Triple
T12797585
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Algebraic Topology |
E305928
|
entity |
| Predicate | developsConcept |
P201
|
FINISHED |
| Object | universal coefficient theorem |
E911366
|
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: universal coefficient theorem | Statement: [Algebraic Topology, developsConcept, universal coefficient theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: universal coefficient theorem Context triple: [Algebraic Topology, developsConcept, universal coefficient theorem]
-
A.
universal coefficient theorem
chosen
The universal coefficient theorem is a fundamental result in algebraic topology that relates the homology or cohomology groups of a space with coefficients in an arbitrary abelian group to those with integer coefficients via Ext and Tor functors.
-
B.
Bockstein homomorphism
The Bockstein homomorphism is a connecting homomorphism in cohomology arising from a short exact sequence of coefficient groups, used to relate and detect characteristic classes and torsion phenomena in topology.
-
C.
Künneth formula
The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
-
D.
Hurewicz homomorphism
The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
-
E.
Grothendieck–Riemann–Roch theorem
The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
- 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_69d7bdf366888190a8cccb982606889c |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d96e6db68481909a2ca8da1287f3e0 |
completed | April 10, 2026, 9:41 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f6850d6ebc8190aaffcac09f4b15eb |
completed | May 2, 2026, 11:13 p.m. |
Created at: April 9, 2026, 5:30 p.m.