Triple

T21046355
Position Surface form Disambiguated ID Type / Status
Subject Thurston norm E518459 entity
Predicate relatedInvariant P37 FINISHED
Object Gromov norm
The Gromov norm is a topological invariant of manifolds that measures the “size” of their fundamental class via the minimal ℓ¹-norm of singular chains representing it, closely linked to simplicial volume and geometric structures.
E1463319 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: Gromov norm | Statement: [Thurston norm, relatedInvariant, Gromov norm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gromov norm
Context triple: [Thurston norm, relatedInvariant, Gromov norm]
  • A. Thurston norm
    The Thurston norm is a topological invariant on the second homology of a 3-manifold that measures the minimal complexity (via Euler characteristic) of embedded surfaces representing a given homology class.
  • B. Gromov’s systolic inequality
    Gromov’s systolic inequality is a fundamental result in Riemannian geometry that bounds the volume of a manifold from below in terms of the length of its shortest non-contractible loop (the systole).
  • C. Gromov compactness theorem
    The Gromov compactness theorem is a fundamental result in symplectic geometry and geometric analysis that provides compactness for families of pseudoholomorphic curves (or Riemannian manifolds with bounded geometry) up to bubbling and degeneration.
  • D. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • E. Dehn function
    The Dehn function is a mathematical tool in geometric group theory that measures the complexity of filling loops with discs in a space or group, quantifying the difficulty of solving the word problem.
  • 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: Gromov norm
Triple: [Thurston norm, relatedInvariant, Gromov norm]
Generated description
The Gromov norm is a topological invariant of manifolds that measures the “size” of their fundamental class via the minimal ℓ¹-norm of singular chains representing it, closely linked to simplicial volume and geometric structures.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gromov norm
Target entity description: The Gromov norm is a topological invariant of manifolds that measures the “size” of their fundamental class via the minimal ℓ¹-norm of singular chains representing it, closely linked to simplicial volume and geometric structures.
  • A. Thurston norm
    The Thurston norm is a topological invariant on the second homology of a 3-manifold that measures the minimal complexity (via Euler characteristic) of embedded surfaces representing a given homology class.
  • B. Gromov’s systolic inequality
    Gromov’s systolic inequality is a fundamental result in Riemannian geometry that bounds the volume of a manifold from below in terms of the length of its shortest non-contractible loop (the systole).
  • C. Gromov compactness theorem
    The Gromov compactness theorem is a fundamental result in symplectic geometry and geometric analysis that provides compactness for families of pseudoholomorphic curves (or Riemannian manifolds with bounded geometry) up to bubbling and degeneration.
  • D. Cheeger–Gromov compactness theorem
    The Cheeger–Gromov compactness theorem is a fundamental result in Riemannian geometry that gives conditions under which a sequence of Riemannian manifolds has a subsequence converging (in the Gromov–Hausdorff or smooth sense) to a limit space.
  • E. Dehn function
    The Dehn function is a mathematical tool in geometric group theory that measures the complexity of filling loops with discs in a space or group, quantifying the difficulty of solving the word problem.
  • 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf3cac081909915a440fbb5c084 completed April 21, 2026, 4:28 a.m.
NED1 Entity disambiguation (via context triple) batch_6a09475512b081908ceb38a118b0f026 completed May 17, 2026, 4:43 a.m.
NEDg Description generation batch_6a09489e80288190b401d11ccde39dc1 completed May 17, 2026, 4:48 a.m.
NED2 Entity disambiguation (via description) batch_6a094995d5bc8190b25d328dbf06b8b1 completed May 17, 2026, 4:52 a.m.
Created at: April 16, 2026, 2:34 p.m.