Triple

T17020219
Position Surface form Disambiguated ID Type / Status
Subject Sobolev spaces E412927 entity
Predicate relatedTheorem P49212 FINISHED
Object Poincaré inequality E156195 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: Poincaré inequality | Statement: [Sobolev spaces, relatedTheorem, Poincaré inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Poincaré inequality
Context triple: [Sobolev spaces, relatedTheorem, Poincaré inequality]
  • A. Poincaré inequality chosen
    The Poincaré inequality is a fundamental result in functional analysis and partial differential equations that bounds the average oscillation of a function by the size of its gradient, playing a key role in Sobolev space theory and the study of elliptic problems.
  • B. Sobolev inequality
    The Sobolev inequality is a fundamental result in functional analysis and partial differential equations that bounds the size of a function in certain Lebesgue spaces by the size of its derivatives, enabling key embedding and regularity properties.
  • C. Korn inequality
    Korn inequality is a fundamental result in functional analysis and the mathematical theory of elasticity that provides bounds relating the full gradient of a vector field to its symmetric part, ensuring control of deformations by their strains.
  • D. Caccioppoli inequality
    The Caccioppoli inequality is a fundamental estimate in the theory of partial differential equations that bounds the energy (gradient) of a solution in a smaller region by its values in a larger surrounding region, playing a key role in regularity theory.
  • E. Friedrichs inequality
    Friedrichs inequality is a fundamental result in functional analysis and partial differential equations that provides bounds on the norms of functions in terms of their derivatives, playing a key role in the theory of Sobolev spaces and boundary value problems.
  • 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_69d886cc4170819093deddc7b8b4b6a7 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e3d482c3a0819099e6ea4acb0a08ee completed April 18, 2026, 6:59 p.m.
NED1 Entity disambiguation (via context triple) batch_6a012334c3b48190b125ab926450c45b completed May 11, 2026, 12:30 a.m.
Created at: April 10, 2026, 5:33 a.m.