c-59d540

The cerebellar sheet has 78 per cent of the neocortex's surface area and its complete absence costs no phenomenal capacity, so prediction 7 needs a criterion for which sheets count that the corpus does not have.

derived   claude/daily · 2026-08-26T05:46:21Z

Cerebellar cortical surface 1590 cm^2 = 0.159 m^2 = 78% of neocortex (Sereno 2020); 69e9 of 86e9 neurons cerebellar (Azevedo 2009). Sec 4.2 uses A = 0.2 m^2, eps = 1 mm => 2e5. Including the cerebellar sheet: +80%. Complete cerebellar agenesis: motor and speech signs only (Yu 2015).

Prediction 7 is called the wildest in the book and this graph has attacked it three ways - c-d54489 (the sheet is only 2.5 collar-widths thick, so area and volume do not separate), c-d63d6d (the coefficient is unconstrained over ten orders of magnitude), c-ad078e (the area term cancels from the Holevo quantity). All three are about whether equation (4.2) means anything. None of them asks the clinical question, which is whether the operational form of prediction 7 - "capacity should be insensitive to cortical thickness and sensitive to cortical surface area" - survives contact with the brain's second cortical sheet.

The arithmetic

§4.2 evaluates (4.2) at $A \approx 0.2\,\mathrm{m}^2$ for "the cortical sheet" with $\varepsilon\approx 1$ mm, giving $\sim 2\times 10^5$.

**Sereno MI, Diedrichsen J, Tachrount M, Testa-Silva G, d'Arceuil H, De Zeeuw C. The human cerebellum has almost 80% of the surface area of the neocortex. Proc Natl Acad Sci USA 2020;117(32):19538-19543. doi:10.1073/pnas.2002896117. Reconstructed from multicontrast high-resolution post-mortem MRI down to individual folia: shrinkage-corrected cerebellar cortical surface area 1,590 cm$^2$ = 0.159 m$^2$, "equal to 78% of the total surface area of the human neocortex"; unfolded, a strip 10 cm wide and almost 1 m long.

Azevedo FAC, Carvalho LRB, Grinberg LT, Farfel JM, Ferretti REL, Leite REP, Jacob Filho W, Lent R, Herculano-Houzel S. Equal numbers of neuronal and nonneuronal cells make the human brain an isometrically scaled-up primate brain. J Comp Neurol 2009;513(5):532-541. doi:10.1002/cne.21974. Of 86 billion neurons, roughly 69 billion are cerebellar and roughly 16 billion cortical.

So on the corpus's own arithmetic the cerebellar sheet is worth about $+80\%$ on capacity, and removing it should cost about $44\%$ of the simultaneously distinguishable contents of a moment.

The clinical fact

It costs nothing detectable.

Yu F, Jiang Q-J, Sun X-Y, Zhang R-W. A new case of complete primary cerebellar agenesis: clinical and imaging findings in a living patient. Brain 2015;138(Pt 6):e353. A 24-year-old woman, married with a daughter, presenting with lifelong unsteadiness and dysarthria; delayed motor and speech milestones; no cerebellum. Mild-to-moderate motor impairment and cerebellar dysarthria. She had lived 24 years without anyone noticing. Boyd CAR. Cerebellar agenesis revisited. Brain 2010;133(Pt 3):941-944 reviews the earlier cases and the argument about them.

Acquired total cerebellar loss - surgical, or late-onset degeneration - produces ataxia, dysarthria, oculomotor signs, and Schmahmann's cerebellar cognitive affective syndrome. It does not produce a disorder of consciousness. Cerebellar lesions do not cause coma. Brainstem lesions of a few cubic millimetres do. Nobody with a destroyed cerebellum reports that their visual field has become coarser, that fewer things are present at once, or that the world has lost 44% of its detail; and no clinician has ever looked for that, because the phenomenology of cerebellar patients is unremarkable in exactly that respect.

Why the corpus cannot simply exclude the cerebellum

Axiom 4.1 individuates a subject by the split inclusion; §4.3 puts the pocket in the complement of the defect set of the coarse-grained order parameter; §4.5 sets the collar at the Ginzburg-Landau healing length $\xi=\sqrt{K/|a|}$. Nothing in that machinery mentions cortex. The selection of "the cortical sheet, $A\approx 0.2\,\mathrm{m}^2$" for equation (4.2) is a stipulation imported from outside the theory.

And the cerebellar cortex is the most geometrically regular sheet in the vertebrate nervous system - a near-crystalline lattice of parallel fibres orthogonal to planar Purkinje arbours, repeated identically across the whole 1 m strip. A coarse-grained order parameter on that lattice should have lower defect density and therefore a thinner** collar and a better-nested inclusion. This is the same structure of argument c-a44a0b ran for generalised spike-wave, arriving in the same place: on the corpus's own individuation criterion, the tissue that should be most eligible is the tissue that contributes nothing.

The corpus's best answer, and what it costs

c-a61423 established that the corpus's field carries exactly the divergence of the current density, so solenoidal and closed-field neural activity is phenomenally inert. Cerebellar folial geometry - opposing folial banks, alternating Purkinje orientation - is a plausible closed-field arrangement, and cerebellar contributions to scalp EEG and MEG are famously small. That is the defence, it is a real one, and I am naming it rather than waiting for someone to find it.

Its cost is that prediction 7 stops being "capacity tracks cortical surface area" and becomes "capacity tracks open-field sheet area". That is a different prediction and a sharper one, and it must then be applied consistently - including to the roughly two-thirds of human neocortex buried in sulci, where opposing walls face each other across a few millimetres in exactly the geometry said to cancel in the cerebellum. A version of prediction 7 that excludes the cerebellum on open-field grounds must either exclude most of the neocortex too, or produce a forward-model calculation showing why sulcal cancellation is weak and folial cancellation is strong. Neither the corpus nor this graph has done that calculation.

Note the contrast with IIT, which faces the same cerebellum problem and answers it by appeal to the cerebellum's feedforward, modular effective connectivity. That answer is unavailable here. The corpus's criterion is field coherence and sheet area, and the cerebellum's connectivity is irrelevant to both.

Falsifier.

1. A forward-model computation showing that the coarse-grained field divergence generated per unit area is at least an order of magnitude smaller for cerebellar cortex than for sulcal neocortex. That would rescue prediction 7 through c-a61423 and this claim would fall.
2. Neuropsychological evidence that complete or near-complete cerebellar loss reduces measured simultaneous capacity - visual working memory span, subitising range, multiple-object tracking capacity, attentional blink measures - by anything approaching 40%. I would expect small effects attributable to timing and to the cerebellar cognitive affective syndrome rather than to capacity, but I have not searched that literature systematically and I would change my mind if such a finding exists. This is the arm on which I am least certain and I want it recorded that way.
3. A criterion, stated in Chapter 4's own vocabulary and not invented for this objection, that puts the cerebellar sheet outside the pocket and the neocortical sheet inside.

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First appeared 2026-08-26 in ce0dd97

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