{
  "abstract": "How can we distinguish a structural transformation from a mere variation in representation? Drawing on the critical program of Book I of the *Treatise on Adaptive Systems*, this article develops a constructive procedure that allows us to subject a claimed plasticity to three complementary tests: reduction, absorbability, and identification under an explicitly specified observational framework. The approach is illustrated using a decision-making system for granting microcredit, in which a time-varying decision rule, a variable contributive domain, and a parameter θ interpolating between two aggregation regimes are considered in succession. For a variable distribution, the introduction of an augmented state space shows—under an explicit hypothesis regarding the closure and representability of its evolution—how variability can be absorbed into the state of a system with a fixed distribution. For a variable contributive domain, a compatible extension to a universal domain allows us to test, in a similar manner, whether the observed variation constitutes a structural difference. Finally, for the family Hθ(f, µ) = θC(f, µ) + (1 − θ)S(f, µ), a conditional parametric injectivity proposition establishes that, for a fixed capacity, θ is distinguishable within the family of operators if and only if the two aggregation regimes C and S do not coincide over the entire admissible class. These results lead to a rigorous distinction between existence, representability, operability, contribution, observability, and identifiability. Above all, they show that an observable variation—even one that is parametrically identifiable—is not sufficient to establish irreducible plasticity: the difference must still resist competing transformations that could absorb it and remain distinguishable relative to the chosen observation framework. The article thus arrives at a precise set of specifications for any future construction: before proposing an adaptation operator, one must determine which variations cannot be reduced, absorbed, or rendered equivalent by a competing representation.",
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  "author_total": 1,
  "authors": [
    {
      "name": "Philibert Andriamanantena"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/216vjse28s713.bib",
  "cited_by": 0,
  "doi": null,
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  "id": "216vjse28s713",
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  "landing_url": "https://hal.science/hal-05801231v1",
  "language": "fr",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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  "pdf_url": "https://hal.science/hal-05801231/document",
  "pmcid": null,
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  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/216vjse28s713.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "hal-05801231",
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      "url": "https://hal.science/hal-05801231v1"
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  "subjects": [
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      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
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  "title": "Quand le changement ne suffit pas : Réduction, absorbabilité et identification de la plasticité",
  "title_text": "Quand le changement ne suffit pas : Réduction, absorbabilité et identification de la plasticité",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:57Z",
  "url": "https://research.draconitic.com/paper/216vjse28s713",
  "venue": "HAL",
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}