Triple

T5393011
Position Surface form Disambiguated ID Type / Status
Subject Håstad’s switching lemma E120579 entity
Predicate toolFor P24520 FINISHED
Object Håstad’s optimal lower bounds for small-depth circuits E120580 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’s optimal lower bounds for small-depth circuits | Statement: [Håstad’s switching lemma, toolFor, Håstad’s optimal lower bounds for small-depth circuits]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Håstad’s optimal lower bounds for small-depth circuits
Context triple: [Håstad’s switching lemma, toolFor, Håstad’s optimal lower bounds for small-depth circuits]
  • A. “Almost optimal lower bounds for small depth circuits” chosen
    “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.
  • B. Håstad’s switching lemma
    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.
  • C. “Inapproximability results for SAT and other problems”
    “Inapproximability results for SAT and other problems” is a seminal theoretical computer science paper by Johan Håstad that establishes tight hardness-of-approximation bounds for satisfiability and related optimization problems using probabilistically checkable proofs.
  • D. Interactive Proofs and the Hardness of Approximating Cliques
    "Interactive Proofs and the Hardness of Approximating Cliques" is a seminal theoretical computer science paper that introduced powerful interactive proof techniques to show that finding near-maximum cliques in graphs is computationally intractable to approximate within strong bounds.
  • E. Blum complexity measures
    Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
  • 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_69bf336d43a081909ab05d237c297c7b completed March 22, 2026, 12:10 a.m.
Created at: March 20, 2026, 2:04 p.m.