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.