Triple

T33761209
Position Surface form Disambiguated ID Type / Status
Subject Macdonald polynomials E865108 entity
Predicate hasCombinatorialModel P164152 FINISHED
Object Haglund–Haiman–Loehr formula
The Haglund–Haiman–Loehr formula is a combinatorial expression that gives a statistic-based expansion of Macdonald polynomials in terms of fillings of Young diagrams.
 E865108 NE FINISHED

How this triple was built (3 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: Haglund–Haiman–Loehr formula | Statement: [Macdonald polynomials, hasCombinatorialModel, Haglund–Haiman–Loehr formula]
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: Haglund–Haiman–Loehr formula
Triple: [Macdonald polynomials, hasCombinatorialModel, Haglund–Haiman–Loehr formula]
Generated description
The Haglund–Haiman–Loehr formula is a combinatorial expression that gives a statistic-based expansion of Macdonald polynomials in terms of fillings of Young diagrams.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasCombinatorialModel
Context triple: [Macdonald polynomials, hasCombinatorialModel, Haglund–Haiman–Loehr formula]
  • A. hasCombinatorialNature
    Indicates that something possesses properties or behavior fundamentally based on combinations, arrangements, or discrete configurations of elements.
  • B. hasCombinatorialInterpretation chosen
    Indicates that something can be meaningfully interpreted or explained in terms of counting, arrangements, or other combinatorial structures or arguments.
  • C. hasHodgeNumbers
    Indicates that an entity (typically a geometric or algebraic object) is associated with specific Hodge numbers describing its Hodge decomposition or Hodge structure.
  • D. isCombinatorialGame
    Indicates that the subject is a game defined by discrete, well-structured moves and positions, typically with perfect information and no chance elements, suitable for analysis using combinatorial game theory.
  • E. isAdditivelyIndecomposable
    Indicates that an entity (typically an ordinal or algebraic object) cannot be expressed as a nontrivial sum of two smaller entities of the same kind.
  • F. None of above.

Provenance (6 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_69f3498d3b748190aa3c4006c1f32f38 completed April 30, 2026, 12:22 p.m.
NER Named-entity recognition batch_6a037e0953908190b2930b3c06a40129 completed May 12, 2026, 7:22 p.m.
NED1 Entity disambiguation (via context triple) batch_6a365c995f188190b40b5eff42eff403 completed June 20, 2026, 9:25 a.m.
NEDg Description generation batch_6a365d1385648190a48b5817d3ec67f9 completed June 20, 2026, 9:27 a.m.
NED2 Entity disambiguation (via description) batch_6a365e57afc48190bd3fad174217b2c3 completed June 20, 2026, 9:33 a.m.
PD Predicate disambiguation batch_6a0379f6c3308190b954f7810214ceed completed May 12, 2026, 7:05 p.m.
Created at: May 1, 2026, 1:45 a.m.