Triple
T6929709
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cantor–Bernstein–Schröder theorem |
E160401
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Schröder–Bernstein theorem |
E160401
|
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: Schröder–Bernstein theorem | Statement: [Cantor–Bernstein–Schröder theorem, relatedTo, Schröder–Bernstein theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schröder–Bernstein theorem Context triple: [Cantor–Bernstein–Schröder theorem, relatedTo, Schröder–Bernstein theorem]
-
A.
Cantor–Bernstein–Schröder theorem
chosen
The Cantor–Bernstein–Schröder theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
-
B.
Cantor’s theorem
Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
-
C.
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.
-
D.
Cantor’s paradox
Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
-
E.
Baire category theorem
The Baire category theorem is a fundamental result in topology and functional analysis stating that complete metric (or locally compact Hausdorff) spaces cannot be written as countable unions of nowhere dense sets, with powerful consequences for the structure of such spaces.
- 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_69c6884e15208190b9e91487eaafcf85 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6da1f5fcc8190b43f53f90fc1821c |
completed | March 27, 2026, 7:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7585e45448190accdddcbb4bd69ed |
completed | March 28, 2026, 4:26 a.m. |
Created at: March 27, 2026, 2:27 p.m.