Triple
T18479502
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | W. V. D. Hodge |
E451519
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
The Theory and Applications of Harmonic Integrals
The Theory and Applications of Harmonic Integrals is a foundational mathematical monograph by W. V. D. Hodge that developed Hodge theory, linking harmonic forms, topology, and algebraic geometry.
|
E1325985
|
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: The Theory and Applications of Harmonic Integrals | Statement: [W. V. D. Hodge, notableWork, The Theory and Applications of Harmonic Integrals]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: The Theory and Applications of Harmonic Integrals Context triple: [W. V. D. Hodge, notableWork, The Theory and Applications of Harmonic Integrals]
-
A.
Harmonic Integrals in the Theory of Analytic Functions
"Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
-
B.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Theory of Multiply Periodic Functions
Theory of Multiply Periodic Functions is a foundational mathematical work by Henry Frederick Baker that systematically develops the theory of functions with multiple complex periods, including abelian and related functions.
-
E.
Theory of the Integral
Theory of the Integral is a classic mathematical monograph that systematically develops the theory of integration, particularly Lebesgue integration, and has been influential in real analysis.
- 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: The Theory and Applications of Harmonic Integrals Triple: [W. V. D. Hodge, notableWork, The Theory and Applications of Harmonic Integrals]
Generated description
The Theory and Applications of Harmonic Integrals is a foundational mathematical monograph by W. V. D. Hodge that developed Hodge theory, linking harmonic forms, topology, and algebraic geometry.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: The Theory and Applications of Harmonic Integrals Target entity description: The Theory and Applications of Harmonic Integrals is a foundational mathematical monograph by W. V. D. Hodge that developed Hodge theory, linking harmonic forms, topology, and algebraic geometry.
-
A.
Harmonic Integrals in the Theory of Analytic Functions
"Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
-
B.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
-
C.
The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
-
D.
Theory of Multiply Periodic Functions
Theory of Multiply Periodic Functions is a foundational mathematical work by Henry Frederick Baker that systematically develops the theory of functions with multiple complex periods, including abelian and related functions.
-
E.
Theory of the Integral
Theory of the Integral is a classic mathematical monograph that systematically develops the theory of integration, particularly Lebesgue integration, and has been influential in real analysis.
- 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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53065e8388190bb216dae89f8cf75 |
completed | April 19, 2026, 7:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a043f2f64848190808075254008e6e1 |
completed | May 13, 2026, 9:06 a.m. |
| NEDg | Description generation | batch_6a043fb7db388190bb50cfade4f025f9 |
completed | May 13, 2026, 9:09 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a044063c6048190b65620af8ceed897 |
completed | May 13, 2026, 9:12 a.m. |
Created at: April 10, 2026, 11:35 a.m.