Triple

T12797585
Position Surface form Disambiguated ID Type / Status
Subject Algebraic Topology E305928 entity
Predicate developsConcept P201 FINISHED
Object universal coefficient theorem E911366 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: universal coefficient theorem | Statement: [Algebraic Topology, developsConcept, universal coefficient theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: universal coefficient theorem
Context triple: [Algebraic Topology, developsConcept, universal coefficient theorem]
  • A. universal coefficient theorem chosen
    The universal coefficient theorem is a fundamental result in algebraic topology that relates the homology or cohomology groups of a space with coefficients in an arbitrary abelian group to those with integer coefficients via Ext and Tor functors.
  • B. Bockstein homomorphism
    The Bockstein homomorphism is a connecting homomorphism in cohomology arising from a short exact sequence of coefficient groups, used to relate and detect characteristic classes and torsion phenomena in topology.
  • C. Künneth formula
    The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
  • D. Hurewicz homomorphism
    The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
  • E. Grothendieck–Riemann–Roch theorem
    The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
  • 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_69d7bdf366888190a8cccb982606889c completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d96e6db68481909a2ca8da1287f3e0 completed April 10, 2026, 9:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69f6850d6ebc8190aaffcac09f4b15eb completed May 2, 2026, 11:13 p.m.
Created at: April 9, 2026, 5:30 p.m.