The ephaptic threshold - is the endogenous near-field strong enough to matter?

The capstone left one soft word: the brain's incidental field is weak. That is true of the scalp signal, not the local near-field. Scaled by measured sensitivity, the endogenous cortical field induces a membrane polarization that sits inside the directly-measured bound and at the ephaptic threshold - not negligible. Whether cognition uses it stays open.

This chapter sharpens, with measurement, the boundary §18 deferred. The §15/§18 modules built the near-field but left its absolute magnitude (the radiation efficiency αₑₘ) explicitly open; here three independent labs supply that absolute and the induced polarization is derived rather than asserted. The carrier is the §18 near-field - nearest-neighbour-dominated (felt-field fraction 0.3976), with a radiated fraction near 1.143e-16 and an EM lag of 3.402e-09 of a cycle, so the far-field carrier stays retired. The endogenous cortical field is 2.290 mV/mm in vivo (peak 2.360, up to 4.520; 0.870 in vitro, a ratio of 2.632), and the somatic field-to-polarization sensitivity is 0.120 mV per mV/mm. Their product is a derived polarization ΔVm = 0.2748 mV (range 0.1414-0.4352), which is contained inside the independently-measured bound of 0.500 mV with a margin of 0.2252 mV, and reaches 0.5424 mV at the peak field. Since the entrainment threshold lies within the endogenous range, the field sits at the threshold, ρ ≈ 1; the polarization is only 0.0229 of a representative distance-to-threshold yet measurably entrains spike timing.

What this chapter adds, and what it does not

The capstone built the physics of the brain's near-field circulation and then stopped at a deliberate boundary, writing that the incidental field is weak and that whether near-field or ephaptic coupling carries a functional signal is open. This chapter does not re-open a retired claim and does not assert a function. It does one thing: it replaces the qualitative word weak with a quantitative, fully-cited comparison, so the boundary is drawn by measurement rather than by an adjective.

It is an integration, not a new mechanism. The near-field object is the capstone's own - the same one-over-r-cubed, nearest-neighbour-dominated field - imported directly, so the field that delivers the polarization computed here is literally the field §18 built. The source is the §13 momentum balance, the lattice is the one that carries light, and the absolute scale that §15 and §18 left open is now supplied from measurement.

The carrier is the near field, not a far-field broadcast

Everything here concerns the quasi-static near-field, and that distinction is the whole point. Imported from the capstone, the nearest-neighbour share of the field a region feels is 0.3976, so the coupling is a local chain, not a global broadcast; the radiative far-field amplitude is only about 1.143e-16 of the near-field, and an electromagnetic disturbance crosses the head in 3.402e-09 of a cycle. The far-field radiative carrier therefore stays retired, exactly as in §9 and §18 - this chapter revives none of it.

The weak field of the capstone's closing sentence is the scalp EEG: the volume-conducted, heavily attenuated signal read outside the head, which is indeed small. The local field potential near its sources, inside the tissue, is a different and far larger object. Conflating the two is what makes a near-field question look settled when it is not.

The measured absolute scale that the link chapter left open

The link chapter measured what one ionic source radiates but left the absolute coupling magnitude - the radiation efficiency αₑₘ - as a measured input, not something the lattice fixes. That open number is now supplied. The endogenous cortical electric field during physiological network activity is 2.290 mV/mm on average in vivo, with a positive peak of 2.360 mV/mm and values up to 4.520 mV/mm; in vitro the same activity gives 0.870 mV/mm, a ratio of 2.632 that shows the absolute is state-dependent and stays open. This is a measured input, the αₑₘ the chain declared open, now pinned to a number.

The induced polarization is derived, and contained

The field is not asserted to do anything; the membrane polarization it induces is derived from it. The relationship between a uniform field and the somatic polarization it produces is linear, measured at 0.120 mV per mV/mm. Multiplying the measured sensitivity by the measured field gives a derived somatic polarization of ΔVm = 0.2748 mV, with an uncertainty range of 0.1414 to 0.4352 mV, rising to 0.5424 mV at the peak endogenous field.

This derived value is then checked against an entirely independent measurement: direct intracellular recording finds the ephaptically-induced subthreshold polarization to be below 0.500 mV. The derived 0.2748 mV - and the whole 0.1414 to 0.4352 range - sits inside that measured bound, with a margin of 0.2252 mV. Two independent labs and two independent methods, field-times-sensitivity and direct recording, agree; the polarization is validated by containment, not fitted to a target. This is the same discipline as the §16 plateau and the §14 rheobases.

At the threshold, not negligibly weak

The decisive comparison is between the endogenous field and the field needed to have an effect. The slow oscillation is entrained by weak fields with an amplitude threshold that lies within the range of in-vivo endogenous field strengths - so the endogenous field sits at the entraining threshold, a dimensionless ratio ρ ≈ 1, not far below it. And although the induced polarization is small - 0.2748 mV is only 0.0229 of a representative distance-to-threshold - direct recording shows that such fields nonetheless strongly entrain spike timing, especially for slow rhythms, because near threshold the slow membrane trajectory makes a sub-millivolt nudge bite.

The honest verdict is therefore not the capstone's adjective. The local near-field is at the measured ephaptic-effect threshold, strong enough to measurably shift spike timing; the claim that it is too weak to matter is not supported by measurement. That bias is removed. The representative distance-to-threshold is illustrative and open; what is validated is the containment and the at-threshold ratio.

Boundary - the field is at threshold, the function is still open

What this chapter establishes is physical and graded honestly: the source must produce a field (forced); the carrier is the local near-field with a negligible radiated fraction (the far carrier stays retired); the induced polarization is derived and contained in the independently-measured bound, and the endogenous field sits at the entrainment threshold (validated). The absolute field magnitude in the chain's own units remains a measured input - the αₑₘ - supplied here rather than derived, and its in-vitro to in-vivo state dependence stays open.

What stays open is one rung up, and it has moved. Whether the brain actually uses this measured spike-timing entrainment for cognition - rather than carrying it as a measurable but incidental feedback - is open because the in-vivo behavioural role is untested, not because the field is weak. The question now has a decidable endpoint: a behaviour-labelled intracranial recording in which the local endogenous field is cancelled versus augmented in real time, the in-vivo form of the feedback-loop experiment already done in vitro. If cancelling the field degrades the behaviour, the coupling is functional; if not, it is incidental. That experiment, carried to the companion paper on mind, is where the electromagnetic thread that opened the chain is meant to close. The retired claims stay retired throughout: the axon is not a light-speed fibre, the EEG is not a radiative carrier, low-frequency sums do not become information, there is no DNA phase memory, and there is no vortex field.