Triple

T12596929
Position Surface form Disambiguated ID Type / Status
Subject Hamiltonian mechanics E300756 entity
Predicate relatedConcept P37 FINISHED
Object Liouville’s theorem E620665 NE 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: Liouville’s theorem | Statement: [Hamiltonian mechanics, relatedConcept, Liouville’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Liouville’s theorem
Context triple: [Hamiltonian mechanics, relatedConcept, Liouville’s theorem]
  • A. Liouville's theorem
    Liouville's theorem is a fundamental result in complex analysis stating that any bounded entire function must be constant.
  • B. Liouville's theorem in Hamiltonian mechanics chosen
    Liouville's theorem in Hamiltonian mechanics states that the phase-space volume occupied by an ensemble of systems evolving under Hamiltonian dynamics is conserved over time, implying incompressible flow in phase space.
  • C. Liouville equation
    The Liouville equation is a fundamental differential equation in statistical mechanics and Hamiltonian dynamics that governs the time evolution of a system’s phase-space probability density.
  • D. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • E. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
Created at: April 9, 2026, 5:08 p.m.