03 / EVIDENCE STATUS
Measured, scoped, audited.
Exact finite checking, archived benchmark replays, mock studies, and prospective real-world experiments carry different validity labels. These values describe their specific populations, not universal deployment guarantees.
Known limitations: a previously stated resource-frontier band was refuted and excluded. The CaMeL call-level replay is a heuristic sensitivity analysis, not a verified end-to-end attack. SourceBound's reviewer-derived regressions were seen during repair, so successful replay is not blinded evaluation.
04 / SEPARATE IMPLEMENTATION
SourceBound.
An auditable publication gate for web-extracted source assertions, distinct from the abstract safety theorems. It checks source-version provenance, a restricted evidence-to-triple binding, browser-visible evidence, temporal conflicts, and revision-aware links before admission.
Guarantee boundary: restricted-source assertion traceability is different from external truth. The next required validation is a preregistered, domain-held-out natural-web study comparing unsupported published edges and answer quality at matched recall.
05 / REVIEW INVITATION
Challenge the boundary.
Referees are invited to attack the protocol quantifiers, formal composition results, benchmark causal lineage, semantic support assumptions and statistical design. Report a claim ID, counterexample and reproducible artifact. Review findings remain open until independently resolved.
Binary archive SHA-256: c2cd8db71f7116a90d6ba0d0ddfaf6a08b6d710328c0c7d463fa1d1af5f74618. The full 116-file ZIP is hosted as a GitHub Release asset, reconstructed by GitHub Actions and checked for exact SHA-256 and ZIP integrity. This page remains a textual research overview. Release record ↗