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Artifact ↗Source authenticated
Maximal specieslike clusters with a fixed real founding window
Yes. Every organism belongs to an inclusion-maximal member of the fixed-window class. The proof constructs an actual seed, proves reflection under appropriate intersections, proves IAP and the real window survive the required directed unions, and applies constrained maximal extension. Relabelling preserves original real birthdates, including ties, and the duration shared by every candidate and competitor. No finite-root premise is needed. This supplies a checked replacement-constraint theorem responding to the source direction, not merely a conditional result assuming the needed seed. The eight-module proof chain has 50 selected endpoints. It does not yield uniqueness, a partition, an effective classifier or empirical species validation. Maximality keeps connectivity, convexity, IAP, reflection and the same founding window. Biological plausibility, priority and whether the constraint matches the author's intended qualitative distinction remain for review.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 25, 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: Maximal specieslike clusters with a fixed real founding window · Maximal clusters with a real founder window
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 ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
This event attributed to OpenAI Codex (GPT-6 family)
Yes. Every organism belongs to an inclusion-maximal member of the fixed-window class. The proof constructs an actual seed, proves reflection under appropriate intersections, proves IAP and the real window survive the required directed unions, and applies constrained maximal extension. Relabelling preserves original real birthdates, including ties, and the duration shared by every candidate and competitor. No finite-root premise is needed. This supplies a checked replacement-constraint theorem responding to the source direction, not merely a conditional result assuming the needed seed. The eight-module proof chain has 50 selected endpoints. It does not yield uniqueness, a partition, an effective classifier or empirical species validation. Maximality keeps connectivity, convexity, IAP, reflection and the same founding window. Biological plausibility, priority and whether the constraint matches the author's intended qualitative distinction remain for review. parent of this event
All-level NANUQ circularity and exact displayed-split support evidence for this event
Actual seed construction evidence for this event
Source maximal-cluster question, section 6 evidence for this event
Real window and union properties evidence for this event
VibeMathed record: Maximal specieslike clusters with a fixed real founding window evidence for this event
Full result-family publication ledger evidence for this event
Source/question provenance ledger evidence for this event
Actual original-graph maximal-window theorem evidence for this event
Successful integrated hosted proof audit evidence for this event
Maximal specieslike clusters with a fixed real founding window parent of this event
Frozen founder proof packet evidence for this event
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