Triple
T12797584
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Algebraic Topology |
E305928
|
entity |
| Predicate | developsConcept |
P201
|
FINISHED |
| Object | Künneth formula |
E860097
|
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: Künneth formula | Statement: [Algebraic Topology, developsConcept, Künneth formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Künneth formula Context triple: [Algebraic Topology, developsConcept, Künneth formula]
-
A.
Künneth formula
chosen
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.
-
B.
Lefschetz duality
Lefschetz duality is a generalization of Poincaré duality that relates the homology of a compact manifold with boundary to the cohomology of the manifold relative to its boundary.
-
C.
Whitehead product
The Whitehead product is a fundamental operation in algebraic topology that combines homotopy classes of maps to produce higher-order homotopy information, playing a key role in the structure of homotopy groups of spheres and related spaces.
-
D.
Serre spectral sequence
The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
-
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.