Triple

T18365075
Position Surface form Disambiguated ID Type / Status
Subject Michael Aizenman E440021 entity
Predicate knownFor P22 FINISHED
Object Aizenman–Barsky method for phase transitions
The Aizenman–Barsky method for phase transitions is a probabilistic technique in statistical mechanics used to rigorously analyze and prove properties of phase transitions, particularly in percolation and related lattice models.
E1320840 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: Aizenman–Barsky method for phase transitions | Statement: [Michael Aizenman, knownFor, Aizenman–Barsky method for phase transitions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Aizenman–Barsky method for phase transitions
Context triple: [Michael Aizenman, knownFor, Aizenman–Barsky method for phase transitions]
  • A. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • B. Landau theory of second-order phase transitions
    Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
  • C. Yang–Lee theory
    Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
  • D. Yang–Lee edge singularity
    The Yang–Lee edge singularity is a critical point in the complex plane of an external field where the zeros of a system’s partition function accumulate, defining a non-unitary universality class in statistical mechanics and quantum field theory.
  • E. Mayer cluster expansion in statistical mechanics
    The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
  • 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: Aizenman–Barsky method for phase transitions
Triple: [Michael Aizenman, knownFor, Aizenman–Barsky method for phase transitions]
Generated description
The Aizenman–Barsky method for phase transitions is a probabilistic technique in statistical mechanics used to rigorously analyze and prove properties of phase transitions, particularly in percolation and related lattice models.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Aizenman–Barsky method for phase transitions
Target entity description: The Aizenman–Barsky method for phase transitions is a probabilistic technique in statistical mechanics used to rigorously analyze and prove properties of phase transitions, particularly in percolation and related lattice models.
  • A. Ehrenfest classification of phase transitions
    The Ehrenfest classification of phase transitions is an early theoretical scheme that categorizes phase transitions by the order of discontinuity in thermodynamic derivatives, such as entropy or specific heat, at the transition point.
  • B. Landau theory of second-order phase transitions
    Landau theory of second-order phase transitions is a phenomenological framework that explains continuous phase transitions by expanding the free energy in terms of an order parameter and analyzing symmetry-breaking behavior near critical points.
  • C. Yang–Lee theory
    Yang–Lee theory is a framework in statistical mechanics and phase transition theory that studies the distribution of zeros of the partition function in the complex plane to understand critical phenomena.
  • D. Yang–Lee edge singularity
    The Yang–Lee edge singularity is a critical point in the complex plane of an external field where the zeros of a system’s partition function accumulate, defining a non-unitary universality class in statistical mechanics and quantum field theory.
  • E. Mayer cluster expansion in statistical mechanics
    The Mayer cluster expansion in statistical mechanics is a mathematical method that expresses the thermodynamic properties of interacting particle systems as a series in terms of cluster integrals, enabling systematic analysis of non-ideal gases and liquids.
  • 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_69d8b918221c8190a9f7b563d64ac677 completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e5174d31608190851a5bab6878c203 completed April 19, 2026, 5:56 p.m.
NED1 Entity disambiguation (via context triple) batch_6a03d7748558819093969d121d385126 completed May 13, 2026, 1:44 a.m.
NEDg Description generation batch_6a03d8512d4c8190b113f7ed1f8a044c completed May 13, 2026, 1:48 a.m.
NED2 Entity disambiguation (via description) batch_6a03d8d863cc819098b46d5d26db05cd completed May 13, 2026, 1:50 a.m.
Created at: April 10, 2026, 10:38 a.m.