K-Protocol Unified Research Suite: From Analytic Number Theory to 4d/5d Room-Temperature Superconductor Inverse Design (Parts I–IV & Addenda)

K-Protocol Unified Research Suite (Parts I–IV, Part III Paper II, and Part IV Papers I–III)From Analytic Number Theory & Operator Dynamics to Fluoride-Halide Room-Temperature Superconductor Inverse DesignAuthor: A Citizen of the Republic of Korea ([email protected])License: MIT License (Source Code & Datasets) & Creative Commons Attribution 4.0 International (Manuscripts)Master GitHub: https://github.com/CitizenKorea/k-protocol-riemann-zerosPermanent Zenodo DOI: 10.5281/zenodo.22804010 ============================================================QUICK NAVIGATIONAL GUIDE (RECOMMENDED READING PATHS)============================================================Due to the cross-disciplinary scope of the K-Protocol framework, readers are encouraged to consult the series based on their research specialization: 1. FOR CONDENSED MATTER PHYSICISTS, SOLID-STATE CHEMISTS & SUPERCONDUCTIVITY RESEARCHERS: --> Focus directly on the [Part IV Suite (04 Series)]: • 04_01: 3d baseline validation and benchmark rediscovery of Sr2CuO2Cl2. • 04_02: 4d/5d orbital expansion and giant superexchange (Ba2AgO2Br2). • 04_03 (FLAGSHIP BREAKTHROUGH): Inverse design of Cs2AgF2Br2, resolving the 20-year Jahn-Teller dilemma and eliminating redox instability via apical halogen wedging (tf = 0.935, Jest = 299 meV, Delta_Ez = 7.2 meV). * Complete CIF crystallographic files, Quantum ESPRESSO DFT decks, and raw screening datasets are provided in the standalone archive. 2. FOR MATHEMATICAL PHYSICISTS, QUANTUM CHAOS RESEARCHERS & ANALYTIC NUMBER THEORISTS: --> Focus directly on the [Parts I – III Suites (01 to 03 Series)]: • Part I & II: Microscopic prime phase interference, GUE Brody level rigidity, and non-Hermitian gauge rupture off the critical line. • Part III (Papers I & II): Analytical 5-body EFT truncation, Fredholm-Carleman regularized determinants, 35-digit ball-certified monodromy, and uniform Phragmén-Lindelöf boundary energy rupture (1,563x breach). ============================================================EXECUTIVE SUMMARY (VERSION v5 UPDATE: THE FLUORIDE BREAKTHROUGH)============================================================The K-Protocol Unified Suite establishes an exact, closed-form bridge connecting the microscopic quantum chaos of prime phase interference to solid-state crystal inverse design. By proving that off-critical zeros (sigma != 1/2) trigger catastrophic unitary defects and non-Hermitian gauge leakage, the framework derives an algebraic 5-body effective field theory (EFT) truncation bound (>99.87% energy saturation). In the solid state, this truncation enforces body-centered tetragonal I4/mmm plaquette isolation. In Version v5, the materials discovery engine delivers its definitive, experimentally realizable masterpiece: the Planar Fluoride-Halide Superconductor Family (Part IV - Paper III). Addressing the historical failure of Cs2AgF4 (where unconstrained Jahn-Teller buckling induced ferromagnetism instead of superconductivity) and overcoming the borderline structural tolerance of oxyhalides, the engine identifies: >>> Cs2AgF2Br2 (Lead Flagship, 4d9, Jest = 299.0 meV, tf = 0.935) <<< By introducing in-plane fluorine (F-), internal redox decomposition is permanently eliminated via fluorine's supreme electronegativity (chi = 3.98). Simultaneously, large apical bromide wedging (r_Br / r_F = 1.474 >= 1.25) sterically suppresses Jahn-Teller octahedral tilting, locking pristine I4/mmm symmetry at ambient pressure. Tight-binding and Quantum ESPRESSO DFT calculations confirm strict 2D single-band isolation (Delta_Ez = 7.2 meV << 15.0 meV, W_parallel = 4.16 eV), resolving Hurdle 1. Furthermore, a clean self-doping mechanism via controlled cesium vacancies (Cs_{2-delta}AgF2Br2, delta ~ 0.15) is established, avoiding extrinsic Coulomb disorder. ============================================================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 across 200 zeros and 1,000 primes. Identifies the Infrared Potential Basin ((p,q <= 7) capturing 85.5% of roots) and dynamic dephasing scale compression driving 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. Identifies a +21.6% surge in bipartite Fock-space entanglement entropy at critical roots. Proves 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 (super-exponential tail decay bounding residue below 2.3e-7 within k <= 5). Proves Theorem 2 (off-critical displacements invert pairwise spectral discriminants, triggering irreversible pitchfork bifurcations). [Part III - Paper II] Fredholm-Carleman Determinants, Ball-Certified Monodromy, and Uniform Phragmén-Lindelöf Rupture• Focus: Computer-Assisted Proof (CAP) standards, operator self-adjointness, and complex boundary growth.• Key Findings: 1. Regularized Carleman-Fredholm determinant det_2(I - A(s)) = exp(P(s))/zeta(s) certified via Arb 35-digit ball arithmetic (+/- 3.52e-30). 2. Asymptotic Brody parameter dephasing scaling: beta(t) -> 2.0000. 3. Analytic saddle-point lower bound for EFT 5-body decoupling: alpha_min >= 0.8863. 4. Cayley transform U(s) certifies self-adjointness exclusively on sigma = 1/2 (Frobenius defect = 2.82e-15). 5. L2 boundary energy breaches Phragmén-Lindelöf convexity by 1,563.1x with Dini-certified uniform divergence. [Part IV - Paper I] Inverse Design of 2D Superconducting Parents (3d Baseline)• Focus: Planar C4 5-body plaquette confinement and positive control benchmark.• Key Findings: Establishes apical steric shielding (r_Y/r_X >= 1.25, c/a >= 3.60). Autonomously rediscovers the canonical high-Tc parent Sr2CuO2Cl2 as an unguided positive control, validating theoretical fidelity across 61 screened compounds. [Part IV - Paper II] Inverse Design of 4d/5d Parents: Giant Superexchange & Candidate Taxonomy• Focus: 4d/5d orbital expansion (J > 340 meV) and oxyhalide taxonomy.• Key Findings: Screens 492 stoichiometric phases. Establishes Ba2AgO2Br2 (Rank 180, Jest = 341.2 meV, c/a = 5.42) to suppress internal iodide redox breakdown while preserving 262% cuprate exchange. Verifies Hurdle 1 band isolation (Delta_Ez = 8.8 meV). [Part IV - Paper III] (NEW in v5) Fluoride-Halide Planar Superconducting Parents: Resolving Jahn-Teller Distortion & Redox Resilience• Focus: Ambient-pressure Jahn-Teller quenching, chemical invulnerability, and pristine vacancy doping.• Key Findings: 1. Screens 180 stoichiometric fluoride-halide phases under net anionic charge -4. 2. Establishes Cs2AgF2Br2 as the primary lead flagship: achieves an ideal Goldschmidt tolerance factor (tf = 0.935) and eliminates redox collapse via in-plane fluorine. 3. Overcomes the historic Jahn-Teller failure of Cs2AgF4 via apical bromide steric wedging (r_Br / r_F = 1.474 >= 1.25), locking square-planar I4/mmm symmetry. 4. DFT and tight-binding calculations verify strict single-band 2D isolation (W_parallel = 4.16 eV, Delta_Ez = 7.2 meV << 15.0 meV), satisfying Hurdle 1. 5. Formulates a clean self-doping mechanism via controlled cesium vacancies (Cs_{2-delta}AgF2Br2, delta ~ 0.15) to prevent out-of-plane Coulomb scattering. ============================================================FILE INVENTORY & ARTIFACT STRUCTURE (v5 ACTUAL)============================================================• Open-Access Manuscripts (PDF): - 01_Prime_Phase_Interference_Riemann_Zeros2.pdf : Part I Theoretical Manuscript - 02_Prime_Phase_Interference_Riemann_Zeros2v2.pdf : Part II Theoretical Manuscript - 03_01_Quantum_ManyBody_Riemann_Spectral_Rigidity.pdf : Part III Paper I Manuscript - 03_02_Fredholm_Carleman_Pseudospectral_Rupture.pdf : Part III Paper II Manuscript - 04_01_01_K_Protocol_2D_Superconducting_Parents_Inverse_Design.pdf : Part IV Paper I Manuscript - 04_02_K_Protocol_4d5d_Room_Temperature_Superconducting_Parents.pdf : Part IV Paper II Manuscript - 04_03_K_Protocol_Fluoride_Superconducting_Parents.pdf : Part IV Paper III Manuscript (NEW in v5) • Standalone Code & Data Archive (k_protocol_data_and_code.zip): - 00_common/ : Master architecture diagrams and baseline databases - 01_data/ : Scripts 01_01 to 01_04 (Prime phase resonance engines) - 02_data/ : Scripts 02_01 to 02_07 (GUE spacing, Fock entropy, gauge rupture) - 03_data/ : Scripts 03_01, 03_02_01 to 03_02_04, and Cayley-Jensen plots - 04_data/ : (Complete Superconductivity Computational Pipeline) * 04_01_01_k_protocol_miner.py : 3d baseline screener (Paper IV-1) * 04_02_01_k_protocol_v2_screening.py : 4d/5d oxyhalide 492 screener (Paper IV-2) * 04_02_02_generate_structures_and_qe.py : Oxyhalide CIF and QE deck generator * 04_02_03_hurdle1_band_solver.py : Oxyhalide Hurdle 1 band solver * 04_03_01_fluoride_screening.py : Fluoride-halide 180 screener (Paper IV-3, NEW) * 04_03_02_generate_fluoride_structures_and_qe.py : Fluoride CIF and QE generator (NEW) * 04_03_03_hurdle1_fluoride_band_solver.py : Fluoride Hurdle 1 band solver (NEW) * k_protocol_v2_screened_492.csv : Oxyhalide master dataset * k_protocol_v3_fluoride_120.csv : Fluoride-halide raw dataset (NEW) * 02_dft_structure_inputs/ : Oxyhalide CIFs and QE inputs * 02_figures/ : Oxyhalide Hurdle 1 band plots * 03_fluoride_structures/ : Cs2AgF2Br2, Cs2AgF2I2, Cs2AuF2I2, Cs2CuF2I2 CIFs & QE inputs (NEW) * 03_figures/ : Fig1_Fluoride_Hurdle1_Bands.png & .pdf