Triple

T10973518
Position Surface form Disambiguated ID Type / Status
Subject John Tate E259307 entity
Predicate notableWork P4 FINISHED
Object Tate’s non-archimedean uniformization of elliptic curves
Tate’s non-archimedean uniformization of elliptic curves is a foundational theory in arithmetic geometry that describes certain elliptic curves over non-archimedean fields via analytic uniformization using formal q-expansions, leading to what are now called Tate curves.
E896827 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: Tate’s non-archimedean uniformization of elliptic curves | Statement: [John Tate, notableWork, Tate’s non-archimedean uniformization of elliptic curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Tate’s non-archimedean uniformization of elliptic curves
Context triple: [John Tate, notableWork, Tate’s non-archimedean uniformization of elliptic curves]
  • A. Sato–Tate distribution (for families of elliptic curves)
    The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
  • B. Introduction to Elliptic Curves and Modular Forms
    Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
  • C. Lectures on Elliptic Curves
    Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
  • D. 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.
  • E. Hasse bound for elliptic curves
    The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
  • 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: Tate’s non-archimedean uniformization of elliptic curves
Triple: [John Tate, notableWork, Tate’s non-archimedean uniformization of elliptic curves]
Generated description
Tate’s non-archimedean uniformization of elliptic curves is a foundational theory in arithmetic geometry that describes certain elliptic curves over non-archimedean fields via analytic uniformization using formal q-expansions, leading to what are now called Tate curves.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Tate’s non-archimedean uniformization of elliptic curves
Target entity description: Tate’s non-archimedean uniformization of elliptic curves is a foundational theory in arithmetic geometry that describes certain elliptic curves over non-archimedean fields via analytic uniformization using formal q-expansions, leading to what are now called Tate curves.
  • A. Sato–Tate distribution (for families of elliptic curves)
    The Sato–Tate distribution (for families of elliptic curves) is a probabilistic law describing how the normalized Frobenius traces (or equivalently, the angles in the Hasse bound) of elliptic curves are distributed, typically following a specific sine-squared measure on the interval [0, π].
  • B. Introduction to Elliptic Curves and Modular Forms
    Introduction to Elliptic Curves and Modular Forms is a graduate-level mathematics textbook that develops the theory of elliptic curves and their deep connections to modular forms, number theory, and arithmetic geometry.
  • C. Lectures on Elliptic Curves
    Lectures on Elliptic Curves is a classic introductory monograph by J. W. S. Cassels that systematically develops the arithmetic theory of elliptic curves for advanced undergraduates and beginning graduate students in number theory.
  • D. 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.
  • E. Hasse bound for elliptic curves
    The Hasse bound for elliptic curves is a fundamental result in number theory that gives tight limits on how far the number of points on an elliptic curve over a finite field can deviate from the size of the field plus one.
  • 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_69d6aa895f4c8190887a15460ef622f4 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d7719c16648190ab5a87abb1c61990 completed April 9, 2026, 9:30 a.m.
NED1 Entity disambiguation (via context triple) batch_69e2d7a0b3dc819084fbda3227caf5b5 completed April 18, 2026, 1 a.m.
NEDg Description generation batch_69e2ff211ae88190a40380cd25a61812 completed April 18, 2026, 3:48 a.m.
NED2 Entity disambiguation (via description) batch_69e32634397481908284c04448274b25 completed April 18, 2026, 6:35 a.m.
Created at: April 8, 2026, 9:24 p.m.