Triple

T14506454
Position Surface form Disambiguated ID Type / Status
Subject Penrose spin networks E340275 entity
Predicate vertexCondition P114496 FINISHED
Object Clebsch–Gordan constraints E262449 NE FINISHED

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: Clebsch–Gordan constraints | Statement: [Penrose spin networks, vertexCondition, Clebsch–Gordan constraints]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Clebsch–Gordan constraints
Context triple: [Penrose spin networks, vertexCondition, Clebsch–Gordan constraints]
  • A. Clebsch–Gordan coefficients chosen
    Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
  • B. Wigner–Eckart theorem
    The Wigner–Eckart theorem is a fundamental result in quantum mechanics that factorizes matrix elements of tensor operators into a reduced matrix element and a purely geometric part given by Clebsch–Gordan coefficients, greatly simplifying angular momentum calculations.
  • C. Schur–Weyl duality
    Schur–Weyl duality is a fundamental result in representation theory that links representations of the symmetric group and the general linear group via their commuting actions on tensor powers of a vector space.
  • D. Wigner 3j symbols
    Wigner 3j symbols are mathematical coefficients used in quantum mechanics and angular momentum theory to describe the coupling and recoupling of three angular momenta with well-defined symmetry properties.
  • E. Clebsch representation
    The Clebsch representation is a mathematical formulation in fluid dynamics and vector calculus that expresses a three-dimensional vector field, particularly a velocity field, in terms of scalar potential functions.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d822d9c0408190b9a2b3643e58bb4d completed April 9, 2026, 10:06 p.m.
NER Named-entity recognition batch_69de94e25a2481908b8394e9a19f3b64 completed April 14, 2026, 7:26 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd6da07ff481909fb2463b0ea92849 completed May 8, 2026, 4:59 a.m.
Created at: April 10, 2026, 1:21 a.m.