Triple
T5425435
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schauder fixed-point theorem |
E121350
|
entity |
| Predicate | formalStatement |
P19806
|
FINISHED |
| Object | Every continuous compact map from a nonempty closed bounded convex subset of a Banach space into itself has a fixed point. |
—
|
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: Every continuous compact map from a nonempty closed bounded convex subset of a Banach space into itself has a fixed point. | Statement: [Schauder fixed-point theorem, formalStatement, Every continuous compact map from a nonempty closed bounded convex subset of a Banach space into itself has a fixed point.]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: formalStatement Context triple: [Schauder fixed-point theorem, formalStatement, Every continuous compact map from a nonempty closed bounded convex subset of a Banach space into itself has a fixed point.]
-
A.
statement
Indicates that an entity makes, issues, or expresses a declarative assertion, claim, or remark about something.
-
B.
formalization
Indicates that an informal concept, process, or agreement is being expressed, structured, or codified in a formal, explicit, and often standardized way.
-
C.
formalContent
chosen
Indicates that the content is expressed in a formal, structured, or official manner, as opposed to casual or informal expression.
-
D.
formalizedUnder
Indicates that something has been officially established, defined, or codified within the framework, authority, or provisions of a particular formal system, agreement, or institution.
-
E.
isFormalizedBy
Indicates that something is given a defined, structured, or official form through a specific method, process, or representation.
- 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_69bd463b58d88190b258261573de9e91 |
completed | March 20, 2026, 1:06 p.m. |
| NER | Named-entity recognition | batch_69bd8911a7348190ad9378a248190f07 |
completed | March 20, 2026, 5:51 p.m. |
| PD | Predicate disambiguation | batch_69bd846b8bdc81909dcdc2a3084226f2 |
completed | March 20, 2026, 5:31 p.m. |
Created at: March 20, 2026, 2:06 p.m.