Triple

T36363522
Position Surface form Disambiguated ID Type / Status
Subject Pósa’s theorem E895558 entity
Predicate hasWeakerFormulation P185415 FINISHED
Object If G is a graph on n ≥ 3 vertices with degree sequence d1 ≤ d2 ≤ … ≤ dn and for every integer k with 1 ≤ k < n/2, dk ≥ k+1 or dn−k ≥ n−k, then G has a Hamiltonian cycle — LITERAL FINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: If G is a graph on n ≥ 3 vertices with degree sequence d1 ≤ d2 ≤ … ≤ dn and for every integer k with 1 ≤ k < n/2, dk ≥ k+1 or dn−k ≥ n−k, then G has a Hamiltonian cycle | Statement: [Pósa’s theorem, hasWeakerFormulation, If G is a graph on n ≥ 3 vertices with degree sequence d1 ≤ d2 ≤ … ≤ dn and for every integer k with 1 ≤ k < n/2, dk ≥ k+1 or dn−k ≥ n−k, then G has a Hamiltonian cycle]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasWeakerFormulation
Context triple: [Pósa’s theorem, hasWeakerFormulation, If G is a graph on n ≥ 3 vertices with degree sequence d1 ≤ d2 ≤ … ≤ dn and for every integer k with 1 ≤ k < n/2, dk ≥ k+1 or dn−k ≥ n−k, then G has a Hamiltonian cycle]
  • A. hasEquivalentFormulation
    Indicates that two representations, statements, or formulations express the same underlying meaning, condition, or effect, even if they differ in form.
  • B. hasCanonicalFormulation
    Indicates that one entity is the standard or officially accepted formulation or expression of another entity.
  • C. hasFormulation
    Indicates that one entity is expressed, prepared, or configured in a particular form or composition defined by another entity.
  • D. weakerThan
    Indicates that one entity has less strength, power, or effectiveness than another entity.
  • E. hasFormulationType
    Indicates the specific way something is physically prepared or presented, such as its dosage form, composition, or delivery format.
  • F. None of above. chosen

Provenance (4 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69f76e5044248190b390d8887dc03254 completed May 3, 2026, 3:48 p.m.
NER Named-entity recognition batch_69f7be9d07ac8190adf796cbef60daf6 completed May 3, 2026, 9:31 p.m.
PD Predicate disambiguation batch_69f7bcccd7988190aa5c931ff347d33c completed May 3, 2026, 9:23 p.m.
PDg Predicate description generation batch_69f7be9b9ab481908328e0e8d8ac73d4 completed May 3, 2026, 9:31 p.m.
Created at: May 3, 2026, 4:10 p.m.