Triple
T3748398
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Erhard Schmidt |
E81265
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Schmidt decomposition
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
|
E384561
|
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: Schmidt decomposition | Statement: [Erhard Schmidt, notableWork, Schmidt decomposition]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schmidt decomposition Context triple: [Erhard Schmidt, notableWork, Schmidt decomposition]
-
A.
Clebsch–Gordan coefficients
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.
Kronecker product
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
-
D.
SVD
SVD is the abbreviation for the Special Victims Division, a specialized police unit that investigates sensitive crimes such as sexual offenses and crimes against vulnerable victims.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- 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: Schmidt decomposition Triple: [Erhard Schmidt, notableWork, Schmidt decomposition]
Generated description
The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Schmidt decomposition Target entity description: The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
-
A.
Clebsch–Gordan coefficients
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.
Kronecker product
The Kronecker product is a matrix operation that forms a large block matrix from two smaller matrices and is widely used in linear algebra, quantum computing, and signal processing.
-
D.
SVD
SVD is the abbreviation for the Special Victims Division, a specialized police unit that investigates sensitive crimes such as sexual offenses and crimes against vulnerable victims.
-
E.
Born–Huang expansion
The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
- 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_69ad8b19b7b08190a6188804e99c53e9 |
completed | March 8, 2026, 2:43 p.m. |
| NER | Named-entity recognition | batch_69adcb6ac5ac8190934ec1a6c887a8f5 |
completed | March 8, 2026, 7:18 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b4db2f5e9881908c10feafbb569f48 |
completed | March 14, 2026, 3:51 a.m. |
| NEDg | Description generation | batch_69b4df1cfd348190831cc472de055436 |
completed | March 14, 2026, 4:07 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69b4df7b2da881908aef158d79c2834c |
completed | March 14, 2026, 4:09 a.m. |
Created at: March 8, 2026, 3:35 p.m.