Triple
T11961124
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Haag-Ruelle scattering theory |
E284670
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object |
Haag’s theorem
Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
|
E956267
|
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: Haag’s theorem | Statement: [Haag-Ruelle scattering theory, isRelatedTo, Haag’s theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Haag’s theorem Context triple: [Haag-Ruelle scattering theory, isRelatedTo, Haag’s theorem]
-
A.
Halász theorem
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
-
B.
Gelfand–Naimark theorem
The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
-
C.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
D.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
E.
Bose–Nair theorem
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
- 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: Haag’s theorem Triple: [Haag-Ruelle scattering theory, isRelatedTo, Haag’s theorem]
Generated description
Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Haag’s theorem Target entity description: Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
-
A.
Halász theorem
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
-
B.
Gelfand–Naimark theorem
The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
-
C.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
D.
Kesten’s theorem
Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
-
E.
Bose–Nair theorem
The Bose–Nair theorem is a result in combinatorial design theory that provides conditions for the existence and construction of certain balanced incomplete block designs, contributing to the foundations of modern combinatorics and coding theory.
- 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_69d6ab2eaeb881909f7914758f859413 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9036941948190b150369094551731 |
completed | April 10, 2026, 2:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f4592fa9a48190a0450e3d0c57c4d3 |
completed | May 1, 2026, 7:41 a.m. |
| NEDg | Description generation | batch_69f4645ef63881909b46937f73d637a3 |
completed | May 1, 2026, 8:29 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f465be4db08190882898a17d077019 |
completed | May 1, 2026, 8:35 a.m. |
Created at: April 8, 2026, 9:45 p.m.