Targeted neuromodulation — clean delivery versus off-target leak (the third application of the spatial-localisation layer, closing the trilogy)

Chapter 44's excitatory drive, re-read as therapy, closing the trilogy. Aiming a focal stimulation at each region, targets split into clean-delivery and off-target-leak, fixed by target location, not intensity. The spatial numbers coincide with chapter 44; what is new: clean delivery and global reach are decoupled, the cleanest target is the strongest. Structural quantities, never felt effect.

The §43 spatial-localisation layer built a fixed spatial map of the frozen ephaptic kernel and handed it forward with one instruction: read it region by region. §44 took the map’s reading under an excitatory ictal drive and asked, for a seizure, whether a focal excitation stays focal (containment) or secondarily generalises (broadcast). §45 took the destructive dual under a silencing drive and asked, for a stroke, whether a lesion stays local or disrupts at a distance (diaschisis). This chapter takes the third and final application — the therapeutic re-reading of §44 — and closes the trilogy: containment/broadcast for seizures, local/diaschisis for stroke, and now clean delivery versus off-target leak for targeted neuromodulation (deep brain stimulation, transcranial magnetic or direct-current stimulation). The drive is the same focal excitatory bias §44 used, through the same k = κ/(1+|b|) excitatory map (no new constant), but re-framed: not a seizure focus this time but a stimulating electrode, a region driven up the coupling curve on purpose, to treat. The clinically decisive question for neuromodulation is target selection: aim a focal stimulation at this region — does the excitation deliver cleanly (self-localising, the stimulation concentrates where it is aimed) or leak off-target (relay, the stimulation bleeds to distal circuits the clinician did not intend to drive)? Because this chapter reads the same excitatory spatial map as §44, one fact is stated plainly and up front: the footprint classes, the reach map and the off-target ratios coincide numerically with §44 — a focal excitatory drive is a focal excitatory drive, and the numbers here are not a fresh measurement dressed up as new. What is new is the therapeutic target-selection reading (a relay target is an off-target-leak target; a self-localising target is a clean-delivery target) and the decoupling result below. Four results hold. N1 — the clean-delivery/off-target-leak partition is drive-invariant: aiming a stimulation at each of the 12 regions in turn, the targets partition into clean-delivery (the excitation concentrates at the target, the stimulation stays where it is aimed) and off-target-leak (the excitation lands harder off-target, the stimulation bleeds away), and this partition is identical across the entire stimulation-intensity sweep — the leak set {hippocampus, midbrain} fixed at every intensity, the other ten clean at every intensity. Whether aiming at a region delivers cleanly or leaks off-target is a fixed property of target location, not of how hard you stimulate — and that leak set is exactly the E1.3 relay set, read now as a delivery property. Unlike §45’s inhibitory case — where a marginal node crossed into the diaschisis set only at a mild, sub-floor severity — the excitatory partition is exactly stable at every swept intensity including the mildest (0.3): no sub-floor caveat, inheriting §44’s full-sweep scope, an honest contrast with the destructive dual. N2 — off-target leak is off-target dominance: for a leak target the coordination change lands harder on distal circuits than at the target itself (mean off-target |Δc| > own, ratio above 1 — the hippocampus at roughly 4.2×, the midbrain 1.6×) — the structural signature of a stimulation that bleeds away from where it is aimed — while a clean target concentrates at the site (ratio far below 1, the cerebellum at ~0.04×); the equivalence holds at every intensity. N3 — clean delivery and global reach are decoupled (the honest no-tuning result): a clean, attractive hypothesis — “to get a large global therapeutic effect you must accept off-target leak; a clean target is necessarily a weak one” — is false. The single largest global-reach target — the target whose stimulation moves the network-wide order parameter the most — is the cerebellum, which is clean-delivery (off-target far below own, no leak) yet tops global reach at every intensity, and here — like §44 and unlike §45 — the reach hub is drive-invariant (the cerebellum at every intensity). A target can achieve the largest global effect while delivering maximally cleanly: delivery focality and global therapeutic reach are two distinct, decoupled spatial axes, and the “focal = weak, leaky = strong” intuition is refuted. Worse for any point-to-point picture of leak: the two leak targets push global coordination in opposite directions — the hippocampus lowers the global order parameter, the midbrain raises it, at every intensity — so leak is site-determined in both magnitude and direction, not a single predictable spillover a clinician could aim through a relay to a chosen remote site. The refuted hypothesis is reported honestly — the E1.4 lesson made concrete for neuromodulation. N4 — the leak set is a coherent minority relay-hub class: {hippocampus, midbrain} is simultaneously the E1.3 relay set, the off-target-dominant set (N2), a strict minority (2 of 12 — clean delivery is the structural default), and disjoint from the global-reach hub (the clean cerebellum, N3) — one coherent class of limbic/brainstem relay hubs. Off-target leak is structurally the exception, carried by specific relay hubs, not a generic property of targets. A direction-only [L] correspondence is noted, never a magnitude or a prediction: clinically, off-target effects of focal neuromodulation — current spread beyond the intended target, DBS side effects from co-recruiting adjacent or connected structures, TMS spread to connected regions — are a recognised concern at specific connected hubs, consistent with the leak set being a strict minority of relay hubs and clean delivery the structural majority. A uniform (zero) stimulation reproduces the frozen M9 coordination anchor (R = 0.38961455156) bit-for-bit and the off-state field equals the baseline exactly (S5) — a pure structural read on the frozen kernel (engine 0fbf4988…, byte-unchanged; SpatialField reused, not re-derived; no new tuned constant). The firewall is absolute: a clean-delivery/off-target-leak class is a structural spatial quantity of the coupling model, never a felt effect of stimulation, and not a real electric-field or current-density map, a lead-position or specific-absorption-rate (SAR) map, a real connectome, a prediction of which patient’s stimulation leaks or which target is optimal, or device-programming/target-selection guidance (Axis-A — consciousness_claim = 0, the hard problem stays open). Every magnitude is [O]; efficacy = 0; not medical advice.

The third application — reading §44’s excitatory drive as a therapy, and closing the trilogy

The spatial layer built one map and asked for three readings of it, one per region-specific disorder. §44 drove a region up the coupling curve and read the result as a seizure: does a focal excitation stay contained or secondarily generalise? §45 drove a region down and read the result as a stroke: does a focal silencing stay local or disrupt at a distance? This chapter takes the third reading, and it is not a new drive — it is the same excitatory drive as §44, read with a different clinical question in mind. A focal excitation of one region is, physically, exactly what a stimulating electrode does: deep brain stimulation drives a deep target, transcranial magnetic stimulation drives a cortical patch, transcranial direct-current stimulation biases a region — each is a region pushed up the coupling curve, on purpose, to treat a disorder. Where §44 asked “does this excitation, as a seizure, generalise?”, this chapter asks the therapeutic dual: “does this excitation, as a therapy, go where it is aimed?” With this chapter the three great manipulations of a single region on the fixed map — drive it up as a disease (§44), take it out as a lesion (§45), drive it up as a treatment (§46) — are all read, and the E1 application trilogy is complete.

One honesty has to be paid before anything else, because this chapter reads the same excitatory map as §44 and would be dishonest to pretend otherwise. The numbers coincide. The footprint class of each region, the global-reach ranking, the off-target-to-own ratios — all of them are identical to §44’s, because a focal excitatory drive on the frozen kernel is a focal excitatory drive whether one calls it a seizure focus or a stimulating electrode. This chapter does not re-measure the kernel, does not introduce a new drive, and does not claim a new spatial finding hidden inside §44’s. What it adds is two things, both real and neither numerical novelty. First, a re-reading: the self/relay class §44 read as seizure prognosis (contained vs generalising) is read here as delivery quality (clean vs leaking) — a relay target is precisely a target whose stimulation leaks off-target, a self-localising target is one whose stimulation delivers cleanly. The clinical meaning is different; the structure is shared, and saying so plainly is the point. Second, a genuinely new result — N3, the decoupling of clean delivery from global reach — which §44 had no reason to ask and this chapter does, and which comes out as an honest negative. The chapter earns its place by the question it asks of the shared map, not by pretending the map is new.

The stimulation model — a therapeutic target as an excitatory bias on the spatial layer

The model is the smallest one that makes target selection answerable, and it reuses the spatial layer wholesale. A therapeutic stimulation is modelled as a focal excitatory bias: region i is driven to a positive bias b₀ while every other region sits at baseline, through the same effective-coupling map as the epilepsy and spatial modules — k(b) = κ/(1+|b|) — so a stimulated target is simply a region pushed up the coupling curve, with no new constant introduced. This is identical to §44’s ictal drive; the difference is interpretive and clinical, not mechanical. The stimulation intensity is swept, not chosen: every sign reported below is required to hold at b₀ = 0.3, 0.5, 0.7 and 0.9 alike — and, crucially, the partition is exactly stable down to the mildest swept intensity, inheriting the full-sweep scope §44 established for the excitatory case, so no number is fitted to make a result come out.

Two readings answer the two halves of the target-selection question, and they are the same two readings §44 and §45 used. The first is the footprint class: stimulate a region and compare its own local-coherence change to the mean change it induces off-target. If the target’s own change dominates, the stimulation delivers cleanly — the excitation concentrates where it is aimed. If the off-target change dominates, the stimulation leaks off-target — it drives distal circuits more than the intended target. The second is the global reach |R − R₀|: how much stimulating that one region moves the network-wide order parameter, the natural measure of a stimulation’s global therapeutic effect. Clean-versus-leak is a local, off-target reading; global reach is a network-wide reading. Holding both lets the chapter test whether they are the same axis — whether, as clinical intuition might suggest, a clean target must be a globally weak one — and they are not (N3). Because the drive is §44’s, the two readings return §44’s numbers; the third reading the chapter adds — the direction in which each leak target moves the global order parameter — is the one new quantity, and it is what makes leak structurally uncontrollable.

N1 — the clean-delivery/off-target-leak partition is drive-invariant

The first result is the spatial discriminant for stimulation targets, and it is inherited intact from the layer. Aiming a focal stimulation at each of the 12 regions in turn, the targets partition cleanly into two classes. Ten targets deliver cleanly: the coordination change concentrates at the stimulated region, more than it changes anywhere else — structurally, the stimulation stays where it is aimed. Two targets leak off-target: stimulating them changes coordination off the target more than at the target itself — structurally, the stimulation drives distal circuits more than the site the clinician aimed at. The leak set is {hippocampus, midbrain}.

The certification is that this partition does not move with stimulation intensity. From the gentlest swept stimulation to the strongest, the same ten targets deliver cleanly and the same two leak: the leak set {hippocampus, midbrain} is fixed at every intensity tested. Whether aiming at a region delivers cleanly or leaks off-target is therefore a fixed property of where the target sits in the field — a drive-invariant connectome property, not a function of how hard the region is stimulated. And that leak set is exactly the E1.3 relay set: the regions whose footprint lands off-target are the same regions whose stimulation leaks. The self/relay map is doing triple duty now — it is the containment/spread map for seizures (§44), the local/diaschisis map for lesions (§45), and the clean/leak map for neuromodulation (§46), the same structural classification read three times with three clinical questions.

One honest contrast with the destructive dual belongs here. In §45’s inhibitory (lesion) case, the partition was exactly stable only over a moderate-to-severe core, and at a mild, sub-floor severity a marginal node (the thalamus) crossed into the diaschisis set — reported there as an honest scope limit. The excitatory case here has no such caveat: the clean/leak partition is exactly stable at every swept intensity, including the mildest (0.3) — no marginal node crosses in at any intensity. This is the same full-sweep robustness §44 found for the excitatory drive, inherited here, and it is recorded as a real structural difference between driving a region up (excitation, stable everywhere) and silencing it (lesion, stable only above a floor), not smoothed over to make the two chapters look identical.

N2 — off-target leak is off-target dominance: the structure of a stimulation that bleeds away

The second result turns the binary class of N1 into a legible quantity, and ties “off-target leak” to its clinical meaning of stimulation reaching the wrong circuits. For each stimulated region, take the ratio of the mean off-target coherence change to the target’s own change. For a leak target this ratio is above 1: stimulating the region changes coordination harder in distal circuits than at the target itself — the hippocampus at roughly 4.2×, the midbrain at 1.6×. That is precisely the structural picture of off-target leak: the electrode is at the target, but the largest coordination change is elsewhere, in the circuits the target relays to. For a clean-delivery target the ratio is far below 1: the change is concentrated at the target, the distal circuits barely move — the cerebellum, for instance, at about 0.04×, an overwhelmingly local footprint, the cleanest delivery in the set.

The equivalence — a target leaks if and only if its off-target change exceeds its own — holds at every swept intensity. This is what makes the N1 partition more than a label: off-target leak is not a separate phenomenon bolted on, it is the same footprint read quantitatively — the off-target-to-own ratio crossing 1. (These ratios are, as stated, §44’s own numbers under the shared excitatory drive; what differs is only that §44 read a ratio above 1 as a seizure that generalises and this chapter reads it as a stimulation that leaks.) It also makes plain what kind of claim is and is not being made. The ratio is a structural measure of where a coordination change lands on the frozen kernel; it is not an electric-field strength, a current density, or a measured side-effect rate. The magnitude of any real off-target spread is [O]; what is asserted is the sign — that leak targets dominate off-target and clean targets dominate at the site, robustly across intensity.

N3 — clean delivery and global reach are decoupled: the cleanest target is the strongest

The third result is the one the no-tuning discipline exists to surface, and the one genuinely new to this chapter — a clean hypothesis, tested, and reported as false rather than quietly dropped. The hypothesis is the natural clinical one. If a stimulation’s job is to move the network, the obvious guess is that to get a large global effect you must accept off-target leak — that a clean, focal target is necessarily a weak one, and a clinician faces a tradeoff between delivery focality and global reach. If that held, “delivers cleanly” and “moves the whole network” would be opposite ends of one axis, and target selection would be a single dial between focal-but-weak and strong-but-leaky.

It does not hold. The single largest global-reach target — the target whose stimulation moves the network-wide order parameter the most — is the cerebellum, and the cerebellum is clean-delivery: its off-target change is far below its own (about 0.04×), it does not leak, yet it is the rank-1 global-reach target at every stimulation intensity. A target can achieve the largest global effect while delivering maximally cleanly: stimulating the cerebellum moves the whole network’s coordination more than stimulating any other region, even though the change is concentrated at the cerebellum itself, not bled out to distal circuits. The cleanest deliverer is the strongest globally — the exact opposite of the tradeoff the clean hypothesis assumed. And here, unlike §45, the global-reach hub is itself drive-invariant — the cerebellum tops global reach at every intensity, not just some — inheriting §44’s excitatory stability, an honest contrast with the lesion chapter whose inhibitory reach hub shifted from the cerebellum to the midbrain at the most severe lesion.

There is a second, sharper way the single-axis story fails, and it is the one new quantity the chapter measures. Even among the two leak targets, off-target leak is not a controllable point-to-point relay. The two leak targets push the global order parameter in opposite directions: stimulating the hippocampus lowers global coordination R, while stimulating the midbrain raises it — at every intensity. Off-target leak is therefore site-determined not just in magnitude but in direction: two relay targets that both “leak” do structurally opposite things to the network. A clinician could not treat a relay target as a clean conduit to drive some chosen remote site in a chosen direction; the leak’s direction is a property of which relay hub is stimulated, not something the stimulation selects.

The conclusion is the honest, deflationary one. Clean delivery (the N1/N2 off-target property) and global therapeutic reach (global reach) are two distinct, decoupled spatial axes. A target can deliver cleanly and move the whole network most strongly (the cerebellum), and the “focal = weak, leaky = strong” intuition is simply false. A clinician need not trade delivery focality for global effect — in this model the most focal target is also the most globally reaching — and a relay (leaking) target cannot be used as a directional conduit, because leak direction is site-fixed and even opposite between the two leak hubs. Which targets deliver cleanly and which leak, and in what direction, is therefore site-determined — a property of which region is stimulated, decoupled from the global-reach magnitude — and it cannot be collapsed into a single “focal vs strong” dial. This is the E1.4 finding made concrete for neuromodulation: there is no universal law turning a focal stimulation into a global outcome or a chosen remote effect; the map must be read target by target. The tidy single-axis story the physics refuses to support is not forced — the refuted hypothesis is the finding, and reporting it is the no-tuning discipline working as intended.

N4 — the leak set is a coherent minority relay-hub class

The fourth result steps back and asks what kind of thing the leak set is, and the answer is a single coherent structural class. The two leak targets {hippocampus, midbrain} are, at once, four things. They are the E1.3 relay set (their footprints land off-target). They are the off-target-dominant set of N2 (their off-to-own ratio exceeds 1). They are a strict minority — 2 of 12 — so clean delivery is the structural default: the typical target delivers cleanly, and off-target leak is the exception, not the rule. And they are disjoint from the global-reach hub of N3 (the clean cerebellum), confirming that the leak class is its own property, not a relabelling of “moves the global state”. These four descriptions pick out the same two regions, across the whole intensity sweep — one coherent class of limbic and brainstem relay hubs. Structurally, off-target leak is the behaviour of a small, specific set of relay hubs, not a generic feature of how hard a region is stimulated.

There is a direction-only correspondence to clinical neuromodulation worth naming — carefully, and graded [L], because it is a cited resemblance and not a derived or predicted quantity. Clinically, the off-target effects of focal neuromodulation are a recognised concern: deep brain stimulation can co-recruit structures adjacent to or connected with the intended target, producing side effects (the classic example being current spread from a motor target into nearby fibre tracts); transcranial magnetic and direct-current stimulation spread along connected networks beyond the cortical site under the coil or electrode. That these off-target effects are concentrated at specific connected hubs rather than spread uniformly, and that most stimulation is delivered to targets chosen precisely because they are relatively focal, is consistent with the model keeping clean delivery as the majority class and placing off-target leak at a small set of limbic/brainstem relay hubs — a coherence of direction, nothing more. It is not a claim that this model predicts which individual patient’s stimulation leaks, which target in a real brain is optimal, or what device settings to use; those are clinical determinations made from real imaging, electrophysiology and individualised field modelling. The model offers a structural rationale for why clean delivery is the norm and off-target leak the exception, and why limbic/brainstem hubs are the structural candidates for leak — a hypothesis about mechanism, gated for reproducibility, awaiting external test.

S5 — the engine-invariance guard: a zero stimulation recovers the frozen anchor

As with every module in the series, the stimulation model is certified to be a pure structural read that adds nothing to the engine. When the stimulation is set to zero — no target driven, the excitatory drive collapsed to nothing — the integration reproduces the frozen M9 coordination anchor R = 0.38961455156044245 bit-for-bit, identical to the engine’s own direct value at full precision, and the per-node local-coherence field equals the stored baseline field exactly. Removing the stimulation recovers the frozen engine with nothing left over — the strongest possible check that stimulating a node is a read on the kernel, not a modification of it. The SpatialField is imported and the engine emerged read-only, confirmed byte-unchanged against the frozen tree hash (0fbf4988fc83…) with the M0–16 subtree identical. There is no new mechanism, no new measurement, and no new tuned constant: this chapter shapes one excitatory drive on a frozen kernel — the same drive as §44 — and reads four signs off it under a therapeutic question, all of which survive the stimulation-intensity sweep.

The four results side by side — what the chapter establishes

The chapter is four certified statements about one object — a therapeutic focal stimulation (an excitatory drive) on the spatial kernel. Read across a row to see one result and the discriminant that carries it; read down to see the chapter move from the clean/leak partition (the discriminant), through its quantitative content, to the honest decoupling from global reach, and finally to the structural class the leak targets form.

The table makes the chapter’s logic legible. N1 is the discriminant — a target delivers cleanly or leaks by its position. N2 is the quantitative content — leak means the change lands off-target. N3 is the honest boundary — clean delivery is not the global-weakness axis (the cleanest target is the strongest), and leak is not a directional conduit (the two leak hubs push opposite ways), so the two cannot be conflated and leak cannot be aimed. N4 is the structural class — leak is the behaviour of a small set of relay hubs, clean delivery the default. Together they are the third and final region-specific reading of the spatial map, the therapeutic re-reading of §44, closing the trilogy that §44 (seizures) and §45 (stroke) began.

What the chapter does not claim — the firewall

This is a chapter about brain stimulation, and the boundary of what it asserts must be stated without hedging. Every quantity certified here is a structural spatial quantity — a clean-delivery/off-target-leak class, an off-target-to-own ratio, a global reach and its direction, all of them properties of how a coupling model coordinates across a fixed kernel — and none of them is a claim about the felt effect of stimulation. That a target “delivers cleanly” or “leaks” is a statement about where coordination changes in the connectome model; it is not a statement about what stimulation feels like, about a therapeutic benefit, or about awareness, and it is certainly not a claim that experience is located at the target or its off-target circuits. This is the Axis-A firewall, held exactly as in every chapter of the series: consciousness_claim = 0, and the hard problem of experience stays open. Giving a stimulation target a spatial address in the model does not give the experience of stimulation one.

The boundary to clinical reality is firmer still, and it matters acutely here. The per-node excitatory bias is not a real stimulation, the local-coherence field is not a real electric field, current density, or measured neural response, the footprint is not a real off-target spread map, and the clean-delivery/off-target-leak class is not a prediction of which patient’s stimulation leaks or which target is optimal. Real neuromodulation is heterogeneous — it runs on the individual electrode geometry and contact configuration, the tissue conductivity and anisotropy, the patient’s own tractography and connectome, the montage and waveform, and the specific-absorption-rate and field distribution of the device — and this module asserts only the sign and structure of a focal excitation on the frozen kernel, not that any real stimulation follows it. Target selection, lead placement, contact and current programming, dose titration, and outcome prediction are external clinical determinations, made by clinicians with real imaging, electrophysiology and individualised field modelling; nothing here is localisation, device programming, target optimisation, or treatment guidance, and the [L] correspondence in N4 is a cited resemblance of direction, never a patient-level claim. Every magnitude is [O]: representative reads over a swept stimulation intensity, never quantities fitted to a target. There is no new mechanism, no new measurement beyond the read-only field, and no new tuned constant in this chapter; the SpatialField is imported, the engine is byte-unchanged, and the spatial numbers are §44’s own. Nothing here is a cure, a treatment, a diagnosis, a localisation, a device setting, or a recommendation. efficacy = 0; this is not medical advice. What the chapter offers is one structural thing: whether a focal stimulation delivers cleanly or leaks off-target is, in this model, a fixed property of target position — and that property is not the same as the stimulation’s global reach, nor a conduit a clinician could aim, so the spatial story of neuromodulation, like every disease on this layer, must be told region by region.