Triple

T10829392
Position Surface form Disambiguated ID Type / Status
Subject Atiyah–Hirzebruch spectral sequence E255575 entity
Predicate hasVariant P455 FINISHED
Object homological Atiyah–Hirzebruch spectral sequence E255575 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: homological Atiyah–Hirzebruch spectral sequence | Statement: [Atiyah–Hirzebruch spectral sequence, hasVariant, homological Atiyah–Hirzebruch spectral sequence]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: homological Atiyah–Hirzebruch spectral sequence
Context triple: [Atiyah–Hirzebruch spectral sequence, hasVariant, homological Atiyah–Hirzebruch spectral sequence]
  • A. Atiyah–Hirzebruch spectral sequence chosen
    The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
  • B. Cartan–Eilenberg spectral sequence
    The Cartan–Eilenberg spectral sequence is a fundamental tool in homological algebra that computes derived functors (such as Ext and Tor) of composite functors via a double complex construction.
  • C. Grothendieck spectral sequence
    The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
  • D. Serre spectral sequence
    The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • 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_69d6aa8081448190a9324184f2bd1c26 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d74420fa188190b5b3c59e1a9f551d completed April 9, 2026, 6:16 a.m.
NED1 Entity disambiguation (via context triple) batch_69de85a068b08190948c3ca32cdda147 completed April 14, 2026, 6:21 p.m.
Created at: April 8, 2026, 9:19 p.m.