Triple

T16892562
Position Surface form Disambiguated ID Type / Status
Subject Banach–Alaoglu theorem E424210 entity
Predicate originalPublication P15299 FINISHED
Object Alaoglu’s 1940 paper on weak topologies of normed linear spaces E424210 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: Alaoglu’s 1940 paper on weak topologies of normed linear spaces | Statement: [Banach–Alaoglu theorem, originalPublication, Alaoglu’s 1940 paper on weak topologies of normed linear spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Alaoglu’s 1940 paper on weak topologies of normed linear spaces
Context triple: [Banach–Alaoglu theorem, originalPublication, Alaoglu’s 1940 paper on weak topologies of normed linear spaces]
  • A. Produits tensoriels topologiques et espaces nucléaires
    "Produits tensoriels topologiques et espaces nucléaires" is a foundational 1953 doctoral thesis in functional analysis that introduced and developed the theory of nuclear spaces and topological tensor products.
  • B. Schreier family in Banach space theory
    The Schreier family in Banach space theory is a combinatorial collection of finite subsets of natural numbers introduced by Józef Schreier that plays a central role in constructing and analyzing special Banach spaces with unusual structural properties.
  • C. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • D. Tychonoff theorem for products of compact spaces
    The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
  • E. Banach–Alaoglu theorem chosen
    The Banach–Alaoglu theorem is a fundamental result in functional analysis stating that the closed unit ball in the dual of a normed space is compact in the weak-* topology.
  • 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_69d889da3e8c8190a2b118f383f0beac completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e3bbc5a5308190937ebd05356bd91d completed April 18, 2026, 5:13 p.m.
NED1 Entity disambiguation (via context triple) batch_6a00c7a7fd8481908ef82a13418b1c2d completed May 10, 2026, 6 p.m.
Created at: April 10, 2026, 5:29 a.m.