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.