Triple

T1422430
Position Surface form Disambiguated ID Type / Status
Subject Winning Ways for your Mathematical Plays E30253 entity
Predicate coversConcept P1393 FINISHED
Object Sprague–Grundy theorem
The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
E163078 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: Sprague–Grundy theorem | Statement: [Winning Ways for your Mathematical Plays, coversConcept, Sprague–Grundy theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sprague–Grundy theorem
Context triple: [Winning Ways for your Mathematical Plays, coversConcept, Sprague–Grundy theorem]
  • A. Winning Ways for your Mathematical Plays
    Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
  • B. Conway’s Game of Sprouts
    Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
  • C. On Numbers and Games
    On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
  • D. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • E. Surreal numbers
    Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
  • 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: Sprague–Grundy theorem
Triple: [Winning Ways for your Mathematical Plays, coversConcept, Sprague–Grundy theorem]
Generated description
The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Sprague–Grundy theorem
Target entity description: The Sprague–Grundy theorem is a fundamental result in combinatorial game theory that assigns each impartial game position a nonnegative integer (its Grundy value), allowing such games to be analyzed and combined via nim-like addition.
  • A. Winning Ways for your Mathematical Plays
    Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
  • B. Conway’s Game of Sprouts
    Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
  • C. On Numbers and Games
    On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
  • D. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • E. Surreal numbers
    Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
  • 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_69a498fb823c8190a67ce4c4837e641a completed March 1, 2026, 7:52 p.m.
NER Named-entity recognition batch_69a4c4ba798881909c2259987248b030 completed March 1, 2026, 10:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69ad0161e23c819099a1c72627f13dd0 completed March 8, 2026, 4:56 a.m.
NEDg Description generation batch_69ad01c53e808190824b9702c309f0a2 completed March 8, 2026, 4:57 a.m.
NED2 Entity disambiguation (via description) batch_69ad0241546881908f1044616255f146 completed March 8, 2026, 4:59 a.m.
Created at: March 1, 2026, 8 p.m.