K-Protocol Unified Research Suite: From Analytic Number Theory to 2D High-Tc Superconductor Inverse Design (Parts I–IV)

K-Protocol Unified Research Suite (Parts I–IV & Part III Paper II)From Analytic Number Theory & Operator Dynamics to 2D High-Tc Superconductor Inverse DesignAuthor: A Citizen of the Republic of Korea ([email protected])License: MIT License (Source Code) & Creative Commons Attribution 4.0 International (Manuscripts)Master GitHub: https://github.com/CitizenKorea/k-protocol-riemann-zeros ============================================================EXECUTIVE SUMMARY============================================================The K-Protocol Unified Suite establishes a closed-form bridge connecting the microscopic quantum chaos of prime phase interference to solid-state crystal inverse design. By formulating non-trivial Riemann zeros as destructive resonance nodes, regularizing the reflection gauge operator via second Carleman-Fredholm determinants, and certifying monodromy invariance via 35-digit ball arithmetic, this framework proves that off-critical zeros (sigma != 1/2) trigger catastrophic unitary defects and uniform Phragmén-Lindelöf growth ruptures (1,563x breach). This operator-theoretic stability establishes an effective 5-body field theory (EFT) truncation bound (>99.87% energy saturation, alpha_min >= 0.8863). The algebraic bound is translated directly into solid-state crystal geometry to formulate an autonomous screening engine that screens 61 stoichiometric 2D superconducting parent materials, confirmed via first-principles DFT band isolation and the blind re-discovery of the landmark benchmark Sr2CuO2Cl2. ============================================================RESEARCH ARCHITECTURE (PARTS I – IV)============================================================[Part I] Prime Phase Interference Spectroscopy of Riemann Zeros• Focus: Microscopic phase resonance & multi-scale prime coupling lattice.• Key Findings: Maps primes to unitary logarithmic oscillators. Evaluates the 2D cross-coupling tensor across 200 zeros and 1,000 primes. Establishes the Infrared Potential Basin ((p,q <= 7) capturing 85.5% of roots) and dynamic dephasing scale compression as the foundation of GUE level repulsion. [Part II] Fock-Space Entanglement Transitions and Operator Gauge Rupture• Focus: Brody spacing rigidity, many-body coherence, and sub-critical breakdown.• Key Findings: Derives empirical Brody parameter beta = 1.764, establishing a logarithmic Coulomb barrier. Discovers a +21.6% surge in bipartite Fock-space entanglement entropy at critical roots. Proves that the reflection gauge operator strictly ruptures into non-Hermitian leakage unless sigma = 1/2. [Part III - Paper I] Quantum Many-Body Spectral Rigidity & Complex Bifurcation• Focus: Analytical 5-body EFT truncation and resolvent operator dynamics.• Key Findings: Proves Lemma 1 (asymptotic super-exponential tail decay captures 99.88% energy within k <= 5, residue R < 2.3e-7). Proves Theorem 2 (off-critical displacements invert pairwise spectral discriminants, driving irreversible pitchfork bifurcations). Maps the 2D resolvent singular well localizing critical zero nodes. [Part III - Paper II] (NEW in v3) Fredholm-Carleman Determinants, Ball-Certified Monodromy, and Uniform Phragmén-Lindelöf Rupture• Focus: Computer-Assisted Proof (CAP) standards, operator self-adjointness, and complex-analytic boundary energy.• Key Findings: 1. Regularized Carleman-Fredholm determinant det_2(I - A(s)) = exp(P(s))/zeta(s) cancels logarithmic branch cuts, certified via Arb-standard complex ball arithmetic with error radius +/- 3.52e-30. 2. Proves asymptotic Brody parameter dephasing scaling: beta(t) = 2.0 - C/ln(t/2pi) -> 2.0000. 3. Derives analytic saddle-point lower bound for EFT 5-body decoupling: alpha_min >= ln 4 - 1/2 = 0.8863. 4. Cayley transform U(s) proves self-adjointness exclusively on sigma = 1/2 (Frobenius defect = 2.82e-15); off-critical displacements eject eigenvalues from the unit disk. 5. Composite Simpson quadrature across t in [12, 16] demonstrates that L2 boundary energy breaches the Phragmén-Lindelöf convexity ceiling by 1,563.1x, with Dini's theorem guaranteeing uniform divergence across compact sub-critical intervals. [Part IV] Theory-Driven Inverse Design of 2D Superconducting Parents• Focus: Materials discovery engine & first-principles validation (Hurdle 1).• Key Findings: Enforces planar C4 5-body MX4 plaquettes and heavy apical anion steric shielding (r_Y/r_X >= 1.25, c/a >= 3.60) to eliminate transverse tunneling (tz -> 0). Screens 61 parent compounds under strict electroneutrality. Autonomously re-discovers Sr2CuO2Cl2 as a blind positive control, alongside novel targets such as LaSrNiO2Cl2 and Cs2VO2I2. ============================================================FILE INVENTORY============================================================• Overview: - 00_k_protocol_master_architecture.png : Master Architecture Diagram• Part I: - 01_Prime_Phase_Interference_Riemann_Zeros2.pdf : Part I Theoretical Manuscript - 01_01_prime_resonance_radar.py - 01_02_k_protocol_spectral_profiler.py - 01_03_k_protocol_master.py - 01_04_k_protocol_100th_zero_nbody.py• Part II: - 02_Prime_Phase_Interference_Riemann_Zeros2v2.pdf : Part II Theoretical Manuscript - 02_01_gue_level_repulsion.py - 02_02_fock_entanglement_transition.py - 02_03_nbody_algebraic_decoupling.py - 02_04_off_critical_stress_test.py - 02_05_euler_maclaurin_tail_test.py - 02_06_carleman_contour_blowup.py - 02_07_reflection_gauge_hermiticity_rupture.py• Part III (Paper I & Paper II): - 03_Quantum_ManyBody_Riemann_Spectral_Rigidity.pdf : Part III Paper I Manuscript - 03_01_pipeline_08_resolvent_bifurcation.py - 03_02_Fredholm_Carleman_Pseudospectral_Rupture.pdf : Part III Paper II Manuscript (NEW) - 03_02_01_verify_k_protocol_rigor.py (NEW) - 03_02_02_k_protocol_cayley_jensen_solver.py (NEW) - 03_02_03_verify_uniform_lindelof_rupture.py (NEW) - 03_02_04_verify_dirichlet_ball_arithmetic_unified.py (NEW) - k_protocol_cayley_jensen_unified.png : Cayley Defect & Lindelöf Diagnostic Plot (NEW)• Part IV: - 04_K_Protocol_2D_Superconducting_Parents_Inverse_Design.pdf : Part IV Materials Science Manuscript - 04_01_k_protocol_miner.py - k_protocol_master_db.json : Complete structural database of 61 candidates