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.