Triple

T7059206
Position Surface form Disambiguated ID Type / Status
Subject Garrett Birkhoff E164171 entity
Predicate notableWork P4 FINISHED
Object Lattice Theory
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
 E637939 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: Lattice Theory | Statement: [Garrett Birkhoff, notableWork, Lattice Theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lattice Theory
Context triple: [Garrett Birkhoff, notableWork, Lattice Theory]
  • A. The Foundations of Mathematics
    The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
  • B. Hasse diagram (in lattice theory)
    A Hasse diagram is a simplified graphical representation of a finite partially ordered set that shows the order relations by connecting elements with upward lines without drawing implied transitive relations.
  • C. Hilbert-style deductive systems
    Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.
  • D. Theory of Groups
    Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • 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: Lattice Theory
Triple: [Garrett Birkhoff, notableWork, Lattice Theory]
Generated description
Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Lattice Theory
Target entity description: Lattice Theory is a foundational mathematical text that systematically develops the theory of lattices and ordered structures, profoundly influencing modern algebra and order theory.
  • A. The Foundations of Mathematics
    The Foundations of Mathematics is a posthumously published collection of F. P. Ramsey’s influential papers on logic, philosophy of mathematics, and the foundations of knowledge.
  • B. Hasse diagram (in lattice theory)
    A Hasse diagram is a simplified graphical representation of a finite partially ordered set that shows the order relations by connecting elements with upward lines without drawing implied transitive relations.
  • C. Hilbert-style deductive systems
    Hilbert-style deductive systems are axiomatic proof systems in mathematical logic that use a small set of axiom schemas and a few inference rules (typically including modus ponens) to derive theorems in formal theories such as Zermelo–Fraenkel set theory.
  • D. Theory of Groups
    Theory of Groups is a foundational textbook in abstract algebra that systematically develops the theory of groups and has been widely used for advanced mathematical study and research.
  • E. Sheaves in Geometry and Logic
    Sheaves in Geometry and Logic is a foundational monograph that develops the theory of sheaves and topos theory and explores their deep connections to geometry, logic, and the foundations of mathematics.
  • 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_69c68861678881909961ddf4d779f750 completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6e26b2acc8190b212ec77b74c419f completed March 27, 2026, 8:02 p.m.
NED1 Entity disambiguation (via context triple) batch_69c788a8c4b481908193ffc795b75796 completed March 28, 2026, 7:52 a.m.
NEDg Description generation batch_69c789a4a38c8190aee4beecf7c75d48 completed March 28, 2026, 7:56 a.m.
NED2 Entity disambiguation (via description) batch_69c78a11266081908dc24f62ae3fd118 completed March 28, 2026, 7:58 a.m.
Created at: March 27, 2026, 2:38 p.m.