Triple

T1483881
Position Surface form Disambiguated ID Type / Status
Subject Conway polynomial E29419 entity
Predicate relatedInvariant P37 FINISHED
Object 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.
E171994 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 polynomial | Statement: [Conway polynomial, relatedInvariant, HOMFLY-PT polynomial]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: HOMFLY-PT polynomial
Context triple: [Conway polynomial, relatedInvariant, HOMFLY-PT polynomial]
  • A. 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.
  • B. Conway polynomial
    The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
  • C. Dowker–Thistlethwaite notation
    Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
  • D. Conway skein triple (L₊, L₋, L₀)
    The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
  • E. Conway notation for knots
    Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
  • 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 polynomial
Triple: [Conway polynomial, relatedInvariant, HOMFLY-PT polynomial]
Generated description
The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: HOMFLY-PT polynomial
Target entity description: The HOMFLY-PT polynomial is a powerful knot and link invariant in knot theory that generalizes both the Alexander and Jones polynomials.
  • A. 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.
  • B. Conway polynomial
    The Conway polynomial is an invariant of knots and links in topology that assigns a polynomial to each knot, capturing essential information about its structure and helping distinguish non-equivalent knots.
  • C. Dowker–Thistlethwaite notation
    Dowker–Thistlethwaite notation is a numerical encoding system used in knot theory to uniquely represent knot diagrams and facilitate their classification and study.
  • D. Conway skein triple (L₊, L₋, L₀)
    The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
  • E. Conway notation for knots
    Conway notation for knots is a mathematical system introduced by John H. Conway that encodes knot and link diagrams into concise symbolic expressions to classify and study them.
  • 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_69a498da82e08190ba833330d05f380f completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c9e02c188190b87c0aac939eafdd completed March 1, 2026, 11:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad232d039c8190840719485e214bfc completed March 8, 2026, 7:20 a.m.
NEDg Description generation batch_69ad2399f8408190872be9c2f04644ca completed March 8, 2026, 7:22 a.m.
NED2 Entity disambiguation (via description) batch_69ad247476d08190827501ff5b380646 completed March 8, 2026, 7:25 a.m.
Created at: March 1, 2026, 8:12 p.m.