Triple

T7278062
Position Surface form Disambiguated ID Type / Status
Subject Sprague–Grundy theorem E163078 entity
Predicate relatedTo P37 FINISHED
Object Grundy numbers
Grundy numbers are numerical values assigned to positions in impartial combinatorial games that determine their equivalence to piles in the game of Nim and are central to analyzing winning strategies.
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: Grundy numbers | Statement: [Sprague–Grundy theorem, relatedTo, Grundy numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Grundy numbers
Context triple: [Sprague–Grundy theorem, relatedTo, Grundy numbers]
  • A. 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.
  • B. Wythoff Nim
    Wythoff Nim is a classic impartial combinatorial game involving two piles of tokens, whose optimal play is characterized by positions related to the golden ratio.
  • C. 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.
  • D. Conway’s games
    Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
  • E. Hackenbush
    Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
  • 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: Grundy numbers
Triple: [Sprague–Grundy theorem, relatedTo, Grundy numbers]
Generated description
Grundy numbers are numerical values assigned to positions in impartial combinatorial games that determine their equivalence to piles in the game of Nim and are central to analyzing winning strategies.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Grundy numbers
Target entity description: Grundy numbers are numerical values assigned to positions in impartial combinatorial games that determine their equivalence to piles in the game of Nim and are central to analyzing winning strategies.
  • A. Sprague–Grundy theorem chosen
    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.
  • B. Wythoff Nim
    Wythoff Nim is a classic impartial combinatorial game involving two piles of tokens, whose optimal play is characterized by positions related to the golden ratio.
  • C. 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.
  • D. Conway’s games
    Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
  • E. Hackenbush
    Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
  • 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_69c6885c5964819085b209701769877f completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6eb309a648190a2a2f2cca9ce2f56 completed March 27, 2026, 8:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7eedbbc3c81909a02c4fb63e428c0 completed March 28, 2026, 3:08 p.m.
NEDg Description generation batch_69c7ef5b7ce081908702e564f09f2fe1 completed March 28, 2026, 3:10 p.m.
NED2 Entity disambiguation (via description) batch_69c7efb24a488190b53720f521151c61 completed March 28, 2026, 3:11 p.m.
Created at: March 27, 2026, 2:59 p.m.