Triple

T5393057
Position Surface form Disambiguated ID Type / Status
Subject Almost optimal lower bounds for small depth circuits E120580 entity
Predicate relatedTo P37 FINISHED
Object Håstad switching lemma E120579 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: Håstad switching lemma | Statement: [Almost optimal lower bounds for small depth circuits, relatedTo, Håstad switching lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Håstad switching lemma
Context triple: [Almost optimal lower bounds for small depth circuits, relatedTo, Håstad switching lemma]
  • A. Håstad’s switching lemma chosen
    Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
  • B. Valiant–Vazirani theorem
    The Valiant–Vazirani theorem is a fundamental result in computational complexity theory showing that solving unique solutions of NP problems is, under randomized reductions, as hard as solving general NP problems, with major implications for the study of randomness and hardness of approximation.
  • C. Cook–Levin theorem
    The Cook–Levin theorem is a foundational result in computational complexity theory that established the Boolean satisfiability problem (SAT) as the first NP-complete problem, launching the theory of NP-completeness.
  • D. “Almost optimal lower bounds for small depth circuits”
    “Almost optimal lower bounds for small depth circuits” is a seminal theoretical computer science paper by Johan Håstad that establishes near-tight lower bounds on the size of constant-depth Boolean circuits, profoundly influencing circuit complexity theory.
  • E. The Knowledge Complexity of Interactive Proof Systems
    "The Knowledge Complexity of Interactive Proof Systems" is a seminal theoretical computer science paper that introduced the notion of zero-knowledge proofs, fundamentally shaping modern cryptography and complexity theory.
  • 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_69bd4637b92c8190b815b6443ae4b323 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd871b81d08190993928e2c6251226 completed March 20, 2026, 5:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3a9b9ff881908edc10f29f62df1c completed March 22, 2026, 12:40 a.m.
Created at: March 20, 2026, 2:04 p.m.