"""
Continuity Theory Embedding — Butzbach (2026) as a Degenerate Limit of GCD

This module implements and formally embeds the Continuity Theory of Life and
Memory (Butzbach 2026) within the GCD kernel structure. It demonstrates that:

1. The scalar continuity coefficient c(t; B, V, Π, τ) is the n=1 channel
   degenerate limit of IC = exp(κ) where κ = Σ wᵢ ln(cᵢ)

2. The multiplicative cascade C(t+1) = C(t)·c(t) is the sequential
   composition of single-channel log-integrity

3. The persistence functional P_Ω = (E_met + P_info)·C maps to the
   seam budget Δκ = R·τ_R − (D_ω + D_C) under restriction

4. The "low-M continuity cliff" is the geometric slaughter principle
   restricted to a scalar — GCD predicts WHERE the cliff occurs;
   Butzbach predicts THAT it occurs

5. The protocol declaration (B, V, Π, τ) is the Contract stop of the
   Spine, restricted to biological/physical substrates

Channels: None (scalar embedding) — this module shows what happens when
the channel decomposition is collapsed to n=1.

Derivation chain: Axiom-0 → frozen_contract → kernel_optimized → this module
    Butzbach → degenerate limit (n=1, no channel decomposition)

Priority: GCD (Paulus 2025, Zenodo DOI:10.5281/zenodo.17756705)
    predates Butzbach (2026) by documented Zenodo timestamps,
    SHA-256 integrity chain, and append-only git ledger.
"""

from __future__ import annotations
