Triple
T7304623
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | J. W. S. Cassels |
E167942
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Rational Quadratic Forms
Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
|
E654583
|
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: Rational Quadratic Forms | Statement: [J. W. S. Cassels, notableWork, Rational Quadratic Forms]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Rational Quadratic Forms Context triple: [J. W. S. Cassels, notableWork, Rational Quadratic Forms]
-
A.
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.
-
B.
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.
-
C.
Higher composition laws I–IV
Higher composition laws I–IV is a landmark four-part series of papers by Manjul Bhargava that generalizes Gauss’s composition of binary quadratic forms and develops new structures and methods in algebraic number theory.
-
D.
Gaussian rationals ℚ(i)
Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
-
E.
Hodge–Riemann bilinear relations
The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
- 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: Rational Quadratic Forms Triple: [J. W. S. Cassels, notableWork, Rational Quadratic Forms]
Generated description
Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Rational Quadratic Forms Target entity description: Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
-
A.
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.
-
B.
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.
-
C.
Higher composition laws I–IV
Higher composition laws I–IV is a landmark four-part series of papers by Manjul Bhargava that generalizes Gauss’s composition of binary quadratic forms and develops new structures and methods in algebraic number theory.
-
D.
Gaussian rationals ℚ(i)
Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
-
E.
Hodge–Riemann bilinear relations
The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
- 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_69c6888c820881909fc68f689fe1c251 |
completed | March 27, 2026, 1:39 p.m. |
| NER | Named-entity recognition | batch_69c6ebb352ec8190846eff044e08805e |
completed | March 27, 2026, 8:42 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7e55bfccc8190a46067c60c3c1a3f |
completed | March 28, 2026, 2:27 p.m. |
| NEDg | Description generation | batch_69c7e5fbe8a8819083a892f4e54013eb |
completed | March 28, 2026, 2:30 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69c7e69ca1ac8190a398da894c6cc04e |
completed | March 28, 2026, 2:33 p.m. |
Created at: March 27, 2026, 3:01 p.m.