lean artifact · pending
Artifact ↗Source authenticated
Lichter and Schweitzer's question: does witnessed symmetric choice strictly increase the expressive power of CPT with counting?
Theorem 1.1: over a vocabulary of eight binary relations there is a CPT+WSC sentence with a single WSC operator that returns a Boolean value on every finite structure and whose true-model class is not defined by any CPT sentence, even with counting and unbounded set rank; so CPT+WSC is strictly more expressive than CPT in Lichter and Schweitzer's sense. Not shown: whether CPT+WSC captures polynomial time, or the effect of nested WSC operators, both of which the paper leaves open.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Sep 24, 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: Lichter and Schweitzer's question: does witnessed symmetric choice strictly increase the expressive power of CPT with counting? · Witnessed symmetric choice beats CPT
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
lean artifact · pending
Artifact ↗Compute record
No linked compute attempts recorded.
Lineage and corrections
Lichter and Schweitzer's question: does witnessed symmetric choice strictly increase the expressive power of CPT with counting? parent of this event
This event attributed to Unreleased internal OpenAI model
Lichter and Schweitzer's question: does witnessed symmetric choice strictly increase the expressive power of CPT with counting? evidence for this event
Lean solution module OAI/Computability/WitnessedChoice/Main.lean evidence for this event
VibeMathed record: Lichter and Schweitzer's question: does witnessed symmetric choice strictly increase the expressive power of CPT with counting? evidence for this event
Lichter and Schweitzer, Choiceless Polynomial Time with Witnessed Symmetric Choice (arXiv 2205.14003) evidence for this event
Theorem 1.1: over a vocabulary of eight binary relations there is a CPT+WSC sentence with a single WSC operator that returns a Boolean value on every finite structure and whose true-model class is not defined by any CPT sentence, even with counting and unbounded set rank; so CPT+WSC is strictly more expressive than CPT in Lichter and Schweitzer's sense. Not shown: whether CPT+WSC captures polynomial time, or the effect of nested WSC operators, both of which the paper leaves open. parent of this event
Lean statement: WitnessedChoice.lean (comparator challenge) evidence for this event
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