Triple
T11812506
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Elwin Bruno Christoffel |
E280907
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Christoffel words
Christoffel words are special finite binary or k-ary words in combinatorics on words that encode discrete approximations of straight lines and have deep connections to number theory, geometry, and Sturmian sequences.
|
E947536
|
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: Christoffel words | Statement: [Elwin Bruno Christoffel, notableWork, Christoffel words]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Christoffel words Context triple: [Elwin Bruno Christoffel, notableWork, Christoffel words]
-
A.
Kesten’s theorem on random walks on groups
Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
-
B.
On the Arrangement of Words
On the Arrangement of Words is an ancient rhetorical treatise by Dionysius of Halicarnassus that analyzes how word order and stylistic choices affect the clarity, harmony, and persuasive power of prose.
-
C.
Catalan numbers
Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
-
D.
Gelfand–Tsetlin graph
The Gelfand–Tsetlin graph is a combinatorial structure whose vertices encode interlacing patterns corresponding to representations of unitary groups, organizing the branching of these representations in a graded, graph-theoretic form.
-
E.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
- 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: Christoffel words Triple: [Elwin Bruno Christoffel, notableWork, Christoffel words]
Generated description
Christoffel words are special finite binary or k-ary words in combinatorics on words that encode discrete approximations of straight lines and have deep connections to number theory, geometry, and Sturmian sequences.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Christoffel words Target entity description: Christoffel words are special finite binary or k-ary words in combinatorics on words that encode discrete approximations of straight lines and have deep connections to number theory, geometry, and Sturmian sequences.
-
A.
Kesten’s theorem on random walks on groups
Kesten’s theorem on random walks on groups is a fundamental result in probability theory that characterizes amenability of groups via the spectral radius of associated random walks.
-
B.
On the Arrangement of Words
On the Arrangement of Words is an ancient rhetorical treatise by Dionysius of Halicarnassus that analyzes how word order and stylistic choices affect the clarity, harmony, and persuasive power of prose.
-
C.
Catalan numbers
Catalan numbers are a sequence of natural numbers that count a wide variety of combinatorial structures, such as correctly matched parentheses, binary tree shapes, and lattice path configurations.
-
D.
Gelfand–Tsetlin graph
The Gelfand–Tsetlin graph is a combinatorial structure whose vertices encode interlacing patterns corresponding to representations of unitary groups, organizing the branching of these representations in a graded, graph-theoretic form.
-
E.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
- 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_69d6ab26aae88190b2489efcb2a24234 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d8a5cba708819097467bb7aca7fc65 |
completed | April 10, 2026, 7:24 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f131a01aa48190bf5a70759ac886f6 |
completed | April 28, 2026, 10:16 p.m. |
| NEDg | Description generation | batch_69f141b31c9081908f19ff870f5f3c33 |
completed | April 28, 2026, 11:24 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69f14fdb39d48190828668fc535d7f6a |
completed | April 29, 2026, 12:24 a.m. |
Created at: April 8, 2026, 9:42 p.m.