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Metadata 
bibkey: barat2006numeration
authors: Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner
year: 2006
title: 'Dynamical directions in numeration'
doi: 10.5802/aif.2233
claim: The survey treats numeration systems and their associated compactifications, including odometers, and serves as the standing reference for this area.
strata_touched:
  - D5/S1/Digit/Infinite/NoContinuousAdditionExtension
license: citation-only
triage: anchor

Dynamical directions in numeration

Barat, Berthé, Liardet, and Thuswaldner survey numeration systems and their associated compactifications, odometers, and G-scales. The article appeared in Annales de l’Institut Fourier 56(7), 2006, pages 1987–2092. The orchestrator verified these bibliographic details and the abstract’s scope from the NUMDAM record page.

A quality review seat reported that the article treats the same Zeckendorf compactification and states that ordinary addition does not extend continuously to it, using the same two alternating boundary points. This specific passage remains seat-reported: the orchestrator could not reproduce it because the publisher PDF at IRIF returns HTTP 403, and the NUMDAM PDF has no extractable text layer for the tools on this host. Neither the passage nor the alternating cluster-point argument is recorded here as independently verified.

The repository theorem rules out every separately continuous binary operation agreeing with finite addition. No claim is made that this stronger statement has been verified in the published article.

Search log

  • 2026-09-17: Queried Library/ and Blueprint/D5/S1/Digit/ for barat2006, Dynamical directions in numeration, and 10.5802/aif.2233. No existing citation note or Scribe reference matched.
  • 2026-09-17: Fetched the NUMDAM record AIF_2006__56_7_1987_0 (HTTP 200) and searched its metadata and abstract for citation_doi, citation_title, citation_author, compactification, and odometer. The record confirms the orchestrator’s bibliographic details and abstract scope stated above.
  • 2026-09-17: Recorded the orchestrator’s attempts to locate the seat-reported passage about continuous addition and the two alternating cluster points. The reported outcomes are preserved verbatim: “The publisher PDF at IRIF returns HTTP 403”; “the NUMDAM PDF has no extractable text layer for the tools on this host.” These failures leave the specific passage unverified.

Verified locator

  • DOI: https://doi.org/10.5802/aif.2233
  • NUMDAM record: https://www.numdam.org/item/AIF_2006__56_7_1987_0/