Triple

T6370807
Position Surface form Disambiguated ID Type / Status
Subject Church–Rosser property E143338 entity
Predicate relatedTo P37 FINISHED
Object Newman’s lemma
Newman’s lemma is a result in rewriting theory that states a terminating abstract reduction system is confluent if and only if it is locally confluent.
E143338 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: Newman’s lemma | Statement: [Church–Rosser property, relatedTo, Newman’s lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Newman’s lemma
Context triple: [Church–Rosser property, relatedTo, Newman’s lemma]
  • A. Bailey lemma
    The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
  • B. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • C. Church–Rosser property
    The Church–Rosser property is a confluence property of rewriting systems stating that if an expression can be reduced in different ways, all reduction paths can be further reduced to a common equivalent form.
  • D. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • E. Böhm–Jacopini theorem
    The Böhm–Jacopini theorem is a foundational result in computer science stating that any computer program can be written using only sequence, selection, and iteration constructs, without requiring goto statements.
  • 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: Newman’s lemma
Triple: [Church–Rosser property, relatedTo, Newman’s lemma]
Generated description
Newman’s lemma is a result in rewriting theory that states a terminating abstract reduction system is confluent if and only if it is locally confluent.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Newman’s lemma
Target entity description: Newman’s lemma is a result in rewriting theory that states a terminating abstract reduction system is confluent if and only if it is locally confluent.
  • A. Bailey lemma
    The Bailey lemma is a key result in the theory of basic hypergeometric series that provides a systematic method for generating Rogers–Ramanujan-type identities and other q-series relations.
  • B. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • C. Church–Rosser property chosen
    The Church–Rosser property is a confluence property of rewriting systems stating that if an expression can be reduced in different ways, all reduction paths can be further reduced to a common equivalent form.
  • D. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • E. Böhm–Jacopini theorem
    The Böhm–Jacopini theorem is a foundational result in computer science stating that any computer program can be written using only sequence, selection, and iteration constructs, without requiring goto statements.
  • F. None of above.

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_69c008d8c61081908bcaf61510d881ed completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c068277f6c81908e6a55e006f0c229 completed March 22, 2026, 10:07 p.m.
NED1 Entity disambiguation (via context triple) batch_69c62d8bce3481909b0bf7533b330d1f completed March 27, 2026, 7:11 a.m.
NEDg Description generation batch_69c62e2072808190a4f2dd262b631c88 completed March 27, 2026, 7:13 a.m.
NED2 Entity disambiguation (via description) batch_69c62f1bbdac8190b0cff9fbcddd68a7 completed March 27, 2026, 7:17 a.m.
Created at: March 22, 2026, 4:33 p.m.