The full EM link - conduction near, radiation far, and clean multiplex

The unified link is the ionic source's field on the jamming lattice, measured with absorbing boundaries. Near the source the field is steep quasi-static conduction; far away it falls as one-over-r radiation; the zones separate at the near-field boundary near twelve lattice units, the field travels at c, and matched-filter receivers split distinct carriers at parts-per-ten-million cross-talk.

Part A drives an oscillating ionic dipole on a three-dimensional lattice with a graded absorbing layer on all faces, so the boundary reflections that contaminated the prototype are gone. The shell-averaged field then separates: a steep near zone (about 1/r^1.91, the conduction or quasi-static regime, χ→0) and a far zone (about 1/r^1.04 close to 1/r, radiation, χ→90°), crossing over at the near-field boundary r close to λ/2π near 12 while the wavefront moves at c. Part B sums distinct carriers (0.020, 0.034, 0.052 cycles/tick) on one absorbing line and separates them with a matched filter, giving cross-talk near 10⁻⁷ and every channel recovered to within rounding. The field is at c; the slow 0.5 to 120 m/s conduction velocity is the membrane-charging rate, not the field.

The link, stated

The unified link is one object: an ionic source is an electrical source, so its field is electromagnetic, and it propagates on the same elastic lattice that carries light, u_tt = c²∇²u + f with c² = B/ρ. The earlier chapters emerged that source from the gene layer and the ion layer; this chapter measures what it actually radiates, properly.

The two things the prototype could not measure cleanly were the near-to-far transition (because a reflecting boundary contaminated the far field) and the channel separation (because a wide-band reader blurred the carriers). Absorbing boundaries and a matched-filter reader fix both, and the result is the production EM link.

Conduction near, radiation far - separated by the absorbing boundary

Part A drives an oscillating ionic dipole at the centre of a three-dimensional lattice whose six faces are a graded absorbing layer, so outgoing waves leave instead of reflecting back. The shell-averaged field then shows two regimes that the prototype could not resolve.

Near the source the field is steep, falling as about 1/r^1.91 — the quasi-static conduction regime, the χ→0 limit of the angle law. Far from the source it falls as about 1/r^1.04, essentially 1/r — the radiation regime, the χ→90° limit. The crossover sits at the near-field boundary r close to λ/2π, near 12 lattice units, and the wavefront propagates at c.

This is the lattice confirmation of the split that geometry forces: conduction and radiation are not two phenomena but one field read at two distances, ordered by the angle χ.

Multiplex - distinct carriers split by a matched filter

Part B sums several channels at distinct carriers (0.020, 0.034, 0.052 cycles/tick) onto one linear lattice with absorbing ends, then separates them at the receiver with a matched filter — the windowed single-bin projection that is the optimal reader for a sinusoid, with the carriers placed on exact analysis bins.

The off-diagonal leakage of one channel into another's reader is near 10⁻⁷, orders of magnitude below the prototype's wide-band figure and close to the analytic ideal; every channel is recovered to within rounding. Distinct rhythms therefore coexist on one medium and come apart cleanly, which is the frequency-division multiplex the framework needs.

The field is at c; the slow signal is membrane charging

The field propagates at c, as Part A confirms. The action potential is slower, 0.5 to 120 m/s, but that slowness is not the field and not the drift of ions: it is the time each membrane patch needs to charge its capacitance to threshold before igniting the next, a regenerative ignition wave like a burning fuse whose flame crawls while the chemistry is fast.

Because the conduction velocity is a charging rate, myelin — which lowers the capacitance and lets the spike jump between nodes — speeds it up, though still vastly below c (saltatory conduction). So a fast field and a slow spike are both true and not in conflict; reaction times of roughly 150 to 250 ms are the accumulated charging and synaptic delays, confirming the conduction is finite.

Boundary - near-field conduction is the signal, thought is deferred

The neural signal is electromagnetic, carried by ions in the near-field conduction mode (χ→0); the field is at c. A strong far-field radiative broadcast is negligible by geometry, because a neural rhythm's wavelength λ = c/f is enormous, so every biological scale sits deep in the near field; the radiated fraction is about 10⁻¹⁵. EEG and MEG are that measurable near-field, not a radiated carrier.

What stays open is the absolute radiation efficiency αₑₘ, a measured input [O]. What is deferred is the question above this physical layer: whether the brain uses the fast near-field for coordination, and how θ/γ streams become thought and experience, are the Mind paper's domain, not this one.