Triple
T32816511
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kesten’s theorem on random walks on groups |
E839308
|
entity |
| Predicate | equivalenceStatement |
P58587
|
FINISHED |
| Object | a group is amenable if and only if the spectral radius of a symmetric, finitely supported random walk on it equals 1 |
—
|
LITERAL FINISHED |
How this triple was built (2 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: a group is amenable if and only if the spectral radius of a symmetric, finitely supported random walk on it equals 1 | Statement: [Kesten’s theorem on random walks on groups, equivalenceStatement, a group is amenable if and only if the spectral radius of a symmetric, finitely supported random walk on it equals 1]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: equivalenceStatement Context triple: [Kesten’s theorem on random walks on groups, equivalenceStatement, a group is amenable if and only if the spectral radius of a symmetric, finitely supported random walk on it equals 1]
-
A.
equivalentTo
Indicates that two entities represent the same concept, value, or state, and can be treated as interchangeable in the given context.
-
B.
legalEquivalence
Indicates that two legal entities, statuses, or provisions are considered to have the same legal effect, standing, or validity within a given legal framework.
-
C.
equivalentIn
chosen
Indicates that two entities are considered logically or functionally the same in meaning, status, or effect within a given context.
-
D.
isEquiconsistentWith
Indicates that two formal theories or systems have the same consistency strength, such that if one is consistent then the other is also consistent, and if one is inconsistent then so is the other.
-
E.
converseStatement
Indicates that one entity makes a spoken or written statement directed toward another entity in the context of a conversation.
- F. None of above.
Provenance (3 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_69f3493df9008190a8f5d843dcd77704 |
completed | April 30, 2026, 12:21 p.m. |
| NER | Named-entity recognition | batch_69f70b966860819089cf92927f47c5f1 |
completed | May 3, 2026, 8:47 a.m. |
| PD | Predicate disambiguation | batch_69f70abe43e08190b2a30930d96247c1 |
completed | May 3, 2026, 8:43 a.m. |
Created at: May 1, 2026, 1:15 a.m.