Triple
T17020384
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Closed Graph Theorem |
E412931
|
entity |
| Predicate | equivalence |
P6530
|
FINISHED |
| Object | A linear operator between Banach spaces is continuous if and only if its graph is closed in the product space |
—
|
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 linear operator between Banach spaces is continuous if and only if its graph is closed in the product space | Statement: [Closed Graph Theorem, equivalence, A linear operator between Banach spaces is continuous if and only if its graph is closed in the product space]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: equivalence Context triple: [Closed Graph Theorem, equivalence, A linear operator between Banach spaces is continuous if and only if its graph is closed in the product space]
-
A.
equivalentTo
chosen
Indicates that two entities represent the same concept, value, or state, and can be treated as interchangeable in the given context.
-
B.
equivalentIn
Indicates that two entities are considered logically or functionally the same in meaning, status, or effect within a given context.
-
C.
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.
-
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.
oftenEquatedWith
Indicates that one entity is frequently regarded, interpreted, or treated as being the same as or equivalent to another entity, though not necessarily strictly identical.
- 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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| PD | Predicate disambiguation | batch_69e35d5be7f48190af9db67a1e23850f |
completed | April 18, 2026, 10:30 a.m. |
Created at: April 10, 2026, 5:33 a.m.