Triple

T14265466
Position Surface form Disambiguated ID Type / Status
Subject Stefan Mazurkiewicz E353631 entity
Predicate notableWork P4 FINISHED
Object Mazurkiewicz trace theorem
The Mazurkiewicz trace theorem is a result in geometric measure theory that characterizes the boundary behavior and trace properties of Sobolev functions on domains.
E1090240 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: Mazurkiewicz trace theorem | Statement: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz trace theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz trace theorem
Context triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz trace theorem]
  • A. Petri’s theorem
    Petri’s theorem is a fundamental result in algebraic geometry that characterizes the ideal of a canonically embedded algebraic curve by describing it as being generated by quadrics under suitable conditions.
  • B. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • C. Tarski’s fixed point theorem
    Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
  • D. Böhm–Jacopini theorem
    The Böhm–Jacopini theorem is a foundational result in computer science stating that any computer program can be written using only sequence, selection, and iteration constructs, without requiring goto statements.
  • E. 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.
  • 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: Mazurkiewicz trace theorem
Triple: [Stefan Mazurkiewicz, notableWork, Mazurkiewicz trace theorem]
Generated description
The Mazurkiewicz trace theorem is a result in geometric measure theory that characterizes the boundary behavior and trace properties of Sobolev functions on domains.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Mazurkiewicz trace theorem
Target entity description: The Mazurkiewicz trace theorem is a result in geometric measure theory that characterizes the boundary behavior and trace properties of Sobolev functions on domains.
  • A. Petri’s theorem
    Petri’s theorem is a fundamental result in algebraic geometry that characterizes the ideal of a canonically embedded algebraic curve by describing it as being generated by quadrics under suitable conditions.
  • B. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • C. Tarski’s fixed point theorem
    Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
  • D. Böhm–Jacopini theorem
    The Böhm–Jacopini theorem is a foundational result in computer science stating that any computer program can be written using only sequence, selection, and iteration constructs, without requiring goto statements.
  • E. 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.
  • 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
NEDg Description generation batch_69fd3417e8e88190b099bfe4ba30f364 completed May 8, 2026, 12:53 a.m.
NED2 Entity disambiguation (via description) batch_69fd37df3dfc8190a594abb2c14e11bb completed May 8, 2026, 1:09 a.m.
Created at: April 10, 2026, 1:09 a.m.