Triple

T5191845
Position Surface form Disambiguated ID Type / Status
Subject Charles Hermite E117173 entity
Predicate knownFor P22 FINISHED
Object Hermitian forms (work on quadratic forms)
Hermitian forms (work on quadratic forms) are a class of complex-valued quadratic forms that are linear in one variable and conjugate-linear in the other, generalizing real symmetric quadratic forms and playing a central role in linear algebra and functional analysis.
E502192 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: Hermitian forms (work on quadratic forms) | Statement: [Charles Hermite, knownFor, Hermitian forms (work on quadratic forms)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hermitian forms (work on quadratic forms)
Context triple: [Charles Hermite, knownFor, Hermitian forms (work on quadratic forms)]
  • A. Über die Bildung des Formensystems der ternären biquadratischen Form
    "Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
  • B. Hilbert’s seventeenth problem
    Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
  • C. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • D. Jacobi’s four-square theorem
    Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
  • E. Theorie der binären algebraischen Formen
    "Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
  • 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: Hermitian forms (work on quadratic forms)
Triple: [Charles Hermite, knownFor, Hermitian forms (work on quadratic forms)]
Generated description
Hermitian forms (work on quadratic forms) are a class of complex-valued quadratic forms that are linear in one variable and conjugate-linear in the other, generalizing real symmetric quadratic forms and playing a central role in linear algebra and functional analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hermitian forms (work on quadratic forms)
Target entity description: Hermitian forms (work on quadratic forms) are a class of complex-valued quadratic forms that are linear in one variable and conjugate-linear in the other, generalizing real symmetric quadratic forms and playing a central role in linear algebra and functional analysis.
  • A. Über die Bildung des Formensystems der ternären biquadratischen Form
    "Über die Bildung des Formensystems der ternären biquadratischen Form" is the 1907 doctoral dissertation of mathematician Emmy Noether, in which she investigates the invariant theory of certain higher-degree algebraic forms.
  • B. Hilbert’s seventeenth problem
    Hilbert’s seventeenth problem is a famous question in real algebraic geometry asking whether every nonnegative polynomial can be represented as a sum of squares of rational functions.
  • C. The Classical Groups: Their Invariants and Representations
    The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
  • D. Jacobi’s four-square theorem
    Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
  • E. Theorie der binären algebraischen Formen
    "Theorie der binären algebraischen Formen" is a foundational 19th-century mathematical treatise by Alfred Clebsch on the theory of binary algebraic forms and invariants.
  • 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_69bd44620ff48190bcac01782107a397 completed March 20, 2026, 12:58 p.m.
NER Named-entity recognition batch_69bd79ed61c88190bda492f6489f44de completed March 20, 2026, 4:46 p.m.
NED1 Entity disambiguation (via context triple) batch_69bee0943ce48190838aff0cfd12c655 completed March 21, 2026, 6:16 p.m.
NEDg Description generation batch_69bee5fc0c408190b4ad4b77e0045182 completed March 21, 2026, 6:39 p.m.
NED2 Entity disambiguation (via description) batch_69bee6b954c08190a353ebcfe829888a completed March 21, 2026, 6:43 p.m.
Created at: March 20, 2026, 1:46 p.m.