Dipolar String Model: an Exploratory Framework for the Vacuum from Transmission-Line Electrodynamics

Dipolar String Model: an Exploratory Framework for the Vacuum from Transmission-Line Electrodynamics This working document (V2.9.2) presents an exploratory phenomenological model in which the physical vacuum is treated as a gas of massless dipolar cells (Dipolar Quantum Doubles, DQD) modeled as impedance-matched bifilar transmission lines. Gravity is described as vacuum refraction driven by an impedance field Z(x); electric charge and mass are attributed to the topology of dipolar strings. Results. The framework yields the parameter-free geometric ratio D/r = 2cosh(π) ≈ 23.18 and the interface coefficient Γ_pole = 1/3; a scalar gravitational sector indistinguishable from General Relativity at first post-Newtonian order (γ = β = 1); a uniqueness theorem identifying the Johns symmetric condensed node as the only scattering matrix compatible with the model's constraints, from which the three-dimensional isotropic light cone follows; and a stable branch of horizonless, singularity-free compact objects ("substrate stars") with critical mass M_crit ≈ 1.29×10⁶ M☉ ∝ ℓ₁² and maximal compactness r_s/R = 0.81. On the quantum side, the envelope of a localized excitation on a surrogate Johns lattice is shown to obey the free Schrödinger equation as its single-band quadratic truncation, with one action quantum closing the de Broglie relations and the inertial response. Withdrawals since V2.6. Successive internal audits have reduced the model's claims, and the reader should note four in particular. (i) The predicted shadow-diameter deviation of +4.63% is withdrawn: once the tensor sector is driven to General Relativity by the Deser bootstrap, the exterior of every compact object is Schwarzschild and no shadow, ISCO, or post-Newtonian deviation is predicted. (ii) The electron characteristic impedance Z_e ≈ 0.73 Z₀ ≈ 275 Ω is reclassified from derived to calibrated: it depends on an aspect ratio R₃/r that the framework does not derive. What survives as input-independent is the inequality Z_e < Z₀ over the whole plausible range. (iii) The consistent application of Axiom A8 (non-gravitating native energy) to the source term lowers M_crit from 1.62×10⁶ to 1.29×10⁶ M☉ and the maximal compactness from 1.22 to 0.81, so stable substrate stars no longer lie inside their Schwarzschild radius. (iv) In the quantum sector, the low-impedance entanglement corridor and its v_sync falsification front are withdrawn at the root — the relation follows from no field equation, no constitutive law, and no conservation statement — and the phase-opposition pair postulate is downgraded to a phenomenological ansatz of conditional scope. Registered prediction. The deposit retains a time-stamped prediction: under electron-scattering-corrected mass calibrations, ≥70% of substrate-star candidates should accumulate in the half-decade below log M_crit = 6.11, followed by a hard cutoff, with the calibration-invariant van Hove exponent dN/dM ∝ (M_crit − M)^(−1/2) immediately below it. The statistical criteria are frozen as stated in the manuscript. This channel is now disfavoured: a direct dynamical black-hole mass in a lensed little red dot returns ≈5×10⁷ M☉, consistent with the virial calibration and above the model's cutoff. We record this without mitigation. Falsification hierarchy. (1) The permanent absence of primordial-black-hole evaporation bursts — a single confirmed detection falsifies the model, though a non-detection concludes nothing, so this is a standing exposure rather than a decidable test. (2) Non-periodic post-merger echoes at geometrically growing spacing from fresh remnants, outside current quasi-periodic template searches — currently the only channel that is both decidable and open. (3) The hard LRD mass cutoff and the −1/2 caustic exponent (demoted, see above). (4) The absence of a gravitational-wave breathing mode, stated at the level of an assumption of the construction rather than a derived prediction. Status. Speculative working document by an independent researcher; no human peer review has taken place. All external critical evaluation to date was performed by an AI-based review tool, and the manuscript was developed with extensive AI assistance (Claude, Anthropic); the division of contributions is disclosed in full in the Acknowledgments. Both numerical implementations originate from the same collaboration and independent third-party verification has not been performed. The model's open problems — foremost the absence of a microscopic derivation of the medium, and a demonstrated conformal obstruction making the electron mass a structural input rather than a derivable quantity — are inventoried explicitly. Codes, figure scripts, and symbolic verifications are included and maintained at: https://github.com/rstpier/DipolarString