Triple

T7743537
Position Surface form Disambiguated ID Type / Status
Subject Birch and Swinnerton-Dyer Conjecture E175567 entity
Predicate relatesConcept P463 FINISHED
Object Tamagawa numbers
Tamagawa numbers are arithmetic invariants attached to algebraic groups or elliptic curves that measure certain volume or local factor contributions in number theory, notably appearing in the Birch and Swinnerton-Dyer conjecture.
E685697 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: Tamagawa numbers | Statement: [Birch and Swinnerton-Dyer Conjecture, relatesConcept, Tamagawa numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Tamagawa numbers
Context triple: [Birch and Swinnerton-Dyer Conjecture, relatesConcept, Tamagawa numbers]
  • A. Namba
    Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
  • B. Namba Marui
    Namba Marui is a major Marui department store and shopping complex located in Osaka’s bustling Namba district, known for its fashion, dining, and entertainment options.
  • C. Temwaiku
    Temwaiku is a village and district within South Tarawa in Kiribati, known as one of the populated islets forming the country's capital area.
  • D. Namba Grand Kagetsu
    Namba Grand Kagetsu is a famous comedy theater in Osaka, Japan, known as a central venue for Yoshimoto Kogyo’s manzai and variety performances.
  • E. Eightfold Way
    The Eightfold Way is a classification scheme for hadrons in particle physics that organizes them into symmetry-based groups, laying the groundwork for the quark model.
  • 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: Tamagawa numbers
Triple: [Birch and Swinnerton-Dyer Conjecture, relatesConcept, Tamagawa numbers]
Generated description
Tamagawa numbers are arithmetic invariants attached to algebraic groups or elliptic curves that measure certain volume or local factor contributions in number theory, notably appearing in the Birch and Swinnerton-Dyer conjecture.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Tamagawa numbers
Target entity description: Tamagawa numbers are arithmetic invariants attached to algebraic groups or elliptic curves that measure certain volume or local factor contributions in number theory, notably appearing in the Birch and Swinnerton-Dyer conjecture.
  • A. Namba
    Namba is a major commercial and entertainment district in Osaka, Japan, known for its bustling nightlife, shopping, and iconic neon-lit streets.
  • B. Namba Marui
    Namba Marui is a major Marui department store and shopping complex located in Osaka’s bustling Namba district, known for its fashion, dining, and entertainment options.
  • C. Temwaiku
    Temwaiku is a village and district within South Tarawa in Kiribati, known as one of the populated islets forming the country's capital area.
  • D. Namba Grand Kagetsu
    Namba Grand Kagetsu is a famous comedy theater in Osaka, Japan, known as a central venue for Yoshimoto Kogyo’s manzai and variety performances.
  • E. Eightfold Way
    The Eightfold Way is a classification scheme for hadrons in particle physics that organizes them into symmetry-based groups, laying the groundwork for the quark model.
  • 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_69c6995f9c60819092e386192bd63c6f completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c70388d58081909aad2c03b4501e78 completed March 27, 2026, 10:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8be48d61c8190aba1e5f23d7cb1be completed March 29, 2026, 5:53 a.m.
NEDg Description generation batch_69c8bf664390819093c2381ff0f8aaca completed March 29, 2026, 5:57 a.m.
NED2 Entity disambiguation (via description) batch_69c8bff4965881909a341db7d234632a completed March 29, 2026, 6 a.m.
Created at: March 27, 2026, 4:07 p.m.