Triple

T5544544
Position Surface form Disambiguated ID Type / Status
Subject Ehud Kalai E145373 entity
Predicate notableConcept P201 FINISHED
Object Kalai–Smorodinsky solution E15614 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: Kalai–Smorodinsky solution | Statement: [Ehud Kalai, notableConcept, Kalai–Smorodinsky solution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kalai–Smorodinsky solution
Context triple: [Ehud Kalai, notableConcept, Kalai–Smorodinsky solution]
  • A. Kalai–Smorodinsky bargaining solution chosen
    The Kalai–Smorodinsky bargaining solution is a cooperative game theory concept that selects a fair agreement between parties by preserving proportional gains relative to their best possible outcomes.
  • B. Nash bargaining solution
    The Nash bargaining solution is a foundational concept in game theory that defines a fair and efficient outcome for two-party bargaining problems based on axioms of rationality and symmetry.
  • C. Rubinstein bargaining model
    The Rubinstein bargaining model is a foundational game-theoretic framework that analyzes how two parties reach agreement over time through alternating offers under the influence of impatience and strategic delay.
  • D. Kuhn’s theorem
    Kuhn’s theorem is a fundamental result in game theory that shows any finite extensive-form game with perfect recall has an equivalent normal-form (strategic-form) representation, ensuring the existence of mixed-strategy equilibria.
  • E. Knaster–Kuratowski–Mazurkiewicz lemma
    The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
  • 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_69c008fa64888190adae56c8f9ea4031 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c01fcad7d88190b83bb4ecb3b34bfd completed March 22, 2026, 4:58 p.m.
NED1 Entity disambiguation (via context triple) batch_69c04cec35248190bae940a95e79a586 completed March 22, 2026, 8:11 p.m.
Created at: March 22, 2026, 3:35 p.m.