Triple
T7011080
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Samuel Eilenberg |
E162580
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Eilenberg–Steenrod axioms
The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
|
E634843
|
NE FINISHED |
How this triple was built (4 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: Eilenberg–Steenrod axioms | Statement: [Samuel Eilenberg, notableWork, Eilenberg–Steenrod axioms]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Eilenberg–Steenrod axioms Context triple: [Samuel Eilenberg, notableWork, Eilenberg–Steenrod axioms]
-
A.
Atiyah–Segal axioms
The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
-
B.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
C.
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
D.
Pontryagin classes
Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
-
E.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Eilenberg–Steenrod axioms Triple: [Samuel Eilenberg, notableWork, Eilenberg–Steenrod axioms]
Generated description
The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Eilenberg–Steenrod axioms Target entity description: The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
-
A.
Atiyah–Segal axioms
The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
-
B.
Alexandrov–Čech cohomology
Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
-
C.
"Algebraic Topology"
"Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
-
D.
Pontryagin classes
Pontryagin classes are characteristic classes associated with real vector bundles that capture topological information about the bundle’s curvature and play a central role in differential topology and geometry.
-
E.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
- F. None of above. chosen
Provenance (5 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_69c6885a127c8190867b059bdccf13ff |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6dc5729448190af66dbd6f3e8936e |
completed | March 27, 2026, 7:36 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c76a4bd424819097e1543ec59979ff |
completed | March 28, 2026, 5:42 a.m. |
| NEDg | Description generation | batch_69c76b1ef6f481908f4c4f610328f633 |
completed | March 28, 2026, 5:46 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c76c01679c8190b61f642c23c25ed5 |
completed | March 28, 2026, 5:49 a.m. |
Created at: March 27, 2026, 2:34 p.m.