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.