Triple
T22423291
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Erdős distinct distances problem |
E554301
|
entity |
| Predicate | improvedLowerBoundProvedBy |
P144592
|
FINISHED |
| Object | Larry Guth and Nets Hawk Katz |
—
|
NE NERFINISHED |
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: Larry Guth and Nets Hawk Katz | Statement: [Erdős distinct distances problem, improvedLowerBoundProvedBy, Larry Guth and Nets Hawk Katz]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Larry Guth and Nets Hawk Katz Context triple: [Erdős distinct distances problem, improvedLowerBoundProvedBy, Larry Guth and Nets Hawk Katz]
-
A.
Larry Guth
Larry Guth is an American mathematician known for his influential work in combinatorial geometry, harmonic analysis, and incidence geometry.
-
B.
Michael Ellenberg
Michael Ellenberg is a television producer and media executive best known for developing and producing high-profile prestige series, including the Apple TV+ drama "The Morning Show."
-
C.
Gil Kalai
Gil Kalai is an Israeli mathematician and computer scientist known for his influential work in combinatorics, convexity, and the study of the foundations and limitations of quantum computing.
-
D.
Gábor Tardos
Gábor Tardos is a Hungarian mathematician and computer scientist known for his contributions to combinatorics and theoretical computer science.
-
E.
Terence Tao
Terence Tao is an Australian-American mathematician renowned for his groundbreaking work in harmonic analysis, partial differential equations, additive combinatorics, and analytic number theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Larry Guth and Nets Hawk Katz Target entity description: Larry Guth and Nets Hawk Katz are mathematicians renowned for their breakthrough work in combinatorial geometry, particularly their landmark improvement of the lower bound in the Erdős distinct distances problem.
-
A.
Larry Guth
chosen
Larry Guth is an American mathematician known for his influential work in combinatorial geometry, harmonic analysis, and incidence geometry.
-
B.
Michael Ellenberg
Michael Ellenberg is a television producer and media executive best known for developing and producing high-profile prestige series, including the Apple TV+ drama "The Morning Show."
-
C.
Gil Kalai
Gil Kalai is an Israeli mathematician and computer scientist known for his influential work in combinatorics, convexity, and the study of the foundations and limitations of quantum computing.
-
D.
Gábor Tardos
Gábor Tardos is a Hungarian mathematician and computer scientist known for his contributions to combinatorics and theoretical computer science.
-
E.
Terence Tao
Terence Tao is an Australian-American mathematician renowned for his groundbreaking work in harmonic analysis, partial differential equations, additive combinatorics, and analytic number theory.
- F. None of above.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: improvedLowerBoundProvedBy Context triple: [Erdős distinct distances problem, improvedLowerBoundProvedBy, Larry Guth and Nets Hawk Katz]
-
A.
knownLowerBoundProvedBy
Indicates that a specific lower bound has been formally established or proven by a particular method, proof, or source.
-
B.
provedInFullBy
chosen
Indicates that something (such as a claim, theorem, or statement) has been completely and rigorously demonstrated or established by a particular agent or source.
-
C.
givesBoundOn
Indicates that one quantity provides an upper or lower limit (a bound) on the value or behavior of another quantity.
-
D.
partiallyProvenFor
Indicates that something has been shown to hold or be true for part of a domain or set of cases, but not yet for all cases.
-
E.
wasFirstProvedBy
Indicates that a particular statement, theorem, or result was originally and for the first time demonstrated or established as true by a specified agent.
- F. None of above.
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_69e11e4f2d0c819091aa3558ea2ee630 |
completed | April 16, 2026, 5:37 p.m. |
| NER | Named-entity recognition | batch_69f15a2af620819083338127e78137dc |
completed | April 29, 2026, 1:08 a.m. |
| PD | Predicate disambiguation | batch_69e898a327948190beee5e168006a0a7 |
completed | April 22, 2026, 9:45 a.m. |
Created at: April 16, 2026, 8:47 p.m.