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docs(research): distinguish gate levels and explore identity across representations and time - #135

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Oct 29, 2026
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hyperpolymath merged 5 commits into
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docs/kategoria-open-ended-type-programme

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@hyperpolymath hyperpolymath commented Oct 29, 2026 •

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Scope correction

This PR distinguishes VCL-UT's compatibility-sensitive L0–L10 query-safety predicates from Kategoria's different type-feature taxonomy and TypeLL's other property levels. It does not cap VCL-UT's future research at ten type systems.

It also adds an exploratory, non-normative note, docs/research/TYPE-TROPE-IDENTITY-SPACES.adoc, in response to the research motivation behind this language: understanding identity and equivalence across representation, context, use and time, not prescribing a universal type/trope framework.

Evidence and scope of the new note

  • Maps parametric, phantom, immutable, dyadic, ceremonial, epistemic, echo, residual-evidence, tropical, choreographic, secret, and occupancy types to their actual source families, distinguishing detector registration from theorem/checker status.
  • Separates typed admissibility, situated particularity, use-relative warrant, sortal identity/counting and institutional role legitimacy.
  • Uses Firmboot for synchronic admission-boundary coherence and diachronic service continuity; Lithoglyph/GNPL for persistent history, evidence-versioned narration and retractable accounts; Tangle for structure-preserving transformations; QuandleDB/KRL for candidate matching versus witnessed equivalence; and Invariant Path for sortal criteria and the double-counting attack.
  • Preserves these repositories' independent purposes and highlights their precise open obligations. Does not claim a global type–trope equivalence, a triangulation theorem, a universal total order of type strength, or a verified all-purpose identity theory.
  • Lists candidate proof questions and optional experiments, explicitly not an agreed implementation plan.

Compatibility

Documentation only. No source-language, Idris2/Rust checker, L0–L10 tags, VCLW/VCLS/VCLT wire semantics or runtime policies change.

This note is intended to open the research question without locking a solution in prematurely.

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  • docs/research/TYPE-TROPE-IDENTITY-SPACES.adoc
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`routes/alpha-extend/README.adoc` and
`routes/delta-aggregate/TYPELL-BRIDGE.adoc`.
Kategoria's first ten *type-theoretic capabilities* are basic types,
ADTs, polymorphism, type classes, GADTs, dependent types, linear types,

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P2 Badge Name Kategoria's fourth level correctly

The referenced Kategoria taxonomy defines level 4 as Higher-Kinded Types, not type classes. Since this section is intended to distinguish the exact meanings of two numbered schemes, substituting a related but different capability makes the crosswalk factually inaccurate; replace “type classes” with “higher-kinded types.”

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Comment on lines +45 to +46
This L0–L10 is the existing, fixed *VCL-UT query safety / wire
compatibility* numbering. It is NOT the Kategoria 1–10 language-feature

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P2 Badge Describe L10 outside query safety

This labels the entire L0–L10 range as query-safety numbering even though docs/2026-07-21-workup-consonance-and-verisim.adoc explicitly identifies L10 EpistemicSafe as not being a query-safety property, but rather a property about whether an answer is warranted. Because L10 is included in the range being defined here, this wording reintroduces the category confusion the new section is meant to eliminate; describe it as statement/gate safety or explicitly carve out L10.

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@hyperpolymath hyperpolymath changed the title docs: distinguish the L0–L10 gate from Kategoria's open-ended type programme docs(research): distinguish gate levels and explore identity across representations and time Oct 29, 2026
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hyperpolymath enabled auto-merge (squash) October 29, 2026 22:57
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hyperpolymath merged commit 002b654 into main Oct 29, 2026
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hyperpolymath deleted the docs/kategoria-open-ended-type-programme branch October 29, 2026 22:57
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