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.