Triple

T11085938
Position Surface form Disambiguated ID Type / Status
Subject Hurwitz bound on automorphism groups of curves E262119 entity
Predicate relatedResult P96512 FINISHED
Object Accola–Maclachlan bound
The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
E904004 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: Accola–Maclachlan bound | Statement: [Hurwitz bound on automorphism groups of curves, relatedResult, Accola–Maclachlan bound]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Accola–Maclachlan bound
Context triple: [Hurwitz bound on automorphism groups of curves, relatedResult, Accola–Maclachlan bound]
  • A. Barankin bound
    The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
  • B. Alon–Boppana bound
    The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
  • C. Hamming bound
    The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
  • D. Graham–Pollak theorem
    The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
  • E. Cramér–Rao bound
    The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
  • 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: Accola–Maclachlan bound
Triple: [Hurwitz bound on automorphism groups of curves, relatedResult, Accola–Maclachlan bound]
Generated description
The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Accola–Maclachlan bound
Target entity description: The Accola–Maclachlan bound is a refinement in algebraic geometry that gives an improved upper limit on the size of the automorphism group of a compact Riemann surface (or algebraic curve), sharpening the classical Hurwitz bound in certain cases.
  • A. Barankin bound
    The Barankin bound is a fundamental lower bound in statistical estimation theory that generalizes and can be tighter than the Cramér–Rao bound for the variance of unbiased estimators, especially in non-regular or finite-sample settings.
  • B. Alon–Boppana bound
    The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
  • C. Hamming bound
    The Hamming bound is a fundamental limit in coding theory that specifies the maximum number of codewords a block code can have for a given length and minimum distance while still allowing reliable error detection and correction.
  • D. Graham–Pollak theorem
    The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
  • E. Cramér–Rao bound
    The Cramér–Rao bound is a fundamental result in statistical estimation theory that gives a lower limit on the variance of any unbiased estimator of a parameter, characterizing the best possible precision achievable.
  • 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_69d6aa9983c08190b0ef61603b69feac completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d799c2c7d4819087ac793153340178 completed April 9, 2026, 12:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69e3e7a6dfa8819096f822294eb64dd1 completed April 18, 2026, 8:20 p.m.
NEDg Description generation batch_69e3f2cafc008190a3504999297f1e4e completed April 18, 2026, 9:08 p.m.
NED2 Entity disambiguation (via description) batch_69e3f488819081908f9a4225279cde6b completed April 18, 2026, 9:15 p.m.
Created at: April 8, 2026, 9:27 p.m.