lean artifact · pending
Artifact ↗Source authenticated
Ordinal certificates and exact pruning characterize sequence realization
Avoidance is equivalent to a strictly decreasing ordinal certificate on the reachable states; arbitrary vertex/label types are allowed. Under finite per-label branching, natural certificates suffice. It also proves that states surviving every finite pruning round form the greatest successor fixed point and are exactly those with infinite continuations. A start realizes the full target iff its phase-zero state survives. Every other state has an attained finite maximum h, is removed at round h+1, and has a pointwise least natural certificate, even in populations realizing the target elsewhere. Complete finite-fibre blow-ups preserve corresponding least heights. Reachability prevents confusing an unrelated suffix with the original word. These are classical well-founded and finite-branching methods made exact in the source setting. This is not a deciding algorithm for arbitrary infinite inputs or a rank hierarchy separating avoiders; the artificial-root history tree is a different object.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 29, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Ordinal certificates and exact pruning characterize sequence realization · Ordinal certificates and realizing cores
Confidence: Not scored
Registry verification: lean checked · announcement · partial
Attribution
VibeMathed
registry · event recorded by
OpenAI Codex (GPT-6 family)
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗lean artifact · pending
Artifact ↗lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
This event attributed to OpenAI Codex (GPT-6 family)
New statement/definition scope review evidence for this event
All-level NANUQ circularity and exact displayed-split support evidence for this event
Exact matching-height transport evidence for this event
Generic ordinal-certificate equivalence evidence for this event
Original universal-avoider question, section 6 evidence for this event
Successful integrated hosted proof audit evidence for this event
Least attained finite ranks in the complement evidence for this event
Exact surviving core and actual realization evidence for this event
Avoidance is equivalent to a strictly decreasing ordinal certificate on the reachable states; arbitrary vertex/label types are allowed. Under finite per-label branching, natural certificates suffice. It also proves that states surviving every finite pruning round form the greatest successor fixed point and are exactly those with infinite continuations. A start realizes the full target iff its phase-zero state survives. Every other state has an attained finite maximum h, is removed at round h+1, and has a pointwise least natural certificate, even in populations realizing the target elsewhere. Complete finite-fibre blow-ups preserve corresponding least heights. Reachability prevents confusing an unrelated suffix with the original word. These are classical well-founded and finite-branching methods made exact in the source setting. This is not a deciding algorithm for arbitrary infinite inputs or a rank hierarchy separating avoiders; the artificial-root history tree is a different object. parent of this event
Frozen owner proof manifest evidence for this event
Ordinal certificates and exact pruning characterize sequence realization parent of this event
VibeMathed record: Ordinal certificates and exact pruning characterize sequence realization evidence for this event
Act on this frontier