Triple

T22328673
Position Surface form Disambiguated ID Type / Status
Subject Strominger–Yau–Zaslow conjecture E551966 entity
Predicate relatedTo P37 FINISHED
Object Gross–Siebert program
The Gross–Siebert program is a research framework in algebraic and symplectic geometry that reconstructs and studies mirror pairs of Calabi–Yau varieties using tropical and log geometry inspired by the Strominger–Yau–Zaslow approach to mirror symmetry.
E1531313 NE FINISHED

How this triple was built (4 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: Gross–Siebert program | Statement: [Strominger–Yau–Zaslow conjecture, relatedTo, Gross–Siebert program]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gross–Siebert program
Context triple: [Strominger–Yau–Zaslow conjecture, relatedTo, Gross–Siebert program]
  • A. Strominger–Yau–Zaslow conjecture
    The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
  • B. Simons Collaboration on Homological Mirror Symmetry
    The Simons Collaboration on Homological Mirror Symmetry is a research initiative that brings together mathematicians and physicists to advance the theory and applications of homological mirror symmetry.
  • C. Donaldson–Thomas theory
    Donaldson–Thomas theory is a branch of algebraic geometry and mathematical physics that counts stable sheaves or ideal sheaves on Calabi–Yau threefolds, providing integer-valued invariants related to curve counting and string theory.
  • D. Duistermaat–Heckman formula
    The Duistermaat–Heckman formula is a result in symplectic geometry that describes how the pushforward of the Liouville measure under a moment map behaves, showing it is piecewise polynomial and linking geometry with equivariant localization techniques.
  • E. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Gross–Siebert program
Triple: [Strominger–Yau–Zaslow conjecture, relatedTo, Gross–Siebert program]
Generated description
The Gross–Siebert program is a research framework in algebraic and symplectic geometry that reconstructs and studies mirror pairs of Calabi–Yau varieties using tropical and log geometry inspired by the Strominger–Yau–Zaslow approach to mirror symmetry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gross–Siebert program
Target entity description: The Gross–Siebert program is a research framework in algebraic and symplectic geometry that reconstructs and studies mirror pairs of Calabi–Yau varieties using tropical and log geometry inspired by the Strominger–Yau–Zaslow approach to mirror symmetry.
  • A. Strominger–Yau–Zaslow conjecture
    The Strominger–Yau–Zaslow conjecture is a proposal in mirror symmetry stating that mirror pairs of Calabi–Yau manifolds can be understood as dual special Lagrangian torus fibrations, providing a geometric explanation of mirror symmetry.
  • B. Simons Collaboration on Homological Mirror Symmetry
    The Simons Collaboration on Homological Mirror Symmetry is a research initiative that brings together mathematicians and physicists to advance the theory and applications of homological mirror symmetry.
  • C. Donaldson–Thomas theory
    Donaldson–Thomas theory is a branch of algebraic geometry and mathematical physics that counts stable sheaves or ideal sheaves on Calabi–Yau threefolds, providing integer-valued invariants related to curve counting and string theory.
  • D. Duistermaat–Heckman formula
    The Duistermaat–Heckman formula is a result in symplectic geometry that describes how the pushforward of the Liouville measure under a moment map behaves, showing it is piecewise polynomial and linking geometry with equivariant localization techniques.
  • E. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • F. None of above. chosen

Provenance (5 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15769fdb48190b84e0c019ab63579 completed April 29, 2026, 12:57 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0ad523ecec8190a85eb932288965fb completed May 18, 2026, 9 a.m.
NEDg Description generation batch_6a0ad992b43c8190b0e409d64db83308 completed May 18, 2026, 9:19 a.m.
NED2 Entity disambiguation (via description) batch_6a0adac48bec8190989dd7c5e28d283a completed May 18, 2026, 9:24 a.m.
Created at: April 16, 2026, 8:43 p.m.