TRIDENT Mini Case Card — Shannon Channel Capacity: Informational Coherence Threshold in AWGN Channels (INFO-SHANNON-001.v1)

This mini case card applies the TRIDENT-Z0 diagnostic framework to Shannon channel capacity under the classical Shannon–Hartley theorem for additive white Gaussian noise (AWGN) channels. The maximum reliable transmission rate is given by C = B log₂(1 + S/N), where B is bandwidth and S/N is signal-to-noise ratio. If transmission rate R exceeds C, error probability cannot be driven arbitrarily close to zero under fixed boundary conditions.

Scope boundary: This evaluation is limited to classical AWGN channels. Quantum channels, network information theory, multi-user or interference channels, and feedback-capacity extensions are explicitly excluded.

G1–G3 pass cleanly: the theorem is mathematically proven and experimentally realized; signal propagation under additive Gaussian noise is well-defined; and bandwidth and noise constitute an explicit constraint field. G4 receives a full PASS: informational coherence (decodability) depends strictly on R ≤ C. Collapse is irreversible under fixed B and S/N. Increasing either boundary parameter raises C and restores decodability. The limit is a property of the constraint field, not of the signal.

This case demonstrates a fully closed informational coherence threshold. Exceeding channel capacity produces predictable and quantifiable loss of decodability within the defined boundary conditions. Produced under the Sympathetic Harmonic Resonance Framework (SHRF) evidence-bound analysis protocol. Corpus node: INFO.

KEYWORDS

TRIDENT
SHRF
Shannon channel capacity
Shannon–Hartley theorem
AWGN channel
signal-to-noise ratio
bandwidth constraint
information theory
error probability
coherence threshold
falsifiability
boundary constraints