{
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  "canonical_url": "https://transduction.systems/entries/concept_recursion/",
  "release": "0.35",
  "citation": "Taylor, B. P. (2026). Recursion. The Necessary Tangle, release 0.35. https://transduction.systems/entries/concept_recursion/",
  "licence": "CC BY-SA 4.0 for original atlas text and data; linked works retain their own terms",
  "entry": {
    "id": "concept_recursion",
    "label": "Recursion",
    "entity_type": "concept",
    "description": "A family of relations in which a definition, operation, organisation or observation is reapplied to instances of the same kind. The domain, recurrence rule and boundary condition must be stated.",
    "aliases": [],
    "boundary_ring": "0",
    "inclusion_reason": "seed_corpus",
    "status": "accepted",
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      "src_sysbok_recursion_2013",
      "src_nist_recursion_dictionary",
      "src_sep_recursive_functions_2024",
      "src_metaphorum_vsm_2026"
    ],
    "set_tags": [
      "systems",
      "cybernetics",
      "core_concept",
      "recursion_pilot",
      "core_cluster"
    ],
    "espoused_labels": [],
    "observed_clusters": [],
    "canonical_definition": "A family of domain-specific relations in which a definition, operation, structure or organisation is reapplied to instances of the same kind. A conforming account must state the domain, recurrence rule and boundary or termination condition; organisational recursion is not automatically computational recursion or visual self-similarity.",
    "valid_from": "",
    "valid_to": "",
    "external_ids": "{}",
    "geographies": [],
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    "x": -0.312849,
    "y": 0.323651,
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    "node_id": "concept_recursion",
    "title": "Recursion",
    "profile_status": "evidence_deepened_research_pass",
    "canonical_definition": "A family of domain-specific relations in which a definition, operation, structure or organisation is reapplied to instances of the same kind. A conforming account must state the domain, recurrence rule and boundary or termination condition; organisational recursion is not automatically computational recursion or visual self-similarity.",
    "summary": "Recursion is a family resemblance across domains, not one universal mechanism. A definition may refer to itself through smaller cases; a computation may call itself; an organisation may contain operational systems with corresponding viability requirements.",
    "why_it_matters": "Nested diagrams easily look profound. A sound recursive claim states what recurs, what changes between levels, what the base or boundary condition is and why the same structural relation applies.",
    "key_distinctions": [
      "recursive definition vs recursive computation",
      "recursion vs iteration",
      "recursion vs hierarchy",
      "recursion vs fractal self-similarity",
      "organisational recursion vs mathematical recursion",
      "recursion vs reflexivity"
    ],
    "historical_lineage": [
      "formal recursive definition and recursive-function theory",
      "computability in the 1930s",
      "linguistic self-embedding",
      "Beer and organisational recursion",
      "second-order observation and reflexivity as a distinct neighbouring lineage"
    ],
    "logical_antecedents": [
      "identity of the operation or structure",
      "rule for moving to another instance or level",
      "base case or boundary condition",
      "domain in which sameness is claimed"
    ],
    "dependent_subsequents": [
      "recursive functions",
      "self-embedding grammars",
      "nested viable systems",
      "some fractal constructions",
      "some forms of self-reference"
    ],
    "practice_connections": [
      "name the system-in-focus",
      "show what recurs and what does not",
      "state stopping and boundary conditions",
      "do not infer sameness from visual nesting"
    ],
    "espoused_lineages": [
      "mathematics",
      "computability",
      "linguistics",
      "management cybernetics",
      "second-order cybernetics"
    ],
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    "common_misreadings": [
      "repetition is recursion",
      "hierarchy and recursion are synonyms",
      "fractal means recursive and vice versa",
      "Turing invented recursion",
      "nested boxes prove organisational recursion"
    ],
    "open_checks": [
      "Dedekind and Skolem primary texts",
      "Church and Kleene",
      "Chomsky precise use",
      "Beer primary theorem and pages",
      "Varela and von Foerster"
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      "creators": [
        "Paul E. Black",
        "Patrick Rodgers"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "US National Institute of Standards and Technology",
      "licence": "US government site terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "research_pass_needs_editor",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_sep_recursive_functions_2024",
      "title": "Recursive Functions",
      "source_type": "scholarly_encyclopaedia_entry",
      "quality_tier": "B",
      "access": "public",
      "url": "https://plato.stanford.edu/entries/recursive-functions/",
      "date": "2024-03-01",
      "notes": "Stanford Encyclopedia of Philosophy entry covering recursive definitions, recursive functions, computability and their history. Useful for separating formal recursion from analogy and later organisational uses.",
      "creators": [
        "Walter Dean"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "Stanford Encyclopedia of Philosophy",
      "licence": "SEP terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "research_pass_needs_editor",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_metaphorum_vsm_2026",
      "title": "Viable System Model - The VSM in 1000 words",
      "source_type": "professional_community_explainer",
      "quality_tier": "C",
      "access": "public",
      "url": "https://metaphorum.org/staffords-work/viable-system-model",
      "date": "2026-08-09",
      "notes": "Metaphorum explainer identifying Ashby's requisite variety, Wiener's cybernetics and the mathematics of recursive systems among the VSM's theoretical bases. Used as a public bridge source pending exact primary-book locators.",
      "creators": [
        "Metaphorum"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "Metaphorum",
      "licence": "site_terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "research_pass_needs_editor",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_turing_computable_numbers_1936",
      "title": "On Computable Numbers, with an Application to the Entscheidungsproblem",
      "source_type": "primary_research_article",
      "quality_tier": "A",
      "access": "public_metadata",
      "url": "https://doi.org/10.1112/plms/s2-42.1.230",
      "date": "1936-11-12",
      "notes": "Alan Turing's foundational computability paper. It is retained as formal context for recursive-function theory, not treated as the origin of recursion itself.",
      "creators": [
        "Alan M. Turing"
      ],
      "doi": "10.1112/plms/s2-42.1.230",
      "isbn": "",
      "publisher": "Proceedings of the London Mathematical Society",
      "licence": "publisher_terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "research_pass_needs_editor",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_beer_diagnosing_system_1985",
      "title": "Diagnosing the System for Organizations",
      "source_type": "primary_book",
      "quality_tier": "A",
      "access": "public_metadata",
      "url": "https://www.wiley-vch.de/en/areas-interest/finance-economics-law/diagnosing-the-system-for-organizations-978-0-471-95136-0",
      "date": "1985-01-01",
      "notes": "Stafford Beer's guide to diagnosing organisations with the Viable System Model. The exact primary-book pages for the recursive-system theorem remain to be located before the organisational-recursion relation is promoted.",
      "creators": [
        "Stafford Beer"
      ],
      "doi": "",
      "isbn": "9780471951360",
      "publisher": "Wiley",
      "licence": "publisher_terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "research_pass_needs_editor",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_grammar_presentation_2022",
      "title": "The Grammar of Systems - SCiO presentation",
      "source_type": "presentation",
      "quality_tier": "C",
      "access": "public",
      "url": "https://www.systemspractice.org/resources/grammar-systems",
      "date": "2022-03-21",
      "notes": "Lists 33 systems laws and principles and describes nine patterns of thinking.",
      "creators": [
        "Patrick Hoverstadt"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "SCiO",
      "licence": "site_terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "checked",
      "last_checked": "2026-08-10",
      "public_link_status": "public_link"
    },
    {
      "id": "src_grammar_2ed_2025",
      "title": "The Grammar of Systems II: From Order to Chaos and Back Again, 2nd edition",
      "source_type": "book",
      "quality_tier": "B",
      "access": "public_metadata",
      "url": "https://www.systemspractice.org/resources/grammar-systems-ii-order-chaos-back-again-2nd-ed",
      "date": "2025-08-01",
      "notes": "Current second-edition metadata. The book presents nine systems-thinking patterns and 33 systems laws and principles.",
      "creators": [
        "Patrick Hoverstadt"
      ],
      "doi": "",
      "isbn": "979-8298960878",
      "publisher": "SCiO",
      "licence": "publisher_terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "checked",
      "last_checked": "2026-08-10",
      "public_link_status": "public_link"
    },
    {
      "id": "src_salah_grammar_part3_2022",
      "title": "Cybersecurity Lessons from The Grammar of Systems, part 3",
      "source_type": "public_secondary_summary",
      "quality_tier": "C",
      "access": "public",
      "url": "https://www.linkedin.com/pulse/cybersecurity-lessons-from-grammar-systems-order-chaos-osama-salah-2f",
      "date": "2022-06-01",
      "notes": "Public secondary summary of Grammar of Systems items 23–33. Used as an accessible orientation aid; the book remains the controlling source.",
      "creators": [
        "Osama Salah"
      ],
      "publisher": "LinkedIn",
      "licence": "publisher_terms",
      "review_status": "checked",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_fpcs_official_toc",
      "title": "Foundational Papers in Complexity Science — official tables of contents",
      "source_type": "publisher_table_of_contents",
      "quality_tier": "A",
      "access": "public",
      "url": "https://www.foundationalpapersincomplexityscience.org/tables-of-contents",
      "date": "2024",
      "notes": "Official item-level contents for the four-volume Santa Fe Institute Press collection. It supports the bibliographic inventory, not the substantive claims of all 89 original papers.",
      "creators": [
        "Santa Fe Institute Press",
        "David C. Krakauer (editor)"
      ],
      "publisher": "Santa Fe Institute Press",
      "licence": "source_terms",
      "review_status": "checked_primary_register",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link",
      "doi": "",
      "isbn": "",
      "archived_url": "",
      "content_hash": ""
    },
    {
      "id": "src_scio_cf_resources_2022",
      "title": "SCiO CF Resources v9 draft",
      "source_type": "professional_framework_resource_guide",
      "quality_tier": "C",
      "access": "no_public_link",
      "url": "",
      "date": "2022-09-15",
      "notes": "SCiO internal competency-resource draft; no public link. Public SCiO accreditation pages are linked separately where possible.",
      "creators": [
        "SCiO"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "",
      "licence": "",
      "archived_url": "",
      "content_hash": "",
      "review_status": "pass4_legacy_internal_register_audit",
      "last_checked": "2026-08-14",
      "public_link_status": "no_public_link"
    },
    {
      "id": "src_scio_accreditation_current",
      "title": "SCiO Professional Accreditation and Competency Framework",
      "source_type": "professional_body_page",
      "quality_tier": "C",
      "access": "public",
      "url": "https://www.systemspractice.org/professional-accreditation",
      "date": "2026-08-09",
      "notes": "Current framework fields and assessment process.",
      "creators": [],
      "doi": "",
      "isbn": "",
      "publisher": "",
      "licence": "",
      "archived_url": "",
      "content_hash": "",
      "review_status": "checked",
      "last_checked": "2026-08-09",
      "public_link_status": "public_link"
    },
    {
      "id": "src_practice_lab_viable_system_model",
      "title": "Viable System Model: diagnose functions and channels",
      "source_type": "practice_resource",
      "quality_tier": "A",
      "access": "public",
      "url": "https://transduction.systems/systems-thinking/practice/viable-system-model/",
      "date": "2026-09-07",
      "notes": "Original fictional exercise. A basic organisational diagnosis. Functions can be distributed or combined in people and groups. The exercise does not establish that every multi-agency network has a single legitimate metasystem.",
      "creators": [
        "The Necessary Tangle editorial practice pack"
      ],
      "doi": "",
      "isbn": "",
      "publisher": "The Necessary Tangle",
      "licence": "Original practice text CC BY-SA 4.0; external material retains source terms",
      "archived_url": "",
      "content_hash": "",
      "review_status": "original_material_and_source_boundary_recorded",
      "last_checked": "2026-09-07",
      "public_link_status": "public_link"
    }
  ],
  "evidence_locators": [
    {
      "id": "ev_nist_algorithmic_recursion",
      "source_id": "src_nist_recursion_dictionary",
      "locator": "definition and note, lines 2-18 of the current entry",
      "review_status": "research_pass_needs_editor"
    },
    {
      "id": "ev_sep_recursive_definition",
      "source_id": "src_sep_recursive_functions_2024",
      "locator": "introductory definition, paragraphs 1-4",
      "review_status": "research_pass_needs_editor"
    },
    {
      "id": "ev_sep_recursion_history",
      "source_id": "src_sep_recursive_functions_2024",
      "locator": "section 1.1, early history of recursive definitions",
      "review_status": "research_pass_needs_editor"
    },
    {
      "id": "ev_metaphorum_vsm_bases",
      "source_id": "src_metaphorum_vsm_2026",
      "locator": "The VSM in 1000 words, paragraphs 2-3",
      "review_status": "research_pass_needs_editor"
    }
  ],
  "reuse_note": "Preserve source attribution, scope, and review status. Source documents and evidence excerpts are excluded."
}