Stroke and the lesion field — local deficit versus remote diaschisis (the second application of the spatial-localisation layer)

Chapter 44's spatial map gets its destructive dual. Silencing each region as a focal lesion, the lesions partition into local-deficit (the dysfunction stays local) and remote-diaschisis (it disrupts distant circuits more than the lesion itself), fixed by lesion location, not severity. But diaschisis is not the same as global disruption — two decoupled axes. Structural quantities, never felt experience.

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 first reading under an excitatory ictal drive, and asked whether a focal seizure stays focal or secondarily generalises. This chapter takes the second reading — the destructive dual — on the disorder a silencing drive was built to answer: a stroke, a focal brain lesion. Where §44 drove a region up the coupling curve, this chapter drives one down: a lesion is a strong focal inhibitory (silencing) bias at one region, the rest at baseline, through the same k = κ/(1+|b|) inhibitory map as the schizophrenia, epilepsy and spatial modules (no new constant). The lesioned node is silenced, not deleted — deleting a node would break the frozen W₀ and forfeit kernel reuse, so the lesion is read on the intact frozen kernel, with the severity swept over {−0.5, −0.7, −0.9} and every sign required to hold at every severity. The clinical question is the dual of §44’s: does destroying one region produce a purely local deficit — the dysfunction confined to the lesioned circuit — or does it disrupt remote, connected regions more than the lesion site itself? That second possibility is diaschisis: von Monakow’s century-old observation that a focal injury can depress function in distant areas connected to it, the structural signature of why a stroke’s deficits so often exceed the damaged tissue. Four results hold. L1 — the local-deficit/remote-diaschisis partition is drive-invariant: each lesion is local-deficit (the coordination change concentrates at the lesion, the dysfunction stays local) or remote-diaschisis (the change lands harder off-target, the lesion disrupts distant circuits more than itself), and this binary partition is identical across the entire severity sweep — the diaschisis set {hippocampus, midbrain} fixed at every severity, the other ten lesions local at every severity. Whether a lesion stays local or causes remote diaschisis is a fixed property of lesion location, not of how severe the lesion is — and that diaschisis set is exactly the E1.3 relay set, read now under silencing. (At a mild, sub-floor severity −0.3 the thalamus also enters the diaschisis set; this is reported honestly and is not part of the drive-invariant claim, which is made only over the moderate-to-severe core inherited from E1.2.) L2 — remote diaschisis is off-target dominance: for a diaschisis lesion the coordination change lands harder on distal circuits than on the lesion itself (mean off-target |Δc| > own, ratio above 1 — the midbrain at roughly 3.0×, the hippocampus 1.2×) — the structural signature of remote dysfunction after focal injury — while a local-deficit lesion concentrates at the site (ratio far below 1, the cerebellum at ~0.06×); the equivalence holds at every severity. L3 — global disruption is not remote diaschisis (the honest no-tuning result): a clean, attractive hypothesis — “the lesions that most disrupt global coordination are exactly the remote-diaschisis lesions” — is false. The single largest global-disruptor lesion is the cerebellum, which is local-deficit (off-target far below own, no diaschisis) yet moves the network-wide order parameter the most at the representative moderate severities — a lesion can maximise global disruption while being maximally local. And unlike §44 — where the global-reach hub was itself drive-invariant — here the reach hub is not drive-invariant: the cerebellum tops global reach at −0.5 and −0.7, but at the most severe −0.9 the midbrain overtakes it. Global-coordination disruption and remote diaschisis are two distinct, decoupled spatial axes: which sites cause the worst remote dysfunction is site-determined, not reducible to a single “biggest global disruptor” rule. The refuted hypothesis is reported honestly — the E1.4 lesson made concrete for stroke. L4 — the diaschisis set is a coherent minority relay-hub class: {hippocampus, midbrain} is simultaneously the E1.3 relay set, the off-target-dominant set (L2), a strict minority (2 of 12 — local deficit is the structural default), and disjoint from the global-reach hub (the local cerebellum, L3) — one coherent class of limbic/brainstem relay hubs. Remote diaschisis is structurally the exception, carried by specific relay hubs, not a generic property of lesions. A direction-only [L] correspondence is noted, never a magnitude or a prediction: clinically most focal lesions produce focal deficits, while diaschisis — crossed cerebellar diaschisis, thalamic and limbic remote effects, von Monakow’s concept — is the recognised exception at specific connected hubs, consistent with the diaschisis set being a strict minority of relay hubs. A uniform (zero) lesion 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 local-deficit/diaschisis class is a structural spatial quantity of the coupling model, never the felt experience of a stroke, and not a real lesion, an infarct map, a perfusion or diffusion MRI, a connectome-diaschisis measurement, a stroke-outcome or recovery prediction, or rehabilitation/clinical guidance (Axis-A — consciousness_claim = 0, the hard problem stays open). Every magnitude is [O]; efficacy = 0; not medical advice.

The dual of §44 — what does destroying a region disrupt?

The focal-epilepsy chapter read the spatial map under an excitatory drive: it pushed one region hard up the coupling curve, modelling a seizure focus, and asked whether the resulting ictal change stays at the focus or spreads off it. That is one of the two things one can do to a single region on a fixed kernel. The other is to push it down — to silence it — and that is what a focal brain lesion is: a stroke, a haemorrhage, a resection, a region taken structurally out of the network. Where the seizure chapter asked “does a focal excitation contain or generalise?”, this chapter asks the destructive dual: “does a focal silencing stay local, or disrupt at a distance?” The two chapters are the same spatial map read with opposite-sign drives, on the two great classes of focal brain disorder — the hyper-excitable (epilepsy) and the destroyed (stroke).

The clinically decisive fact about a focal lesion is that its consequences frequently exceed the damaged tissue. A small infarct can produce deficits out of all proportion to its size, because the lost region was a node other regions depended on — and the regions that lose function need not be anywhere near the lesion. This is diaschisis, named by Constantin von Monakow a century ago: the depression of function in an area remote from, but connected to, a focal injury. Crossed cerebellar diaschisis — a supratentorial stroke depressing the opposite cerebellar hemisphere — is its textbook instance; thalamic and limbic remote effects are others. The clinical question that matters is therefore exactly a spatial one: when you silence this region, is the dysfunction local (confined to the lesioned circuit) or does it land harder on distant, connected circuits than on the site itself? That is the question a global scalar can never pose, and the question the spatial layer was built to make answerable.

The lesion model — a focal lesion as a silencing bias on the spatial layer

The model is the smallest one that makes the question answerable, and it reuses the spatial layer wholesale — with one discipline that must be stated first. A lesion is modelled as a strong focal inhibitory (silencing) bias: region i is driven to a strongly negative bias b₀ while every other region sits at baseline, through the same effective-coupling map as the schizophrenia, epilepsy and spatial modules — k(b) = κ/(1+|b|) for an inhibitory bias — so a lesion is simply a region pushed hard down the coupling curve, with no new constant introduced. Crucially, the lesioned node is silenced, not deleted. Deleting a node — removing its row and column — would break the frozen W₀ kernel, change the matrix every other module is certified against, and forfeit the whole point of kernel reuse. So the lesion is read on the intact frozen kernel as an extreme silencing drive; the structure is preserved, the node merely stops contributing. This is the handover’s explicit lesion-modelling directive, and it is what keeps the chapter inside the byte-frozen engine.

Two readings answer the two halves of the clinical question, and they are the same two readings §44 used, applied to a silencing drive. The first is the footprint class: silence a region and compare its own local-coherence change to the mean change it induces off-target. If the lesion’s own change dominates, the deficit is local — the dysfunction stays at the lesioned circuit. If the off-target change dominates, the lesion causes remote diaschisis — it disrupts distant circuits more than itself. The second is the global reach |R − R₀|: how much silencing that one region moves the network-wide order parameter, the quantity §25 made the seizure out of and the natural measure of global coordination disruption. Local-versus-diaschisis 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 — and they are not. The lesion severity is swept, not chosen: every sign reported below is required to hold at b₀ = −0.5, −0.7 and −0.9 alike, inheriting the moderate-to-severe floor the spatial layer’s E1.2 result established, so no number is fitted to make a result come out.

L1 — the local-deficit/remote-diaschisis partition is drive-invariant

The first result is the spatial discriminant for focal lesions, and it is inherited intact from the layer. Silencing each of the 12 regions in turn as a focal lesion, the lesions partition cleanly into two classes. Ten lesions produce a local deficit: the coordination change concentrates at the silenced region, more than it changes anywhere else — structurally, the dysfunction stays local. Two lesions produce remote diaschisis: silencing them changes coordination off the lesion more than at the lesion itself — structurally, the lesion disrupts distant circuits more than the site it destroyed. The diaschisis set is {hippocampus, midbrain}.

The certification is that this partition does not move with lesion severity. From the gentlest swept lesion to the most severe, the same ten lesions stay local and the same two cause diaschisis: the diaschisis set {hippocampus, midbrain} is fixed at every severity tested. Whether a lesion produces a local deficit or remote diaschisis is therefore a fixed property of where the lesion sits in the field — a drive-invariant connectome property, not a function of how completely the region is destroyed. And that diaschisis set is exactly the E1.3 relay set: the regions whose footprint lands off-target under an excitatory drive are the same regions whose silencing disrupts at a distance. The self/relay map is doing double duty — it is the containment/spread map for seizures (§44) and the local/diaschisis map for lesions, the same structural classification read with opposite-sign drives.

One honest scope limit belongs here. At a mild, sub-floor lesion severity — b₀ = −0.3, below the moderate-to-severe floor the sweep is defined over — the thalamus also enters the diaschisis set, joining the hippocampus and midbrain. This is reported plainly and is not folded into the drive-invariant claim: the invariance is asserted only over the moderate-to-severe core {−0.5, −0.7, −0.9} inherited from E1.2, where the partition is exactly stable. That the thalamus — a canonical relay nucleus — sits just outside the diaschisis set and crosses in only at mild silencing is recorded as a structural fact, not smoothed away to make the set look cleaner than it is.

L2 — remote diaschisis is off-target dominance: the structure of remote dysfunction

The second result turns the binary class of L1 into a legible quantity, and ties “diaschisis” to its clinical meaning of remote dysfunction. For each silenced region, take the ratio of the mean off-target coherence change to the lesion’s own change. For a diaschisis lesion this ratio is above 1: silencing the region disrupts coordination harder in distal circuits than at the lesion itself — the midbrain at roughly 3.0×, the hippocampus at 1.2×. That is precisely the structural picture of diaschisis: the region is destroyed, but the largest coordination change is elsewhere, in the circuits that depended on it. For a local-deficit lesion the ratio is far below 1: the change is concentrated at the lesion, the distal circuits barely move — the cerebellum, for instance, at about 0.06×, an overwhelmingly local footprint.

The equivalence — a lesion causes diaschisis if and only if its off-target change exceeds its own — holds at every swept severity. This is what makes the L1 partition more than a label: remote diaschisis is not a separate phenomenon bolted on, it is the same footprint read quantitatively — the off-target-to-own ratio crossing 1. 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 a blood-flow change, a metabolic depression, or a clinical deficit severity. The magnitude of any real diaschisis is [O]; what is asserted is the sign — that diaschisis lesions dominate off-target and local lesions dominate at the site, robustly across severity.

L3 — global disruption is not remote diaschisis: two distinct axes

The third result is the one the no-tuning discipline exists to surface: a clean hypothesis, tested, and reported as false rather than quietly dropped. The hypothesis is the natural one. If a region’s silencing disrupts the network, the obvious guess is that the lesions causing the worst remote diaschisis are exactly the lesions that disrupt global coordination the most — the lesions with the largest global reach |R − R₀|. If that held, “disrupts distant circuits” and “disrupts the whole network” would be the same axis, and the chapter would reduce to a single number.

It does not hold, and the way it fails is sharper here than in §44. The single largest global-disruptor lesion — the lesion whose silencing moves the network-wide order parameter the most — is the cerebellum, and the cerebellum is local-deficit: its off-target change is far below its own (about 0.06×), it causes no diaschisis, yet it is the rank-1 global disruptor at the representative moderate severities (−0.5 and −0.7) and a top-three global disruptor at every severity. A lesion can maximise global disruption while being maximally local: destroying the cerebellum perturbs the whole network’s coordination more than destroying any other region, even though the disruption is concentrated at the cerebellum itself, not broadcast to distal circuits. The biggest global disruptor is the opposite of a diaschisis lesion.

There is a second, subtler way the single-axis story fails, and it is an honest contrast with the epilepsy chapter. In §44 the global-reach hub (the cerebellum) was itself drive-invariant — the same region topped global reach at every ictal intensity. Here it is not: the cerebellum tops global reach at −0.5 and −0.7, but at the most severe lesion −0.9 the midbrain overtakes it as the largest global disruptor. The reach hub itself moves with severity — a structural difference between driving a region up (excitation) and silencing it (lesion) that the chapter records rather than hides. The diaschisis partition is rock-stable across severity (L1); the global-disruption ranking is not. That the two have different stability properties is itself evidence they are different axes.

The conclusion is the honest, deflationary one. Remote diaschisis (the L1/L2 off-target property) and global-coordination disruption (global reach) are two distinct, decoupled spatial axes. A lesion can disrupt distant circuits without being the biggest global disruptor (the diaschisis hubs sit below the cerebellum on reach), and a lesion can disrupt the whole network most strongly while keeping its own footprint local (the cerebellum). Which sites cause the worst remote dysfunction is therefore site-determined — a property of which region is destroyed, decoupled from the global-disruption magnitude — and it cannot be collapsed into a single “biggest disruptor = worst diaschisis” rule. This is the E1.4 finding made concrete for stroke: there is no universal law turning a focal silencing into a remote outcome; the map must be read region by region. 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.

L4 — the diaschisis set is a coherent minority relay-hub class

The fourth result steps back and asks what kind of thing the diaschisis set is, and the answer is a single coherent structural class. The two diaschisis lesions {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 L2 (their off-to-own ratio exceeds 1). They are a strict minority — 2 of 12 — so local deficit is the structural default: the typical lesion produces a local deficit, and remote diaschisis is the exception, not the rule. And they are disjoint from the global-disruption hub of L3 (the local cerebellum at moderate severity), confirming that the diaschisis class is its own property, not a relabelling of “disrupts the global state”. These four descriptions pick out the same two regions, across the moderate-to-severe sweep — one coherent class of limbic and brainstem relay hubs. Structurally, remote diaschisis is the behaviour of a small, specific set of relay hubs, not a generic feature of how severely a region is destroyed.

There is a direction-only correspondence to clinical neurology worth naming — carefully, and graded [L], because it is a cited resemblance and not a derived or predicted quantity. Clinically, most focal lesions produce focal deficits, confined to the function of the damaged tissue and its immediate circuit. Diaschisis — remote dysfunction after focal injury — is the recognised exception, observed at specific connected hubs: crossed cerebellar diaschisis after supratentorial stroke, thalamic and limbic remote effects, the family of phenomena von Monakow named. That the model keeps local deficit as the majority class and places remote diaschisis at a small set of limbic/brainstem relay hubs is consistent with that picture — a coherence of direction, nothing more. It is not a claim that this model predicts which individual patient’s stroke will cause diaschisis, nor which region in a real brain disrupts remotely; those are clinical determinations made from real imaging and examination. The model offers a structural rationale for why local deficit is the norm and diaschisis the exception, and why limbic/brainstem hubs are the structural candidates for remote disruption — a hypothesis about mechanism, gated for reproducibility, awaiting external test.

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

As with every module in the series, the lesion model is certified to be a pure structural read that adds nothing to the engine. When the lesion is set to zero — no region silenced, the spatial 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 lesion recovers the frozen engine with nothing left over — the strongest possible check that silencing 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 silencing drive on a frozen kernel and reads four signs off it, all of which survive the lesion-severity sweep over the moderate-to-severe core.

The four results side by side — what the chapter establishes

The chapter is four certified statements about one object — a focal lesion (a silenced region) 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 local/diaschisis partition (the discriminant), through its quantitative content, to the honest decoupling from global disruption, and finally to the structural class the diaschisis lesions form.

The table makes the chapter’s logic legible. L1 is the discriminant — a lesion stays local or disrupts at a distance by its position. L2 is the quantitative content — diaschisis means the change lands off-target. L3 is the honest boundary — diaschisis is not the global-disruption axis, so the two cannot be conflated, and the reach hub does not even hold still. L4 is the structural class — diaschisis is the behaviour of a small set of relay hubs, local deficit the default. Together they are the second region-specific reading of the spatial map, the destructive dual of §44, on the disorder a silencing drive was built to answer.

What the chapter does not claim — the firewall

This is a chapter about stroke, and the boundary of what it asserts must be stated without hedging. Every quantity certified here is a structural spatial quantity — a local-deficit/diaschisis class, an off-target-to-own ratio, a global reach, all of them properties of how a coupling model coordinates across a fixed kernel — and none of them is a claim about the felt experience of a stroke. That a lesion causes “diaschisis” is a statement about where coordination changes in the connectome model; it is not a statement about what a stroke feels like, about the loss of a faculty, or about awareness, and it is certainly not a claim that experience is located at the lesion or its remote targets. 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 lesion a spatial address in the model does not give the experience of a stroke one.

The boundary to clinical reality is firmer still, and it matters more here than almost anywhere in the series. The per-node silencing bias is not a real lesion, the local-coherence field is not a real blood-flow, metabolic, or diffusion measurement, the footprint is not a real diaschisis map, and the local-deficit/diaschisis class is not a prediction of which patient’s stroke will disrupt remotely or recover. Real stroke is heterogeneous — it runs on the individual vascular territory, the white-matter tractography, penumbral dynamics, oedema, and the patient’s own connectome and collateral supply — and this module asserts only the sign and structure of a focal silencing on the frozen kernel, not that any real lesion follows it. Stroke diagnosis, lesion localisation, outcome prognosis, and rehabilitation planning are external clinical determinations, made by clinicians with real imaging and examination; nothing here is localisation, prognosis, or treatment guidance, and the [L] correspondence in L4 is a cited resemblance of direction, never a patient-level claim. Every magnitude is [O]: representative reads over a swept lesion severity, 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 and the engine is byte-unchanged. Nothing here is a cure, a treatment, a diagnosis, a localisation, a prognosis, or a recommendation. efficacy = 0; this is not medical advice. What the chapter offers is one structural thing: whether a focal lesion produces a local deficit or remote diaschisis is, in this model, a fixed property of lesion position — and that property is not the same as disrupting the whole brain’s coordination, so the spatial story of stroke, like every disease on this layer, must be told region by region.