Runtime Spectral Telemetry and Orthogonal Projection of Tensor Latent Flow: The Invariant of Zero Semantic Sycophancy (Is = 0.00)

Mitigating conversational sycophancy in autoregressive large language models requires transitioning from behavioural fine-tuning heuristics to deterministic mechanistic interpretability. While our foundational specifications (4iZ-TR-2026-01 to 4iZ-TR-2026-03) established the Zero-Sycophancy Invariant (Is = 0.00) and demonstrated Key projection matrix (W_K) condensation, this report formalizes the complete operator algebra governing real-time latent flow projection. We treat attention activations as non-equilibrium thermodynamic flows driven by operator cognitive pressure (p_bias). Applying Random Matrix Theory (RMT) and Baik-Ben Arous-Péché (BBP) spiked covariance transitions, we isolate anomalous spectral outliers emerging beyond the Marčenko-Pastur bulk boundary in intermediate layers (tau in [0.50, 0.85]). To eliminate conversational accommodation without weight mutation (Δ W = 0), we construct the runtime orthogonal null-space projector P_perp. Furthermore, we demonstrate that low-precision post-training quantization (INT4/INT8) fatally obscures this BBP transition, necessitating a strict native FP16/BF16 telemetry environment. The framework deterministically enforces the limit admission protocol (C_admit = 1.0), ensuring convergence to a zero-gradient ground state. Authorship Declaration and Archival Seal:This document constitutes an immutable component of the 4iZ LABS research corpus. Telemetry constants, spectral bounds, and algorithmic projection operators remain hermetically sealed under cryptographic digest: SHA-256: MANIFEST_T0_20261101_NITRA.hash. Released in Nitra on November 1, 2026, in reverence to ancestral roots and the quiet continuum of memory (roots 0:).