Triple

T7278066
Position Surface form Disambiguated ID Type / Status
Subject Sprague–Grundy theorem E163078 entity
Predicate relatedTo P37 FINISHED
Object 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.
E653413 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: Wythoff Nim | Statement: [Sprague–Grundy theorem, relatedTo, Wythoff Nim]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wythoff Nim
Context triple: [Sprague–Grundy theorem, relatedTo, Wythoff Nim]
  • 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. Hackenbush
    Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
  • C. Kayles
    Kayles is a classic impartial combinatorial game in which players alternately remove one or two adjacent pins from a row, with the goal of making the last move.
  • D. 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.
  • E. Conway’s soldiers
    Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
  • 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: Wythoff Nim
Triple: [Sprague–Grundy theorem, relatedTo, Wythoff Nim]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wythoff Nim
Target entity description: 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.
  • 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. Hackenbush
    Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.
  • C. Kayles
    Kayles is a classic impartial combinatorial game in which players alternately remove one or two adjacent pins from a row, with the goal of making the last move.
  • D. 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.
  • E. Conway’s soldiers
    Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
  • 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_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_69c7db3450208190b67e4329a531ad0c completed March 28, 2026, 1:44 p.m.
NEDg Description generation batch_69c7dc567004819089c6c4b5322f275f completed March 28, 2026, 1:49 p.m.
NED2 Entity disambiguation (via description) batch_69c7dd18f8d481908bd7ac86e4388ce5 completed March 28, 2026, 1:52 p.m.
Created at: March 27, 2026, 2:59 p.m.