Pure (pi, zeta(3)) Hydrogen Soliton Invariants, Proton-to-Electron Mass Ratio, Dipole Charge Radius, and SI Scale Audit on l^2(N >= 2, w) (K-PROTOCOL Series 00-I / Core Monograph IX)

This repository presents the complete hydrogen-soliton and SI scale audit monograph suite, pedagogical companion guide, 17-suite master bibliographic reading index, machine-readable precision audit data, and standalone numerical verification engine of K-PROTOCOL Series 00-I (Core Monograph IX and Companion Guide IX, Version v1.1; Permanent Concept DOI: 10.5281/zenodo.24132324; Version v1 DOI: 10.5281/zenodo.24132325). Continuing directly from the zero-alpha deductive closure of Series 00-H (DOI: 10.5281/zenodo.24107316), Capstone Series 00-G (DOI: 10.5281/zenodo.24074080), and Series 00-A through 00-F (DOIs: 10.5281/zenodo.23117791, 10.5281/zenodo.23355922, 10.5281/zenodo.18797547, 10.5281/zenodo.23911703, 10.5281/zenodo.23913158, 10.5281/zenodo.23972445), this suite derives the dimensionless structural invariants of the neutral hydrogen atom (H) and audits their coupling to the vacuum speed of light (c) on the same shifted discrete Hilbert space H_1 = l^2(N >= 2, w). Preserving standard relativistic kinematics, SU(3)_c color algebra, Ward-Takahashi gauge identities, and bound-state QED perturbation series, all results are strictly partitioned into Layer I (parameter-free mathematical and operator identities on l^2(N >= 2, w) and the 3-branch star-graph Gamma_Y), Layer II (downstream metrological evaluations under the 2019 SI / CODATA 2022 scale dictionary with Local Position Invariance verification), and an explicit Open Dynamical Boundary (Chiral Perturbation Theory pion-cloud currents and isospin breaking), with zero adjustable parameters and zero conditional physics branching. ========================================================================REPOSITORY CONTENTS & FILE ARCHITECTURE======================================================================== 1. Core Monograph IX (K-PROTOCOL_Series_00-I_Core_Monograph_IX.pdf):Provides the formal definition-lemma-proposition-theorem-proof derivations, regularization remarks, and metrological audits across five foundational pillars: - Pillar 1 (Discrete Sector-by-Sector Sum Completion & SU(3)_c Star-Graph Regularization):Decomposes the diagonal self-energy [W_w]ₖₖ = 4 / [k^3 * (k^2 - 1)^2] on l^2(N >= 2, w) with normalized measure w(k) = 4 / [(k-1)k(k+1)] (Sumₖ₌₂^inf w(k) = 1) into three distinct sectors: cubic Casimir 4/k^3, step-2 boundary difference [1/(k-1)^2 - 1/(k+1)^2], and measure counterterm -2*w(k). Proves that while the boundary and measure sums close globally over k >= 2 (+5/4 - 2 = -3/4, eliminating zeta(2) = pi^2 / 6 identically), SU(3)_c quadratic Casimir flux cancellation (Sumₐ₌₁^3 T_a^A)^2 |1_c> = 0 at a 3-branch Kirchhoff Y-junction Gamma_Y (single-branch back-reflection [S_Y]ₐₐ = -1/3, in contrast to the reflectionless linear meson topology [S_2]ₐₐ = 0) unlocks the missing k = 1 ground block +4/1^3 = +4 of the discrete cubic sum with unit symmetric multiplicity. Combining completed 4*zeta(3) with the self-dual chiral-bag Atiyah-Patodi-Singer (APS) Dirac spectral shift (-1/2) and infrared {2, 3}-doublet binding screening (-25/432) against the Galois-selected k = 3 bare lepton mode ([W_w]₃₃ = 1/432) yields the bare baryon-to-lepton ratio mu_0 = 1728*zeta(3) - 241 = 1836.1543286598 (+0.9015 ppm vs. CODATA 2022). - Pillar 2 (Chiral Multiplicative QED Dressing & 105-DPS 1-Loop Operator Benchmark):Chiral symmetry as m^(0) -> 0 enforces strictly multiplicative QED mass renormalization, while the Ward-Takahashi identity cancels infrared k in {2, 3} photon loops identically. Evaluating the differential short-distance Cottingham tail Z_tail = Z_diag - 25/432 on k >= 4 under a leading step-ultraviolet proton form-factor cutoff (G_E^2|k>=4 -> 0) yields the closed-form 1-loop operator benchmark:mu_sym(pi, zeta(3)) = (1728*zeta(3) - 241) * [1 - Xi_polar^-1 * Z_tail * (1 + Z_loop)] = 1836.152665897434830930356698229425650463357255703912473768654486144205862104488598508147314841633929060632610...Certifies 105-decimal-place numerical stability across DPS = 75 to 105 with zero floating-point drift, agreeing with CODATA 2022 (1836.152673426) to -4.100 ppb (corresponding to 0.453% smooth dipole UV transmittance plus O(alpha^2) shifts) and locking the hydrogen nuclear recoil factor 1 + mu_sym^-1 = 1.00054461702372 to +2.23 ppt. - Pillar 3 (Dipole Form-Factor Slope & Proton Charge Radius Puzzle Resolution):Evaluates the relativistic Sachs electric dipole form-factor slope <r_p^2> = -6 * dG_E(Q^2)/dQ^2 |Q^2=0 = 12 / Lambda_D^2 for G_E(Q^2) = (1 + Q^2 / Lambda_D^2)^-2 at Ji's virial confinement scale Lambda_D^2 = Omega_even * lambdabar_p^-2 = (3/4) * lambdabar_p^-2, yielding the exact operator identity r_p = 4 * lambdabar_p = 4 * lambdabar_e / mu_sym = 0.841236 fm (+0.76 sigma vs. CODATA 2022: 0.84075 +/- 0.00064 fm; -0.09 sigma vs. CODATA 2018: 0.8414 +/- 0.0019 fm), resolving the historical 0.8775 fm scattering discrepancy in favor of muonic and electronic hydrogen spectroscopy. - Pillar 4 (Weight-Rescaled Jacobi-Sturmian Coulomb Pencil & Universal Gear Invariant G_H):Maps N >= 2 via invertible diagonal weight rescaling J_k = sqrt((k-1)/w(k)) onto the tridiagonal Laguerre-Sturmian generalized pencil [T(lambda) + V(lambda) - E*S] c = 0 with principal quantum number n = k - 1 >= 1. Taking k >= 2 algebraically decouples the singular k = 1 (n = 0) node (T1,2 = S1,2 = 0), selecting the regular u(0) = 0 Friedrichs domain without continuum collapse, localizing the exact 1S ground state at k = 2 (|c_2|^2 = 1.0, |dE_1S| = 0.0; 4-level N=45 truncation error 6.26e-12), fixing the Sakharov throat Bohr ratio a_H / l_0 = 6.5465168753058e+22, and defining the dimensionless Universal Light-Hydrogen Gear Invariant at I_0:G_H = c / (a_H * nu_1S2S) |I_0 = 2296.03879544472 (~ 16 * Xi_polar / 3). - Pillar 5 (Layer II Metrological Audit, Heterogeneous LPI Invariance & Open ChPT Boundary):Audits MPQ Garching (48.260 N) spectroscopy under the 2019 SI scale dictionary: confirms that global SI coordinate projection acts purely as an overall Rydberg conversion scale while intrinsic relativistic atomic structure factors f_rel(Z*alpha_I0) remain locked at alpha_I0 everywhere, guaranteeing exact Local Position Invariance (Delta(nu_A / nu_B) = 0.0) even across heterogeneous co-located optical clocks (Al+/Hg+, Yb+ E3/E2); reproduces MPQ c*R_inf = 3,289,841,959,824,178.0 Hz (-0.129 ppb, -0.42 sigma within m_e 0.31 ppb uncertainty) and 2-loop bound-state QED nu_1S2S = 2,466,061,413,218,665.0 Hz (+12.8 ppt vs. MPQ observation); distinguishes the exact SI scale-dictionary cancellation identity G_H * a_H(I_0) * nu_1S2S(I_0) == c_0 (299,792,458.0 m/s) from the +48.939 cm/s 2019 SI coordinate offset; and transparently isolates the Open Boundary on the 21 cm hyperfine path (+622 ppm in proton magnetic moment mu_p^(vac) = +2.794583 mu_N, +2.61% in neutron mu_n^(vac) = -1.863055 mu_N, and nucleon isospin mass splitting m_n - m_p) governed by dynamical Chiral Perturbation Theory (ChPT) virtual pion-cloud currents. 2. Companion Guide IX (K-PROTOCOL_Series_00-I_Companion_Guide_IX.pdf):"From Discrete Vacuum Geometry to the Hydrogen Atom and the Speed of Light: A Pedagogical Guide for Physics Students and Researchers" -- Translates the formal operator proofs into four accessible pedagogical models, physical QFT intuition for zeta(2) vs. zeta(3), a 5-step pocket-calculator audit walkthrough, and a Master Translation Dictionary connecting standard QM/QFT/QCD concepts to K-PROTOCOL operators. 3. Master Suite Catalog & Reading Guide (00-0_K-PROTOCOL_Series_Catalog_and_Reading_Guide.pdf):Provides the complete master bibliographic index and pedagogical reading order across all 17 official K-PROTOCOL Zenodo suites (Suites 01 through 17) with verified Permanent Concept DOIs, establishing Series 00-I, Series 00-H, and Series 00-G as the tri-master entry points. 4. Standalone Python Verification Suite, Machine-Readable Archive & 2-Page Report (verify_series_00_I.py, 00-I_Master_Audit_Data.json, & 00-I_Verification_Report.pdf):An autonomous Python verification engine (v1.1) executing all 5 audit stages in ~1.2 seconds using exact rational arithmetic (fractions.Fraction), SciPy generalized tridiagonal eigensolvers, and arbitrary-precision mpmath. Dynamically generates the 2-page A4 landscape publication report with 4-panel diagnostic plots and the 00-I_Master_Audit_Data.json precision archive with zero free parameters.