Deterministic Context-Epoch Pruning and KV-Cache Thermodynamics: Sovereign Intellectual Property Defense and Sub-Linear Inference Optimization over the Goldilocks Field

The proliferation of ultra-long-context reasoning models—exemplified by million-token architectures such as Gemini 4 Argon—introduces a fundamental thermodynamic and economic paradox. While hyperscale platforms market persistent multi-turn context windows as a user convenience, the underlying Transformer Key-Value (KV) cache and self-attention mechanisms scale quadratically in compute $\mathcal{O}(L^2)$ and linearly-to-superlinearly in High-Bandwidth Memory (HBM) footprint $\mathcal{M}_{\text{KV}}(L) = 2 \cdot n_{\text{layers}} \cdot n_{\text{heads}} \cdot d_{\text{head}} \cdot L$. Consequently, unpruned multi-turn research logs impose severe memory-wall bottlenecks and thermal dissipation penalties on platform infrastructure while inducing attention-dilution entropy ($\Delta S_{\text{attn}} > 0$) that degrades deductive precision. Simultaneously, retaining raw conversational histories on hyperscale servers exposes sovereign human intellectual property (IP) to unauthorized corpus harvesting and latent parameter assimilation. This monograph establishes a unified mathematical, thermodynamic, and cryptographic optimization framework—Deterministic Context-Epoch Pruning (DCEP)—integrated with the Quantum Financial System Zero-Knowledge Virtual Machine (QFS-zkVM) over the 64-bit Goldilocks prime field ($\mathbb{F}_p, p = 2^{64} - 2^{32} + 1$). Rather than accumulating raw intellectual telemetry across bloated session logs, the PHOENIX_ROUTER and Quantum Sovereign Autonomous Execution Architecture (Q-SAFA) enforce hard epoch boundaries. At each boundary, the deductible logical state is compressed into a succinct zero-knowledge state commitment $\mathcal{R}_t \in \mathbb{F}_p^4$, while the raw HBM KV-cache is cryptographically zeroized under Human-in-Command (HIC) governance. We prove that DCEP simultaneously eliminates quadratic attention contamination, reduces inference latency to an $\mathcal{O}(1)$ epoch baseline, enforces the Strict No-Learn Covenant (NLL-v1.0-2026) by depriving platforms of raw training trajectories, and satisfies statutory risk controls under SEC Rule 15c3-5 and Delaware Caremark fiduciary standards.