Triple

T22965055
Position Surface form Disambiguated ID Type / Status
Subject Bombieri–Lang conjecture E571015 entity
Predicate relatedTo P37 FINISHED
Object Campana conjecture
The Campana conjecture is a major open problem in arithmetic geometry that predicts strong restrictions on rational and integral points on certain complex varieties, generalizing and refining ideas about hyperbolicity and Diophantine finiteness.
E1563179 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: Campana conjecture | Statement: [Bombieri–Lang conjecture, relatedTo, Campana conjecture]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Campana conjecture
Context triple: [Bombieri–Lang conjecture, relatedTo, Campana conjecture]
  • A. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • B. Poincaré conjecture
    The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
  • C. geometrization conjecture
    The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
  • D. Bieberbach conjecture
    The Bieberbach conjecture, now a theorem, is a landmark result in complex analysis that characterizes the size of Taylor coefficients of normalized univalent (injective) holomorphic functions on the unit disk.
  • E. Mauldin’s conjecture
    Mauldin’s conjecture, more commonly known as the Beal conjecture, is an unsolved problem in number theory asserting that any solution in positive integers to A^x + B^y = C^z with exponents greater than 2 must have A, B, and C sharing a common prime factor.
  • 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: Campana conjecture
Triple: [Bombieri–Lang conjecture, relatedTo, Campana conjecture]
Generated description
The Campana conjecture is a major open problem in arithmetic geometry that predicts strong restrictions on rational and integral points on certain complex varieties, generalizing and refining ideas about hyperbolicity and Diophantine finiteness.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Campana conjecture
Target entity description: The Campana conjecture is a major open problem in arithmetic geometry that predicts strong restrictions on rational and integral points on certain complex varieties, generalizing and refining ideas about hyperbolicity and Diophantine finiteness.
  • A. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • B. Poincaré conjecture
    The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
  • C. geometrization conjecture
    The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
  • D. Bieberbach conjecture
    The Bieberbach conjecture, now a theorem, is a landmark result in complex analysis that characterizes the size of Taylor coefficients of normalized univalent (injective) holomorphic functions on the unit disk.
  • E. Mauldin’s conjecture
    Mauldin’s conjecture, more commonly known as the Beal conjecture, is an unsolved problem in number theory asserting that any solution in positive integers to A^x + B^y = C^z with exponents greater than 2 must have A, B, and C sharing a common prime factor.
  • 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_69e245b212a88190b5259caf51606084 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f181f763688190aab8f444a1a71577 completed April 29, 2026, 3:58 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0bca22caa88190889e965c78477a96 completed May 19, 2026, 2:25 a.m.
NEDg Description generation batch_6a0bcb1904c88190ac32e5709bc95858 completed May 19, 2026, 2:29 a.m.
NED2 Entity disambiguation (via description) batch_6a0bcbb8793881909621b16c9ad51cbb completed May 19, 2026, 2:32 a.m.
Created at: April 17, 2026, 3:47 p.m.