Addendum III to the Berg Theory

Addendum III extends the Berg Theory core article into the electromagnetic sector. It formulates electromagnetism as gauge-guided transport in the same underlying scalar energy-web field Ψ that is used throughout the Berg Theory programme. The standard local U(1) chain is recovered within this framework: gauge-covariant phase guidance, the conserved current j^μ, Maxwell recovery, Lorentz exchange, wave propagation, and closed-loop phase behaviour. Standard electromagnetism is therefore not treated as a rival description, but as the controlled electromagnetic limit of the common field language. The addendum treats charge sign, voltage, current, magnetism, light, and loop phase as electromagnetic readouts of organized transport. Charge sign is used as an orientation label, voltage as a maintained boundary condition, current as guided transport, magnetism as organized circulation and finite order memory, and light as the freely propagating wave limit of the same sector. The field-strength quantity ϱ≡|Ψ|² remains separated from energy-density and stress-energy bookkeeping, so that electromagnetic observables and curvature sourcing can be related through one action without collapsing electric attraction into gravitation. The new material-facing object is the signed path-compatibility class Λ_flow. It records whether a declared material transport branch follows, crosses, or opposes the prepared local organization of a material. Λ_flow is not a response magnitude, heat term, contact artefact, coherence measure, or matter-status label. Those channels remain separated and assigned to their respective owner layers within the Berg Theory series. The observational and protocol layer is organized around a frozen sign-map test. A viable material-facing reconstruction must declare the material class, transport axis, order proxy, temperature bracket, nuisance controls, sign convention, and holdout rule before the decisive comparison is made. The direction-odd transport channel must then follow the declared Λ_flow sign while scalar thermal and contact backgrounds remain common-mode. The sharpest falsification route is a cryogenic angular transport witness under a predeclared low-temperature protocol. This release includes public-data support but does not present the material packet as a completed empirical PASS. Public Mn₂Au MBP-3b data are used as the main benchmark anchor for differential channel splitting and parser-level reproducibility. Additional public directional data support is organized as a sign-map support layer. These records strengthen the material route but do not replace the final pulse–axis–order–thermal–holdout map. The current material status remains bounded: Addendum III provides a structured and falsifiable transport packet with public-data support, while full PASS requires a successful frozen holdout sign test under the declared cryogenic and angular witness conditions. Secondary stress routes are included only as bounded workbench material. Lightning/TGF and related atmospheric routes may stress the same gauge-guided path-growth intuition, but they do not promote or rescue the material Λ_flow packet. Loop-phase and interferometric benchmarks connect the closed-loop guidance structure back to standard electromagnetic phase behaviour. The public release contains the main document, Appendices A, B, C, and X, and a public supplement. Appendix A provides physical derivations, response decomposition, cold-bracket logic, standard-mechanism guardrails, and the electromagnetic five-lock recovery map. Appendix B contains public-data ledgers, source-rights records, parser contracts, status tables, reproducibility material, and package provenance. Appendix C contains extended protocols and secondary stress-route workbench material. Appendix X provides the document-local symbol list, imported-symbol collision guards, and owner-boundary rules. The supplement contains source-policy records, derived outputs, protocol templates, parser scripts, manifests, and reproducibility receipts. The result is a mature electromagnetic module within the Berg Theory. It is not presented as final empirical confirmation of the material path-compatibility claim. It is a concrete, benchmark-organized, and falsifiable same-field formulation of electromagnetic transport and signed material response, with standard U(1) recovery on one side and a risky frozen sign-map prediction on the other. The decisive next step is whether one and the same Λ_flow sign map can carry material class, transport axis, order proxy, temperature bracket, angular discrimination, and holdout comparison without branch-specific rescue terms. Core article collection DOI: 10.5281/zenodo.17937466 This version DOI: 10.5281/zenodo.21210297 Cite-all-versions DOI: 10.5281/zenodo.17984874