Triple

T12093916
Position Surface form Disambiguated ID Type / Status
Subject Sergei Novikov E288018 entity
Predicate knownFor P22 FINISHED
Object Novikov’s higher signature conjecture
Novikov’s higher signature conjecture is a major open problem in topology asserting that certain higher signatures of manifolds are homotopy invariants, linking manifold topology with operator algebras and index theory.
E962547 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: Novikov’s higher signature conjecture | Statement: [Sergei Novikov, knownFor, Novikov’s higher signature conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Novikov’s higher signature conjecture
Context triple: [Sergei Novikov, knownFor, Novikov’s higher signature conjecture]
  • A. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • B. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • C. Atiyah–Bott fixed-point theorem
    The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
  • D. The geometry of four-manifolds
    The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
  • E. Hopf conjecture (on Euler characteristic and curvature)
    The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
  • 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: Novikov’s higher signature conjecture
Triple: [Sergei Novikov, knownFor, Novikov’s higher signature conjecture]
Generated description
Novikov’s higher signature conjecture is a major open problem in topology asserting that certain higher signatures of manifolds are homotopy invariants, linking manifold topology with operator algebras and index theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Novikov’s higher signature conjecture
Target entity description: Novikov’s higher signature conjecture is a major open problem in topology asserting that certain higher signatures of manifolds are homotopy invariants, linking manifold topology with operator algebras and index theory.
  • A. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • B. Atiyah–Singer index theorem
    The Atiyah–Singer index theorem is a fundamental result in mathematics that links the analytical properties of elliptic differential operators to topological invariants of manifolds, unifying analysis, topology, and geometry.
  • C. Atiyah–Bott fixed-point theorem
    The Atiyah–Bott fixed-point theorem is a fundamental result in equivariant cohomology that expresses global invariants, such as indices of elliptic operators, in terms of local data at the fixed points of a group action.
  • D. The geometry of four-manifolds
    The Geometry of Four-Manifolds is a foundational monograph in differential geometry that develops the theory of smooth four-dimensional manifolds using gauge theory and Yang–Mills instantons.
  • E. Hopf conjecture (on Euler characteristic and curvature)
    The Hopf conjecture on Euler characteristic and curvature is an open problem in differential geometry proposing a deep link between the sign of a manifold’s Euler characteristic and the sign of its sectional curvature, especially for even-dimensional manifolds with positive or negative curvature.
  • 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_69d6ab4964708190850585628b287b0c completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d91550ce508190babf5755e1553734 completed April 10, 2026, 3:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69f5f66edf7881908f29b5b40b9d020f completed May 2, 2026, 1:04 p.m.
NEDg Description generation batch_69f5fd79da748190b3f0dd7d7a46314d completed May 2, 2026, 1:34 p.m.
NED2 Entity disambiguation (via description) batch_69f5feeeeb2081908191b1c2d1c2fbfd completed May 2, 2026, 1:41 p.m.
Created at: April 8, 2026, 9:48 p.m.