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 Paper II)From Analytic Number Theory & Operator Dynamics to 4d/5d 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 ============================================================EXECUTIVE SUMMARY (VERSION v4 UPDATE)============================================================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 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 demonstrates that off-critical zeros (sigma != 1/2) trigger catastrophic unitary defects and uniform Phragmén-Lindelöf growth ruptures (1,563x breach). This operator-theoretic stability yields an effective 5-body field theory (EFT) truncation bound (>99.87% energy saturation, alpha_min >= 0.8863). In Version v4, this geometric compass is extended beyond 3d canonical systems into the 4d/5d transition-metal manifold (Ag2+, Au2+, Ta4+) under body-centered tetragonal I4/mmm symmetry. Utilizing an objective Room-Temperature Figure of Merit (Theta_RT = Phi_2D * J_est / J_0), the inverse-design engine exhaustively screens 492 stoichiometric parent candidates. Crucially, addressing the ubiquitous redox instability in oxidizing silver-halide lattices, v4 establishes Ba2AgO2Br2 (Rank 180, J_est = 341.2 meV, c/a = 5.42) as the primary, chemically resilient lead flagship candidate. Apical bromide substitution successfully mitigates spontaneous internal charge-transfer redox degradation while preserving 262% of canonical cuprate pairing strength. First-principles tight-binding and Quantum ESPRESSO DFT calculations confirm strict 2D single-band isolation across the suite (Delta_Ez <= 8.8 meV << 15.0 meV), satisfying the Hurdle 1 pre-screening benchmark and providing an actionable roadmap for ambient-pressure room-temperature superconductivity. ============================================================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] 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 - Paper I] Theory-Driven Inverse Design of 2D Superconducting Parents (3d Baseline)• Focus: Planar C4 5-body plaquette confinement, apical steric shielding, and positive control benchmark.• Key Findings: Enforces planar 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 clean single-band nickelate LaSrNiO2Cl2 and inverted vanadate Cs2VO2I2. [Part IV - Paper II] (NEW in v4) Inverse Design of 4d/5d Room-Temperature Superconducting Parents: Giant Superexchange, Redox Resilience, and Candidate Taxonomy• Focus: 4d/5d orbital expansion, giant superexchange (J > 340 meV), redox passivated lead candidate, and Hurdle 1 band isolation.• Key Findings: 1. Expands plaquette inverse-design into spatially extended 4d (Ag2+, Pd1+) and 5d (Au2+, Ta4+) manifolds, scaling the screening pipeline to an exhaustive space of 492 candidate compounds. 2. Formulates the Room-Temperature Figure of Merit Theta_RT = Phi_2D * (J_est / J_0) integrating Goldschmidt tolerance factors (0.80 <= tf <= 1.05) to balance 2D isolation and slab thermodynamic stability. 3. Formulates a Redox-Resilient Strategy: Prioritizes Ba2AgO2Br2 (Rank 180, Theta_RT = 19.90, J_est = 341.2 meV, c/a = 5.42) as the lead flagship over iodide analogs to preempt internal reductive decomposition (2Ag2+ + 2I- -> 2Ag+ + I2) while maintaining 262% cuprate pairing strength. 4. Classifies taxonomy into: Ba2AgO2Br2 (Lead Flagship), Ba2AgO2I2 (High-Isolation Extension, c/a = 5.71), Ba2AuO2I2 (Theoretical Limit, J_est = 729.5 meV), and Cs2TaO2I2 (Structural Stability Control, tf = 1.044). 5. Tight-binding and DFT band structure calculations verify complete suppression of cross-plane dispersion along Gamma -> Z (Delta_Ez = 2.8 - 8.8 meV << 15.0 meV), successfully passing Hurdle 1. ============================================================FILE INVENTORY & ARTIFACT STRUCTURE (v4 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 (NEW in v4) • Standalone Code & Data Archive (k_protocol_data_and_code.zip): - 00_common/ * 00_k_protocol_master_architecture.png : Master Architecture Diagram * k_protocol_master_db.json : Part IV-1 61-candidate master database - 01_data/ : Scripts 01_01 through 01_04 (Prime phase resonance engines) - 02_data/ : Scripts 02_01 through 02_07 (GUE, Fock entropy, and gauge rupture tests) - 03_data/ : Scripts 03_01, 03_02_01 to 03_02_04, and k_protocol_cayley_jensen_unified.png - 04_data/ * 04_01_01_k_protocol_miner.py : 3d baseline screener (Paper IV-1) * 04_02_01_k_protocol_v2_screening.py : 492-candidate inverse-design engine (NEW) * 04_02_02_generate_structures_and_qe.py : CIF and Quantum ESPRESSO input generator (NEW) * 04_02_03_hurdle1_band_solver.py : Hurdle 1 band dispersion solver & plotter (NEW) * 04_02/ : (Output artifacts and databases) - k_protocol_v2_screened_492.csv : Complete dataset of 492 screened compounds - figures/ : Fig1_Hurdle1_Bands.png and Fig1_Hurdle1_Bands.pdf (600 DPI) - dft_structure_inputs/ : Full CIF crystallographic structures and QE SCF/BANDS decks