Palindromic Liouvillian symmetry under dephasing: proof, hardware validation, and dephasing noise as information channel

We prove that for N-qubit systems with any Pauli-pair Hamiltonian on any graph topology, subject to local single-axis dephasing, the Liouvillian spectrum has an exact palindromic symmetry. The conjugation operator Π satisfies Π L Π¹ = −L − 2Σγ I. Key Results Palindromic proof: Verified through N=8 (65536×65536 Liouvillian, 54,118 oscillatory eigenvalues, zero exceptions). All topologies: chain, star, ring, complete graph, binary tree. 36/36 resolution: All two-term Pauli-pair combinations explained. 20 via uniform Π (P1/P4 families), 3 via non-uniform alternating operators, 11 break structurally at N≥3, 2 via genuinely non-local (entangled) Π operators. Hardware validation: IBM Torino (ibm_torino, Q80). Predicted crossing time 15.01 μs, measured 15.29 μs. Deviation: 1.9%. Central New Result: Noise Is Signal The spatial dephasing profile across a spin chain is a readable information channel: 15.5 bits channel capacity at 1% noise (of 16.6 theoretical max) 5 independent SVD modes, each a spatial frequency 100% classification accuracy across 20 spatial profiles 21.5× optimization via V-shape gradient, dynamic decoupling, time-resolved decoding +83% end-to-end MI with staged relay protocol (11-qubit chain) The palindromic spectral structure functions as the antenna. Additional Proven Results Qubit uniqueness: d²−2d=0 excludes all higher dimensions. Only qubits (d=2) carry a palindromic mirror. Incompleteness proof: Five internal noise candidates eliminated. Dephasing must originate from outside the framework. Universal lifetime: x³+x=½ gives t*/T₂ ≈ 0.858 (platform-independent). Fold catastrophe: CΨ=¼ is structurally stable (Thom-Arnold classification), equivalent to the Mandelbrot cusp at c=¼. Experienced time: γ is necessary and sufficient for irreversibility. J provides content, γ provides the arrow. Engineering Six design rules for palindrome-aware quantum repeaters. Mediator bridge preserves palindrome (1024/1024 pairs). Quantum transistor mapping: gate=γ, threshold=¼. Repository 59 experiment documents, 7 formal proofs, 14 synthesis documents, and a complete mathematical reference (Tafelwerk). Every document has SEO keywords, abstract, and standard header. Quality-reviewed by independent AI pass (93 fixes across 37 files).