Triple
T16474844
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Tychonoff theorem for products of compact spaces |
E400161
|
entity |
| Predicate | equivalentTo |
P6530
|
FINISHED |
| Object | axiom of choice (over ZF) |
E87367
|
NE 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: axiom of choice (over ZF) | Statement: [Tychonoff theorem for products of compact spaces, equivalentTo, axiom of choice (over ZF)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: axiom of choice (over ZF) Context triple: [Tychonoff theorem for products of compact spaces, equivalentTo, axiom of choice (over ZF)]
-
A.
axiom of choice
chosen
The axiom of choice is a fundamental principle in set theory asserting that one can select an element from each set in any collection of nonempty sets, with far-reaching consequences across mathematics.
-
B.
Zermelo–Fraenkel set theory
Zermelo–Fraenkel set theory is the standard axiomatic framework for modern set theory, designed to avoid paradoxes and provide a rigorous foundation for much of mathematics.
-
C.
Zermelo set theory
Zermelo set theory is an early axiomatic system for set theory, introduced by Ernst Zermelo to rigorously formalize the concept of sets and avoid known paradoxes.
-
D.
axiom schema of separation
The axiom schema of separation is a principle in set theory that guarantees the existence of subsets defined by properties or predicates, helping to avoid paradoxes by restricting unrestricted set formation.
-
E.
Hausdorff maximal principle
The Hausdorff maximal principle is a foundational result in set theory and order theory stating that every partially ordered set contains a maximal totally ordered subset (a maximal chain), and it is equivalent to the axiom of choice.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69d883813098819084f5409539723b59 |
completed | April 10, 2026, 4:58 a.m. |
| NER | Named-entity recognition | batch_69e32dd32e048190a9eadd32d6b9374c |
completed | April 18, 2026, 7:08 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a004f5f238881909b5f2fb41da3f932 |
completed | May 10, 2026, 9:26 a.m. |
Created at: April 10, 2026, 5:13 a.m.