Triple

T7450502
Position Surface form Disambiguated ID Type / Status
Subject HOMFLY-PT polynomial E171994 entity
Predicate categorifiedBy P77174 FINISHED
Object HOMFLY-PT homology
HOMFLY-PT homology is a triply graded link homology theory in knot theory whose graded Euler characteristic recovers the HOMFLY-PT polynomial, providing a powerful categorified invariant of links.
E665095 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: HOMFLY-PT homology | Statement: [HOMFLY-PT polynomial, categorifiedBy, HOMFLY-PT homology]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: HOMFLY-PT homology
Context triple: [HOMFLY-PT polynomial, categorifiedBy, HOMFLY-PT homology]
  • A. Khovanov homology
    Khovanov homology is a powerful link invariant in knot theory that lifts the Jones polynomial to a graded homology theory, providing stronger topological information than the polynomial alone.
  • B. HOMFLY-PT polynomial
    The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
  • C. Jones polynomial
    The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
  • D. Kauffman polynomial
    The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
  • E. Witten–Reshetikhin–Turaev invariant
    The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
  • 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: HOMFLY-PT homology
Triple: [HOMFLY-PT polynomial, categorifiedBy, HOMFLY-PT homology]
Generated description
HOMFLY-PT homology is a triply graded link homology theory in knot theory whose graded Euler characteristic recovers the HOMFLY-PT polynomial, providing a powerful categorified invariant of links.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: HOMFLY-PT homology
Target entity description: HOMFLY-PT homology is a triply graded link homology theory in knot theory whose graded Euler characteristic recovers the HOMFLY-PT polynomial, providing a powerful categorified invariant of links.
  • A. Khovanov homology
    Khovanov homology is a powerful link invariant in knot theory that lifts the Jones polynomial to a graded homology theory, providing stronger topological information than the polynomial alone.
  • B. HOMFLY-PT polynomial
    The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
  • C. Jones polynomial
    The Jones polynomial is a powerful knot invariant in topology that assigns to each knot or link a Laurent polynomial, enabling the distinction of many knots that are indistinguishable by classical invariants.
  • D. Kauffman polynomial
    The Kauffman polynomial is a two-variable knot invariant in knot theory that generalizes and extends the information captured by the Jones polynomial.
  • E. Witten–Reshetikhin–Turaev invariant
    The Witten–Reshetikhin–Turaev invariant is a quantum invariant of 3-manifolds and links derived from Chern–Simons theory and quantum groups, playing a central role in low-dimensional topology and quantum topology.
  • 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_69c68a66554c8190add75c65942c0317 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f4ec85488190a1f7fb913e0fbe35 completed March 27, 2026, 9:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69c827b54a4881909f800bf37990a297 completed March 28, 2026, 7:10 p.m.
NEDg Description generation batch_69c828ca24bc81909357b9f40a9004af completed March 28, 2026, 7:15 p.m.
NED2 Entity disambiguation (via description) batch_69c8297c1de4819099acfac611a519e5 completed March 28, 2026, 7:18 p.m.
Created at: March 27, 2026, 3:14 p.m.