Triple
T7450466
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | HOMFLY-PT polynomial |
E171994
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Alexander polynomial
The Alexander polynomial is a classical knot invariant in algebraic topology that assigns a Laurent polynomial to each knot or link, capturing essential information about its topological structure.
|
E665082
|
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: Alexander polynomial | Statement: [HOMFLY-PT polynomial, generalizes, Alexander polynomial]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Alexander polynomial Context triple: [HOMFLY-PT polynomial, generalizes, Alexander 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.
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.
-
C.
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.
-
D.
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.
-
E.
Arf invariant
The Arf invariant is an algebraic invariant in topology and quadratic form theory that classifies certain quadratic forms over fields of characteristic two and plays a key role in knot theory and surgery theory.
- 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: Alexander polynomial Triple: [HOMFLY-PT polynomial, generalizes, Alexander polynomial]
Generated description
The Alexander polynomial is a classical knot invariant in algebraic topology that assigns a Laurent polynomial to each knot or link, capturing essential information about its topological structure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Alexander polynomial Target entity description: The Alexander polynomial is a classical knot invariant in algebraic topology that assigns a Laurent polynomial to each knot or link, capturing essential information about its topological structure.
-
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.
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.
-
C.
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.
-
D.
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.
-
E.
Arf invariant
The Arf invariant is an algebraic invariant in topology and quadratic form theory that classifies certain quadratic forms over fields of characteristic two and plays a key role in knot theory and surgery theory.
- 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_69c6f38af3fc8190bc5c57ca89d976bc |
completed | March 27, 2026, 9:15 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.