Triple

T6150020
Position Surface form Disambiguated ID Type / Status
Subject Enrico Bombieri E137175 entity
Predicate knownFor P22 FINISHED
Object Bombieri–Lang conjecture
The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
E571015 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: Bombieri–Lang conjecture | Statement: [Enrico Bombieri, knownFor, Bombieri–Lang conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bombieri–Lang conjecture
Context triple: [Enrico Bombieri, knownFor, Bombieri–Lang conjecture]
  • A. Faltings' theorem
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • B. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • C. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • E. Taniyama–Shimura–Weil conjecture
    The Taniyama–Shimura–Weil conjecture, now the modularity theorem, asserts that every elliptic curve over the rational numbers is modular and played a central role in the proof of Fermat’s Last 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: Bombieri–Lang conjecture
Triple: [Enrico Bombieri, knownFor, Bombieri–Lang conjecture]
Generated description
The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bombieri–Lang conjecture
Target entity description: The Bombieri–Lang conjecture is a major unsolved conjecture in number theory and arithmetic geometry predicting that varieties of general type over number fields have only finitely many rational points.
  • A. Faltings' theorem
    Faltings' theorem is a landmark result in arithmetic geometry that proves every algebraic curve of genus greater than one over a number field has only finitely many rational points.
  • B. Birch and Swinnerton-Dyer Conjecture
    The Birch and Swinnerton-Dyer Conjecture is a central unsolved problem in number theory that predicts a deep connection between the arithmetic of rational points on an elliptic curve and the behavior of its associated L-function at a specific value.
  • C. Weil conjectures
    The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • E. Taniyama–Shimura–Weil conjecture
    The Taniyama–Shimura–Weil conjecture, now the modularity theorem, asserts that every elliptic curve over the rational numbers is modular and played a central role in the proof of Fermat’s Last 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_69c008a2c6308190a56519b22d55d083 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c05ce329648190a03ba0233df841fa completed March 22, 2026, 9:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c13608944481909e22df6131a06e41 completed March 23, 2026, 12:46 p.m.
NEDg Description generation batch_69c13679dd58819099036d1119fa370b completed March 23, 2026, 12:47 p.m.
NED2 Entity disambiguation (via description) batch_69c1376db6a0819087c0d0aebc2e2b3e completed March 23, 2026, 12:51 p.m.
Created at: March 22, 2026, 4:16 p.m.