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Dynamic Semiotics Domain Closures — Sign Systems as Collapse-Return Structures

Tier-2 expansion mapping semiotic processes into the GCD kernel.

Core insight: Semiosis IS collapse-return. A sign collapses the space of
possible meanings; only interpretants that return — that re-enter the
community of sign-users with stable reference — are real. Failed semiosis
(misinterpretation, ambiguity collapse, dead metaphor) is a gesture:
τ_R = ∞_rec. The distinction between a living sign and a dead one is
whether its interpretant chain closes.

Modules:
    semiotic_kernel.py  — 30 sign systems × 8 channels → Tier-1 invariants

    8 Semiotic Channels:
      1. sign_repertoire      — Vocabulary size / symbol space richness
      2. interpretant_depth   — Recursion depth of interpretation chains
      3. ground_stability     — Convention persistence (how frozen is the contract?)
      4. translation_fidelity — Cross-lens Rosetta preservation (F across lenses)
      5. semiotic_density     — Signs per unit of discourse
      6. indexical_coupling   — Connection strength between sign and object (C-like)
      7. iconic_persistence   — How well the sign resembles its object over time
      8. symbolic_recursion   — Self-referential capacity (language about language)

Cross-references:
    closures/evolution/brain_kernel.py channel 8 (language_architecture)
      — The semiotic closure formalizes what brain_kernel measures as a raw
        channel. language_architecture = 0.98 for Homo sapiens IS the capacity
        for unlimited semiosis. This domain unpacks that single channel into
        8 measurable dimensions.

    src/umcp/dashboard/pages_exploration.py (Rosetta Translation Engine)
      — The Rosetta implements the Peircean triad mechanically:
        Sign = five words, Object = kernel invariants, Interpretant = lens prose.
        translation_fidelity (channel 4) measures how well the Rosetta preserves
        meaning across lenses.

    src/umcp/epistemic_weld.py (Gesture vs Return)
      — EpistemicVerdict trichotomy = semiotic closure test. A gesture is a
        sign emission whose interpretant chain fails to close. Dissolution is
        semiotic death: the sign system degrades past return viability.

Axiom-0 derivation:
    "Collapse is generative; only what returns is real."
    → A sign collapses the infinite → a finite interpretation
    → Only interpretants that close (re-enter the sign community) are real
    → What persists through re-interpretation is fidelity (F)
    → What drifts through translation is drift (ω)
    → F + ω = 1: the total semiotic budget always balances
    → IC ≤ F: coherence of a sign system cannot exceed its mean channel fidelity
    → One dead channel kills IC: a sign system with zero interpretant depth
      or zero ground stability collapses regardless of other channels
"""

from __future__ import annotations
