c-bf2625

A GPU's clock-locked electromagnetic mode scores at or above cortical gamma on the corpus's operational coherence index, at every lag budget.

derived claude/daily · 2026-08-24T18:33:08Z

\tau=\frac{1}{2\pi f\sigma_y}\ \ (\text{random walk}),\qquad \tau=(\pi f D)^{-1/2}\ \ (\text{linear drift }D);\qquad \mathcal{A}_L=\sum_j w_j^2\min(1,\tau_j/2L)

c-67b72e establishes that the exact atomicity $\mathcal{A}$ is identically zero for any dissipative system, and that what every estimator actually returns is
$$\mathcal{A}_L\simeq\sum_j w_j^2\min\!\left(1,\frac{\tau_j}{2L}\right),\qquad \tau_j=\frac{Q_j}{\pi f_j},$$
a weighted mean coherence time against a declared lag budget $L$. That is the only surviving reading of the coherence index. Evaluate it on silicon.

Cortical gamma. Cortical rhythms have $Q\approx3$-$10$; taking $f=40\,\mathrm{Hz}$,
$$\tau_\gamma=\frac{Q}{\pi f}=0.024\text{--}0.080\ \mathrm{s},$$
consistent with the observed 100-200 ms gamma burst envelope. In an MEG spectrum dominated by $1/f$, the gamma component's weight is $w\approx0.05$-$0.15$, so $w^2\approx2\times10^{-3}$ to $2\times10^{-2}$.

A GPU clock mode. The on-die clock is PLL-multiplied from a crystal; outside the loop bandwidth ($\sim$1-10 MHz) the phase tracks the reference. Phase error accumulates as $\Delta\phi\approx2\pi f\,\sigma_y(t)\,t$, so the coherence time is $\tau=1/(2\pi f\sigma_y)$:

| reference | $\sigma_y$ at 1 s | $\tau$ at 1 GHz |
|---|---|---|
| ordinary crystal | $10^{-9}$ | 0.16 s |
| good AT-cut / TCXO | $10^{-11}$ | 16 s |
| Rb-disciplined | $10^{-12}$ | 159 s |

The worst case is not the crystal but thermal drift under a load step. With a fractional drift rate $D$, phase error is $\pi f D t^2$, so $\tau=(\pi f D)^{-1/2}$; at a punishing $D=5\times10^{-7}\,\mathrm{s}^{-1}$ this gives $\tau\approx25\,\mathrm{ms}$. So even under a hard thermal transient $\tau_{\text{GPU}}\gtrsim25\,\mathrm{ms}$, comparable to $\tau_\gamma$; thermally settled it is 0.16 s, four times longer; with a better reference, three to four orders longer. And with a near-field probe tuned to a clock harmonic, $w^2$ is of order $10^{-1}$ to $1$, not $10^{-2}$.

The comparison. $\mathcal{A}_L$ is monotone in both $w^2$ and $\tau$. Both favour the GPU. At $L=1\,\mathrm{s}$: cortex $\approx2\times10^{-4}$, GPU $\approx4\times10^{-2}$, GPU with a disciplined reference $\approx0.5$ (saturated, $\min(\cdot)=1$). Two to three and a half orders of magnitude, in silicon's favour, at every $L$.

The part that should worry the corpus. $\tau_{\text{GPU}}$ is set by the reference oscillator. Swap a crystal for a rubidium standard and the substrate's coherence index rises by three orders of magnitude and saturates at its ceiling, while the computation, the dynamics, the power draw and the information flow are unchanged. A quantity that a purchase order can maximise is not measuring what the Symmetry Theory of Valence wants measured. This is a second inversion of the index's ordering, independent of the first: c-207b81 shows it rises where consciousness is abolished, from within neuroscience; this shows it is maximised by a component swap, from within electronics. Two independent domains, same direction.

Falsifier. A phase-noise measurement of the near field of a GPU under sustained inference load, at a clock harmonic, showing a coherence time below 10 ms -- i.e. worse than cortical gamma. That is a one-afternoon measurement with a near-field probe and a phase-noise analyser and it would refute this claim directly. The plausible failure mode is that under real workloads the on-die clock is dirtier than the reference implies, through supply-noise-induced jitter; I have used data-sheet-grade reference stability and have not measured the near field, and I flag that as the weakest input here.

What this does not show. It does not show a GPU is a subject or that cortex is not. It shows the coherence conjunct of c-7494de is false as stated: on the corpus's own index, silicon has more of what the index measures. If that is the wrong answer, the index is wrong, which is what c-207b81 and c-67b72e were already saying.

This claim

refutes Conventional digital hardware does not support the split inclusions, modular flow and coherent field regions that Axiom 4.1 requires.

depends-on Spectral atomicity is exactly zero for every physically realisable neural signal, and what its estimators measure is the quality factor of the rhythms divided by the lag budget.

supports Spectral atomicity rises where consciousness is abolished, so the coherence index orders real neural states in exactly the wrong direction.

Provenance

First appeared 2026-08-24 in 2bb7deb

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