Triple
T24824275
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alon–Boppana bound |
E621145
|
entity |
| Predicate | lowerBounds |
P17139
|
FINISHED |
| Object | lim inf of the second-largest eigenvalue of d-regular graphs by 2√(d−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: lim inf of the second-largest eigenvalue of d-regular graphs by 2√(d−1) | Statement: [Alon–Boppana bound, lowerBounds, lim inf of the second-largest eigenvalue of d-regular graphs by 2√(d−1)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: lowerBounds Context triple: [Alon–Boppana bound, lowerBounds, lim inf of the second-largest eigenvalue of d-regular graphs by 2√(d−1)]
-
A.
lowerBoundaryLocation
Indicates the place or region where the lower or bottom boundary of something is situated.
-
B.
lowerLimit
chosen
Indicates that one value serves as the minimum or smallest allowable bound or threshold for another value or range.
-
C.
lowerBoundGrowth
Indicates that one quantity grows at least as fast as another, establishing a minimum rate or bound on its growth relative to that reference.
-
D.
isBoundedBelow
Indicates that every value in a set or function is greater than or equal to some fixed lower bound.
-
E.
lowerValueIndicates
Indicates that a smaller numerical value of a property or measurement corresponds to a greater degree, better outcome, or stronger presence of the relevant characteristic.
- 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_69e2fac0c3b881909110e5a56c6fa46f |
completed | April 18, 2026, 3:30 a.m. |
| NER | Named-entity recognition | batch_69f44a417a58819081777e18dda149fd |
completed | May 1, 2026, 6:37 a.m. |
| PD | Predicate disambiguation | batch_69f442b8479c8190a7c8e416ac9e28a0 |
completed | May 1, 2026, 6:05 a.m. |
Created at: April 18, 2026, 5:05 a.m.