Triple
T10543863
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carl Ludwig Siegel |
E248763
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Siegel mass formula
The Siegel mass formula is a fundamental result in number theory that relates the weighted count (mass) of quadratic forms in a given genus to special values of zeta and L-functions, providing deep connections between arithmetic and geometry.
|
E871399
|
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: Siegel mass formula | Statement: [Carl Ludwig Siegel, notableWork, Siegel mass formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Siegel mass formula Context triple: [Carl Ludwig Siegel, notableWork, Siegel mass formula]
-
A.
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.
-
B.
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.
-
C.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
-
D.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
-
E.
Siegel's theorem on integral points
Siegel's theorem on integral points is a fundamental result in number theory and Diophantine geometry stating that certain algebraic curves, notably those of genus at least one, have only finitely many integral points.
- 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: Siegel mass formula Triple: [Carl Ludwig Siegel, notableWork, Siegel mass formula]
Generated description
The Siegel mass formula is a fundamental result in number theory that relates the weighted count (mass) of quadratic forms in a given genus to special values of zeta and L-functions, providing deep connections between arithmetic and geometry.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Siegel mass formula Target entity description: The Siegel mass formula is a fundamental result in number theory that relates the weighted count (mass) of quadratic forms in a given genus to special values of zeta and L-functions, providing deep connections between arithmetic and geometry.
-
A.
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.
-
B.
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.
-
C.
Selberg trace formula
The Selberg trace formula is a fundamental result in analytic number theory and spectral theory that relates lengths of closed geodesics on a Riemannian manifold to the spectrum of its Laplace operator, serving as a non-abelian analogue of the Poisson summation formula.
-
D.
Siegel’s theorem on zeros of L-functions
Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
-
E.
Siegel's theorem on integral points
Siegel's theorem on integral points is a fundamental result in number theory and Diophantine geometry stating that certain algebraic curves, notably those of genus at least one, have only finitely many integral points.
- 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_69d381c733c08190ab1dd6239f5f34ae |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d51911b10481909e6e548879e8de36 |
completed | April 7, 2026, 2:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d9343c5c308190952596e5254b6a65 |
completed | April 10, 2026, 5:32 p.m. |
| NEDg | Description generation | batch_69d938c697f481908a93296ee7f82eae |
completed | April 10, 2026, 5:52 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d940176c988190b7583ce9f2c21898 |
completed | April 10, 2026, 6:23 p.m. |
Created at: April 6, 2026, 12:32 p.m.