Triple
T7281888
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cahit Arf |
E163168
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
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.
|
E654172
|
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: Arf invariant | Statement: [Cahit Arf, knownFor, Arf invariant]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Arf invariant Context triple: [Cahit Arf, knownFor, Arf invariant]
-
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.
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.
-
C.
Milnor number
The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
-
D.
Donaldson invariants
Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
-
E.
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.
- 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: Arf invariant Triple: [Cahit Arf, knownFor, Arf invariant]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Arf invariant Target entity description: 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.
-
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.
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.
-
C.
Milnor number
The Milnor number is an invariant in singularity theory that measures the complexity of an isolated critical point of a complex hypersurface or function.
-
D.
Donaldson invariants
Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
-
E.
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.
- 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_69c6885c5964819085b209701769877f |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6eb4d3e3c8190a05cb5af5f52bd75 |
completed | March 27, 2026, 8:40 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7db3ae6a08190820c7096cbfea521 |
completed | March 28, 2026, 1:44 p.m. |
| NEDg | Description generation | batch_69c7dbe3e2ac8190a112ff01244f6a81 |
completed | March 28, 2026, 1:47 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7dfc15d2c8190afcf8572ff3dbb6d |
completed | March 28, 2026, 2:03 p.m. |
Created at: March 27, 2026, 2:59 p.m.