Triple

T13894243
Position Surface form Disambiguated ID Type / Status
Subject Lectures on Cauchy’s Problem in Linear Partial Differential Equations E334047 entity
Predicate associatedConcept P531 FINISHED
Object Hadamard well-posedness E334044 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: Hadamard well-posedness | Statement: [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, associatedConcept, Hadamard well-posedness]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hadamard well-posedness
Context triple: [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, associatedConcept, Hadamard well-posedness]
  • A. Hadamard’s example of ill-posed problems chosen
    Hadamard’s example of ill-posed problems is a classical mathematical construction illustrating how small changes in input data can cause large, unstable changes in solutions, thereby violating the standard criteria for well-posedness in analysis and partial differential equations.
  • B. Ulam stability
    Ulam stability is a concept in the theory of functional equations that studies when approximate solutions imply the existence of exact solutions nearby, forming the basis of what is now called Hyers–Ulam stability.
  • C. Agmon–Douglis–Nirenberg estimates
    Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
  • D. Hilbert’s nineteenth problem
    Hilbert’s nineteenth problem is one of David Hilbert’s famous list of 23 problems, asking whether solutions to regular variational problems are always analytic.
  • E. Lax–Milgram theorem
    The Lax–Milgram theorem is a fundamental result in functional analysis that guarantees the existence and uniqueness of solutions to certain linear boundary value problems via bounded, coercive bilinear forms on Hilbert spaces.
  • 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_69d81c5dd2d48190b7a5fc1e009de936 completed April 9, 2026, 9:38 p.m.
NER Named-entity recognition batch_69de23a741908190bdf46d76c5f1411a completed April 14, 2026, 11:23 a.m.
NED1 Entity disambiguation (via context triple) batch_69f7ce7419cc81909488871c16d6b356 completed May 3, 2026, 10:38 p.m.
Created at: April 9, 2026, 10:15 p.m.