Triple

T17549862
Position Surface form Disambiguated ID Type / Status
Subject Wirtinger presentation of knot groups E427429 entity
Predicate invariantUnder P4235 FINISHED
Object Reidemeister moves NE NERFINISHED

How this triple was built (2 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: Reidemeister moves | Statement: [Wirtinger presentation of knot groups, invariantUnder, Reidemeister moves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Reidemeister moves
Context triple: [Wirtinger presentation of knot groups, invariantUnder, Reidemeister moves]
  • A. Reidemeister moves chosen
    Reidemeister moves are the three local diagrammatic transformations in knot theory that characterize when two knot or link diagrams represent the same topological knot.
  • B. Dehn surgery
    Dehn surgery is a fundamental operation in 3-manifold topology that modifies a 3-dimensional manifold by cutting out a solid torus and gluing it back in a different way, playing a central role in the classification and study of 3-manifolds.
  • C. Dehn twist
    A Dehn twist is a fundamental type of self-homeomorphism of a surface obtained by cutting along a simple closed curve, twisting one side by 360 degrees, and gluing it back, playing a central role in low-dimensional topology and the study of mapping class groups.
  • D. Dehn–Lickorish theorem
    The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
  • E. Conway skein triple (L₊, L₋, L₀)
    The Conway skein triple (L₊, L₋, L₀) is a standard configuration of three related link diagrams used in knot theory to express how a link invariant, such as the Conway polynomial, changes under local crossing modifications.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d889df6dc081908f67dbadc03c07ee completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e45463ddf88190a2c29f3246adcb6e completed April 19, 2026, 4:04 a.m.
Created at: April 10, 2026, 5:50 a.m.