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.