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The four-gradient \(\partial_\mu A_\nu\) has 16 independent components. Standard electrodynamics uses only the 6 antisymmetric components (\(F_{\mu\nu}\), encoding \(\mathbf{E}\) and \(\mathbf{B}\)). The remaining 10 — including the scalar-longitudinal coupling and the trace that the Lorenz gauge sets to zero — are not proven absent. They are defined absent by convention. This paper traces the construction of that convention through three acts of deletion: Heaviside’s vector reduction, the Lorenz gauge, and the ontological demotion of potentials. It identifies the physical content each removed, drawing on evidence spanning quantum interference to industrial engineering: the Aharonov-Bohm and Maxwell-Lodge effects; the scalar-longitudinal sector recovered independently by multiple research programs via the Stueckelberg Lagrangian, whose uniqueness is established by Woodside’s decomposition theorems; the potential hierarchy from Hertz potentials through Whittaker’s decomposition, where the Lorenz gauge emerges as an algebraic identity (\(\delta^2 = 0\)) rather than a physical law; the persistence of longitudinal and scalar photon modes as dynamical variables in canonical quantum field theory (QFT); the time-symmetric sector hidden in quantum mechanics as \(\psi^*\); the electromagnetic-gravitational bridge deepened by Kaluza-Klein; the vacuum coupling demonstrated by the dynamical Casimir effect; and the violation of Newton’s third law for open circuits, restored when longitudinal forces are included. The engineering implications are not speculative in origin. They are consequences of restoring degrees of freedom that the standard formulation structurally hides.
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This document collects corrections, clarifications, and missing references identified in the first published version of “The Deleted Degrees of Freedom: A Case for Potential-Primary Electrodynamics” [1] since its publication on 19 March 2026. Twenty-four errata entries address: (1) incomplete physical reasoning regarding Faraday cage penetration and charge relaxation screening (E-001–E-005), including the withdrawal of the published field-level Faraday-cage prediction; (2) six missing historical lines spanning 1932–2017 that extend the paper’s convergence record with stratified evidential weight (E-006); (3) the entirely absent Aharonov-Bohm Lagrangian framework (E-007); (4) an unresolved Belinfante-Rosenfeld question regarding scalar-gravitational coupling (E-008); (5) a third electromagnetic wave class not mentioned (E-009); (6) additional missing references, mechanisms, and a critical notational error (E-010–E-016); (7) an attribution error regarding Mead’s superpotential (E-017); (8) algebraic and historical errors in the quaternion/differential-forms paragraph (E-018); (9) a historical completeness note on Whittaker’s 1904 three-function construction (E-019); (10) two computationally verified corrections to the scalar-sector equations — a sign misprint in Eq. (1) whose repair restores the paper’s \(T = -cC\) reconciliation exactly (within the printed two-term sign family, under the stated potential normalization), and a prefactor slip in the S-trace equation (E-020–E-021); and (11) three corrections fixing the sign convention of the Stueckelberg Lagrangian: a sign correction to its scalar-sector term together with an explicit metric-signature statement (E-022), the withdrawal of the free-space scalar-wave entry (E-023), and an explicit source condition on the scalar-wave generation predictions (E-024). The corrections are of three kinds. Most tighten the physical reasoning or expand the convergence evidence; several repair attributions and algebra with no effect on the thesis; and three — E-001, E-023, and E-024 — narrow or withdraw published claims: the field-level Faraday-cage prediction, the free-space scalar-wave entry, and the unconditioned scalar-wave generation story. The two legs of the paper fare differently: the formal thesis — the Lorenz gauge removes the scalar sector — survives all twenty-four corrections; the field-level experimental program does not survive unchanged and is narrower after correction than as published. That split is why a correction ledger, rather than a retraction-and-replace, is the proportionate vehicle: the surviving thesis anchors the document, and each withdrawal is stated against it.
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