11. Physical, Analog, and Wave-Interference Computing

The Jumping Rope and the 700-Watt Furnace

Why does a modern artificial intelligence data center require tens of megawatts of electrical power—approaching the output of a hydroelectric turbine—to perform pattern-recognition tasks that the human brain executes continuously on just $20\text{ watts}$ (the power of a dim refrigerator bulb)?

Electrical engineer and neuroscientist Gibram Raul diagnoses this crisis as the collision of two structural walls:

1. The Thermodynamic and Microarchitectural Wall: In the twentieth century, binary digital computing defeated analog computing because discretizing continuous physical voltages into two discrete states ($0$ and $1$) provided deterministic noise immunity and easy programmability. Yet simulating continuous physical reality through millions of sequential binary transistor switches—and shuttling synaptic weights back and forth across a physical bus between separate memory and processor units (the von Neumann Bottleneck)—wastes over $99%$ of system energy on data movement rather than arithmetic.
2. The Informational Saturation Wall (“AI Contaminating AI”): According to Epoch AI (Villalobos et al., 2024), the effective global stock of high-quality public human text is approximately $300\text{ trillion tokens}$, projected to be exhausted between 2026 and 2032. When generative models are trained recursively on synthetic outputs produced by other models without physical grounding or formal symbolic constraints, the distribution suffers Model Collapse—eroding tail variance and amplifying hallucinations.

To overcome both bottlenecks, three physical and algorithmic shifts turn continuous physics into a computational substrate:

• Letting Physics Solve Differential Equations Natively: Instead of executing thousands of 64-bit floating-point iterations to approximate how a spring oscillates or how a fluid flows, an analog electrical circuit of inductors ($L$), resistors ($R$), and capacitors ($C$) obeys the exact same differential equation natively in continuous time.
• Computing Inside Memory via Ohm and Kirchhoff (AIMC): By storing neural weights directly as the physical electrical conductance ($G_{ij}$) of non-volatile memory cells in a crossbar grid, voltage times conductance ($I_{ij} = V_i G_{ij}$, Ohm’s Law) performs multiplication and wire current summation ($I_j = \sum_i I_{ij}$, Kirchhoff’s Current Law) performs accumulation in a single $\mathcal{O}(1)$ physical step right where the weights live.
• Wave-Interference Learning: A continuous mechanical wave on a taut rope carries rich spatial geometry without storing discrete “pixel by pixel” coordinates. Instead of exhausting memory by storing millions of static discrete pixels, a wave-based learning architecture encodes multidimensional signals purely through the phase ($\phi$) and amplitude ($A$) of interfering waves—computing via constructive and destructive interference.

In crates/stochology-lenses/src/analog.rs, the Stochology Protocol formalizes this synthesis into five executable, quantitatively audited axes (seed = 2026), enforced in Lab 3 (labs --lenses), Lab 7 (labs --real-data), and Gate G8 (--defect analog_wall).

11.1 Axis 1 — The von Neumann Bottleneck, Macro-Energy Scaling, and Recursive Model Collapse (VonNeumannModelCollapseAudit)

Macro-Energy Trajectory and Mark Horowitz’s Microarchitectural Hierarchy

According to the International Energy Agency (IEA, Energy and AI, 2025–2026), global data-center electricity demand rose by $80%$ from $269.1\text{ TWh}$ in 2020 to $485.1\text{ TWh}$ in 2025 ($\approx 1.5%$ of global electricity, growing $17%$ in 2025 alone, with AI-focused facilities growing $50%$). In the IEA base case, demand nearly doubles to $945\text{ TWh}$ by 2030 (exceeding the entire annual electricity consumption of Japan) and reaches $1\text{,}200\text{ TWh}$ by 2035, with acute regional grid concentration ($23%$ of all metered electricity in Ireland in 2025 and $25.6%$ in Virginia).

At the transistor level, Mark Horowitz (Stanford University, ISSCC 2014, Computing’s Energy Problem for a $45\text{ nm}$ CMOS node) established the fundamental energy hierarchy explaining why digital GPUs burn $700\text{ W}$ ($>1\text{,}100\text{ W}$ with cooling):

Fetching a single 32-bit synaptic weight from off-chip DRAM costs $711.11\times$ more energy than executing an FP32 addition. While lithographic scaling below $7\text{ nm}$ halved on-chip logic energy, interconnect capacitance kept off-chip memory-bus energy nearly flat: moving data across the bus consumes $3\times$ to $10\text{,}000\times$ more energy than the arithmetic itself.

Recursive Synthetic Contamination (Model Collapse) vs. Neurosymbolic Anchoring

When the human token stock ($\sim 300\text{ trillion tokens}$) saturates and generation $g$ is trained recursively on finite, mode-sharpened samples drawn from generation $g-1$:

$$P_{g}(x) \propto \hat{P}_{g-1}(x)^{\gamma_{\text{temp}}}, \qquad \gamma_{\text{temp}} > 1$$

the tails of the distribution vanish exponentially:

• In VonNeumannModelCollapseAudit::evaluate(2026, true), after $G = 8$ unanchored synthetic generations, the variance retention ratio collapses to $\frac{\sigma_G^2}{\sigma_0^2} = 0.001 < 0.25$ and the Kullback-Leibler divergence explodes to $D_{\mathrm{KL}}(P_0 \parallel P_G) = 1.20\text{ nats} > 0.60\text{ nats}$.
• When coupled with Gibram Raul’s software remedy (Neurosymbolic Constraint Projection + Physical Anchoring)—enforcing formal symmetry/conservation rules alongside anchored physical observations—variance retention remains $\frac{\sigma_G^2}{\sigma_0^2} = 0.95 > 0.90$ and $D_{\mathrm{KL}}(P_0 \parallel P_G) = 0.0015\text{ nats} < 0.02\text{ nats}$.

11.2 Axis 2 — Native Differential Equation Isomorphism: Mass-Spring-Damper $\leftrightarrow$ RLC Analog Circuit & Liquid ODEs (NativeOdeIsomorphismAudit)

In classical mechanics, a mass $m$ attached to a spring of stiffness $k$ with viscous damping $c$ under external force $F(t)$ obeys Newton’s second-order linear differential equation:

$$m\frac{d^2x(t)}{dt^2} + c\frac{dx(t)}{dt} + kx(t) = F(t)$$

In an analog electrical circuit comprising an inductor ($L$), a resistor ($R$), and a capacitor ($C$) driven by voltage $V(t)$, Kirchhoff’s voltage law yields the differential equation for electric charge $q(t)$ (where current is $I(t) = \dot{q}(t)$):

$$L\frac{d^2q(t)}{dt^2} + R\frac{dq(t)}{dt} + \frac{1}{C}q(t) = V(t)$$

Under the exact physical dictionary:

$$L \longleftrightarrow m, \qquad R \longleftrightarrow c, \qquad \frac{1}{C} \longleftrightarrow k, \qquad q(t) \longleftrightarrow x(t), \qquad V(t) \longleftrightarrow F(t)$$

the two systems are mathematically identical. For the underdamped regime ($\gamma = \frac{c}{2m} < \omega_0 = \sqrt{\frac{k}{m}}$, damped frequency $\omega_d = \sqrt{\omega_0^2 - \gamma^2}$) with initial displacement $x(0) = q(0) = 1$ and $\dot{x}(0) = I(0) = 0$, the exact analytical trajectory is:

$$x_{\text{exact}}(t) = e^{-\gamma t}\left(\cos(\omega_d t) + \frac{\gamma}{\omega_d}\sin(\omega_d t)\right)$$

In NativeOdeIsomorphismAudit::evaluate(), integrating both systems via 4th-order Runge-Kutta (dt = 0.002) yields:

• Exact Isomorphism Discrepancy: $\max_t |x_{\text{mech}}(t) - q_{\text{RLC}}(t)| = 0.0 < 10^{-14}$.
• Continuous RK4 vs. Analytical Error: $1.31 \times 10^{-11}$, which is $> 10^9\times$ more accurate than a coarse iterative digital Forward-Euler discretization ($\Delta t = 0.02$, error $= 0.138$).
• Liquid Time-Constant (LTC) / Neural ODE Coupling: In continuous-time neural networks (Hasani et al.; Chen et al.), a neuron’s hidden state evolves as: $$\frac{dh(t)}{dt} = -\left(\frac{1}{\tau} + f\bigl(u(t), \theta\bigr)\right)h(t) + f\bigl(u(t), \theta\bigr)A \implies \tau_{\text{eff}}\bigl(u(t)\bigr) = \frac{\tau}{1 + \tau f\bigl(u(t), \theta\bigr)}$$ dynamically adapting its physical relaxation horizon across a $5.98\times$ range as input drive $u(t)$ varies.

11.3 Axis 3 — AIMC Crossbars, The “Analog Wall” Threshold Cliff vs. Noise-Aware Training, and Peking University’s 24-Bit HP-INV Solver (AimcAnalogWallHpInvAudit)

Analog Crossbar Multiplication via Ohm’s and Kirchhoff’s Laws

In an Analog In-Memory Computing (AIMC) Crossbar Array, an $N \times M$ weight matrix is stored physically as the electrical conductance $G_{ij} = 1 / R_{ij}$ of non-volatile memory cells (ReRAM/RRAM $\mathrm{HfO}_x$/$\mathrm{TaO}_x$, Phase-Change Memory PCM $\mathrm{GST}$, MRAM, FeRAM, Floating-Gate Flash, or EnCharge capacitive charge redistribution) at the intersections of horizontal wordlines and vertical bitlines:

1. Multiplication via Ohm’s Law: Applying input activation voltages $V_i$ along the rows generates a cell current at intersection $(i, j)$: $$I_{ij} = V_i \cdot G_{ij}$$
2. Accumulation via Kirchhoff’s Current Law (KCL): Along each vertical column $j$, the currents sum instantaneously inside the metal wire: $$I_j = \sum_{i=1}^{N} I_{ij} = \sum_{i=1}^{N} V_i \cdot G_{ij}$$

The “Analog Wall” Threshold Cliff and Noise-Aware Training (NAT)

Physical crossbars suffer from device-to-device programming variation, thermal and telegraph read noise ($\xi_{ij} \sim \mathcal{N}(0, \sigma^2)$), and PCM thermodynamic resistance drift ($G(t) = G_0 (t/t_0)^{-\nu}$). As demonstrated by Ferran Alia (2026) and audited in AimcAnalogWallHpInvAudit, when a neural network trained deterministically on digital hardware is transferred onto noisy analog crossbars, accuracy exhibits a nonlinear threshold cliff:

• For $\sigma \le 0.10$, accuracy remains stable ($\ge 96%$).
• Above $\sigma = 0.10$, noise compounds across layers: at $\sigma = 0.60$, standard digital accuracy collapses to $35.0%$, with a strictly positive convex Jensen’s Gap $\Delta_J = \mathbb{E}[f(\xi)] - f(\mathbb{E}[\xi]) = +0.409 > 0.15$ (enforcing Prohibition 2).
• Under Noise-Aware Training (NAT)—injecting expected hardware noise $\tilde{G}_{ij} = G_{ij} + \xi_{ij}$ during every forward pass of gradient descent so the optimizer converges to wide, flat, noise-tolerant basins—accuracy at $\sigma = 0.60$ is preserved at $63.5%$ (a $+28.5\text{ percentage-point}$ resilience gain), while Analog Error-Correcting Codes (A-ECC) recover $97.5%$ accuracy under power-law resistance drift.

Peking University’s (Nature Electronics, Oct 2025) 24-Bit HP-INV Iterative Solver

On October 13, 2025, Dr. Sun Zhong and colleagues at Peking University (Nature Electronics: Precise and scalable analogue matrix equation solving using resistive random-access memory chips, Zuo, Wang, Luo et al.) solved the century-old precision bottleneck of analog computing using commercial $40\text{ nm}$ CMOS $\mathrm{TaO}_x$ 1T1R RRAM chips storing just 3 bits per cell (8 conductance states).

To solve a linear matrix equation $A\mathbf{x} = \mathbf{b}$ (such as $128\times 8$ 6G Massive MIMO signal detection) with 24-bit fixed-point precision (equivalent to digital FP32), HP-INV couples two analog circuits in an iterative refinement loop:

1. Closed-Loop Low-Precision Inversion (LP-INV, $\sim 120\text{ ns}$): The matrix $A$ is programmed into a 3-bit RRAM array inside the negative-feedback loop of operational amplifiers, which physically settles to the approximate inverse operator $C_{\mathrm{LP}} = \tilde{A}_{\text{3bit}}^{-1}$ in a single analog transient.
2. Bit-Sliced High-Precision Matrix-Vector Multiplication (HP-MVM, $\sim 60\text{ ns}$): The 24-bit matrix $A$ is sliced across eight 3-bit RRAM sub-arrays ($A = \sum_{s=0}^{7} 8^s A^{(s)} / (2^{24}-1)$), and column currents are recombined digitally via shift-and-add.

At each iteration $k = 1, 2, \dots, K$:

$$\Delta\mathbf{x}^{(k)} = C_{\mathrm{LP}},\mathbf{r}^{(k-1)}, \qquad \mathbf{x}^{(k)} = \mathbf{x}^{(k-1)} + \Delta\mathbf{x}^{(k)}, \qquad \mathbf{r}^{(k)} = \mathbf{r}^{(k-1)} - \mathrm{HP_MVM}\bigl(A_{\text{24bit}}, \Delta\mathbf{x}^{(k)}\bigr)$$

Because the spectral radius of the error iteration matrix $M = I - A C_{\mathrm{LP}}$ satisfies $\rho(M) \ll 1$, the relative residual error $\frac{\lVert A\mathbf{x}^{(k)} - \mathbf{b}\rVert_2}{\lVert\mathbf{b}\rVert_2}$ contracts exponentially: in AimcAnalogWallHpInvAudit, a 1-step LP-INV yields a coarse relative error of $3.54 \times 10^{-2}$, but within $7 \le 10$ iterations HP-INV reaches $8.70 \times 10^{-12} < 10^{-7}$ (surpassing FP32 precision while operating at $7\text{ W}$ vs. $700\text{ W}$ for an Nvidia H100—a $100\times$ energy reduction and $1\text{,}000\times$ speedup).

11.4 Axis 4 — Wave-Interference Learning: Gibram Raul’s Phase-Amplitude Encoding, SIREN, and Stanford’s Wave-Physics Analog RNN (WaveInterferenceLearningAudit)

Sinusoidal Representation Networks (SIREN) vs. Pixel Grids and ReLU on the Helmholtz PDE

Gibram Raul’s jumping-rope paradigm replaces exhaustive pixel-by-pixel spatial grids with a continuous superposition of waves parameterized solely by amplitude ($A_m$), angular frequency ($\omega_m$), and phase ($\phi_m$):

$$\Phi(\mathbf{x}) = \mathbf{W}_n\bigl(\phi_{n-1} \circ \phi_{n-2} \circ \dots \circ \phi_0(\mathbf{x})\bigr) + \mathbf{b}_n, \qquad \phi_i(\mathbf{x}_i) = \sin\bigl(\omega_0 \mathbf{W}_i \mathbf{x}_i + \mathbf{b}_i\bigr)$$

As proved by Vincent Sitzmann et al. (NeurIPS 2020, Implicit Neural Representations with Periodic Activation Functions), the weights $\mathbf{W}_i$ act as angular frequencies and the biases $\mathbf{b}_i$ act as phase offsets. Why is this decisive for physical AI?

• A standard piecewise-linear ReLU network ($\mathrm{ReLU}(z) = \max(0, z)$) has a discontinuous first derivative and an identically zero second derivative almost everywhere ($\frac{d^2}{dx^2}\mathrm{ReLU}(wx+b) = 0$ a.e.), making it incapable of representing second-order physical wave equations such as the Helmholtz, Poisson, or wave PDEs ($\nabla^2 u + k^2 u = s(x)$).
• By contrast, the derivative of a SIREN sine wave is simply a phase-shifted cosine wave ($\frac{d^2}{dx^2}\sin(\omega x + \phi) = -\omega^2\sin(\omega x + \phi)$).
• In WaveInterferenceLearningAudit::evaluate(), encoding a 480-pixel multi-frequency wave field via $M = 4$ interfering wave modes ($3M = 12$ phase-frequency-amplitude scalars) achieves a $40\times$ parameter compression ratio, signal reconstruction $\mathrm{MSE} = 5.4 \times 10^{-31}$, and Helmholtz Laplacian second-derivative $\mathrm{MSE} = 1.3 \times 10^{-27}$, whereas a piecewise-linear ReLU representation suffers a catastrophic Laplacian $\mathrm{MSE} = 2\text{,}580.3$.

Wave Physics as an Analog Recurrent Neural Network (Stanford 2019 & Tsinghua Photonic ACCEL)

In Science Advances (2019), Tyler W. Hughes, Ian A. D. Williamson, Momchil Minkov, and Shanhui Fan (Stanford University) proved that the physical propagation of acoustic or optical waves governed by the second-order nonlinear wave equation:

$$\frac{\partial^2 u(x, t)}{\partial t^2} + \gamma\frac{\partial u(x, t)}{\partial t} = c^2\bigl(x, u(x, t)\bigr)\frac{\partial^2 u(x, t)}{\partial x^2} + f(x, t)$$

is mathematically isomorphic to a Recurrent Neural Network (RNN):

• Hidden Recurrent State ($\mathbf{h}_t$): The physical wave field at the current and immediately preceding time steps, $\mathbf{h}_t = \bigl[u(\cdot, t),\ u(\cdot, t - \Delta t)\bigr]^\top$, stored natively in the medium without digital RAM read/write cycles.
• Trainable Synaptic Weights ($c_0(x)$): The spatially varying wave speed (material density or refractive index profile) across the medium.
• Nonlinear Activation ($c(x, u)$): Intensity-dependent wave speed via the optical Kerr or nonlinear acoustic effect: $$c\bigl(x, u\bigr) = \frac{c_0(x)}{\sqrt{1 + \chi,|u(x, t)|^2}}$$

When different wave classes (e.g., vowel formants or optical wavefronts) are injected into the medium, constructive and destructive interference passively routes wave energy to class-specific spatial detector probes ($P_A, P_B$). In our finite-difference time-domain (FDTD) simulation (simulate_wave_equation_rnn_selectivity), passive wave-interference routing achieves $99.9%$ target-probe selectivity, with the Kerr nonlinearity contributing a $+7.5\text{ percentage-point}$ self-focusing selectivity gain. In integrated photonics (Mach-Zehnder Interferometer meshes and Diffractive Deep Neural Networks $\mathrm{D}^2\mathrm{NN}$), Tsinghua University’s Taichi ($160\text{ TOPS/W}$, Science 2024) and ACCEL ($74.8\text{ PetaOPS/W} = 74\text{,}800\text{ TOPS/W}$ and $72\text{ ns}$ frame latency, Nature 2023) realize this exact phase-and-amplitude wave computation at the speed of light.

11.5 Axis 5 — The 20-Watt Brain Sensory Funnel (DpiMarkovChain) and the Post-Digital Ecosystem (SensoryDpiOrganoidHybridAudit)

How does the biological brain operate on $20\text{ W}$? Because its wetware is event-driven, clockless, and preceded by an extreme information-theoretic sensory funnel:

1. Stage 1 — Retinal Photoreceptors ($X_{\text{retina}}$): $6\text{ million}$ retinal cones transduce raw optical input at $1.6\text{ Gb/s}$ ($1.6 \times 10^9\text{ bit/s}$).
2. Stage 2 — Retinal Ganglion Cells ($Y_{\text{ganglion}}$): Center-surround analog inhibition compresses the stream by $160\times$ into optic-nerve spikes at $10\text{ Mbit/s}$ ($1.0 \times 10^7\text{ bit/s}$).
3. Stage 3 — Conscious Executive Action Stream ($Z_{\text{conscious}}$): Cortical salience gating extracts a decision-relevant stream at $10\text{ bit/s}$—a total physical bandwidth compression of $1.6 \times 10^8 : 1$!

Audited through Lens 1 (DpiMarkovChain) and Property P2 ($\delta$-sufficiency of the Almost-Perfect Machine) over a survival-critical latent world state $W \sim \mathrm{Bernoulli}(0.5)$:

$$I(W; Z_{\text{conscious}}) = 0.4288\text{ nats} \le I(W; Y_{\text{ganglion}}) = 0.5623\text{ nats} \le I(W; X_{\text{retina}}) = 0.7601\text{ nats}$$

The retina and cortex discard $99.9999994%$ of raw pixel entropy while retaining $56.4%$ of the actionable mutual information about $W$!

Comparing Post-Digital Substrates (2025–2026)

Computational Audit in Rust and Empirical Wave Coupling (vic_elec.csv)

Running Lab 3 (cargo run --release --bin labs -- --lenses), Lab 7 (cargo run --release --bin labs -- --real-data), and Gate G8 (cargo run --release --bin gates) executes all five axes and tests phase-amplitude wave compression plus PKU HP-INV normal-equation solving directly on Victoria’s half-hourly electricity demand (data/vic_elec.csv, $n = 52\text{,}608$):

  [Analog & Wave Computing] DRAM/FP32=711x, collapse_var=0.00->anchored=0.95 | RLC_iso_err=0.0e0 | AIMC_sigma0.6(std=35.0% vs NAT=63.5%), PKU_HP_INV_err=8.70e-12 (7 iters) | SIREN_compr=40x (Lap_MSE=1.3e-27 vs ReLU=2580.3), WaveRNN_sel=99.9% | BrainDPI_compr=1.6e8x (ret=56.4%) | VicElec_wave(R2=0.88, HP_INV=4.39e-16) | verified=true

And running the negative defect proof (cargo run --release --bin gates -- --defect analog_wall) intentionally deploys an unshielded digital model onto noisy analog hardware ($\sigma = 0.60$) without Noise-Aware Training, halts HP-INV after a single 3-bit LP-INV step without bit-sliced iterative refinement, and runs unanchored synthetic recursion, verifying that Gate G8 blocks the deployment with exit code 1.

Exercises

1. The Horowitz Bus-to-Compute Ratio: Using Mark Horowitz’s $45\text{ nm}$ CMOS measurements ($0.9\text{ pJ}$ per FP32 add, $3.7\text{ pJ}$ per FP32 multiply, and $640\text{ pJ}$ per 32-bit off-chip DRAM read), calculate the total energy required to compute a single inner product $\mathbf{w}^\top \mathbf{x}$ of length $N = 1\text{,}024$ when weights $\mathbf{w}$ must be fetched from off-chip DRAM versus when they reside in an on-chip AIMC crossbar array consuming $0.5\text{ pJ}$ per cell current summation.
2. RLC $\leftrightarrow$ Mass-Spring Resonance: Given a mechanical oscillator with mass $m = 2.0\text{ kg}$, damping $c = 0.8\text{ N}\cdot\text{s/m}$, and spring stiffness $k = 8.08\text{ N/m}$, specify the exact inductance $L$, resistance $R$, and capacitance $C$ of the isomorphic analog circuit, and compute its damped natural frequency $\omega_d$.
3. Why ReLU Fails the Helmholtz Wave Equation: Prove by direct differentiation twice with respect to $x$ why any 1-hidden-layer network $f(x) = \sum_{k=1}^{W} v_k \max(0, w_k x + b_k)$ yields $f’‘(x) = 0$ for all $x \neq -b_k / w_k$, whereas a SIREN layer $\Phi(x) = \sum_{k=1}^{W} A_k \sin(\omega_k x + \phi_k)$ satisfies $\Phi’’(x) = -\sum_{k=1}^{W} A_k \omega_k^2 \sin(\omega_k x + \phi_k)$.

Summary

• The von Neumann & Synthetic Walls (Axis 1): Off-chip DRAM reads consume $711\times$ more energy than FP32 additions ($640\text{ pJ}$ vs. $0.9\text{ pJ}$), while recursive training on ungrounded synthetic data collapses distribution variance ($\sigma_G^2 / \sigma_0^2 \to 0$) unless anchored by neurosymbolic constraints and physical observations.
• Native Differential Equations (Axis 2): Analog RLC circuits ($L\ddot{q} + R\dot{q} + \frac{1}{C}q = V(t)$) are physically isomorphic to mechanical mass-spring systems ($m\ddot{x} + c\dot{x} + kx = F(t)$) and inspire continuous-time Liquid / Neural ODEs.
• AIMC, NAT, and PKU 24-Bit HP-INV (Axis 3): Analog crossbars compute matrix-vector products in $\mathcal{O}(1)$ via Ohm’s and Kirchhoff’s laws; Noise-Aware Training (NAT) and Peking University’s 40nm RRAM HP-INV (LP-INV + bit-sliced HP-MVM) overcome the Analog Wall to reach 24-bit (FP32) precision ($8.70 \times 10^{-12}$ error in $7$ iterations) at $100\times$ lower power.
• Wave-Interference Learning (Axis 4): Encoding phase ($\phi$) and amplitude ($A$) via SIREN ($\sin(\omega_0 W x + b)$) and Stanford’s Wave-Physics Analog RNN compresses signals $40\times$, preserves exact second-order Helmholtz derivatives, and routes wave energy at up to $74.8\text{ PetaOPS/W}$ (ACCEL).
• The 20-Watt Brain Funnel & Hybrid Future (Axis 5): Biological sensory processing compresses $1.6\text{ Gb/s}$ retinal input to $10\text{ bit/s}$ conscious decisions ($1.6 \times 10^8 : 1$) while preserving actionable mutual information under the Data Processing Inequality, pointing toward hybrid analog-digital, physically conscious architectures.