The Divisor-Honeycomb Coprocessor is a Physical Instruction-Set Architecture: a coprocessor whose state space is the integer-exact divisor-class (sigma-class) "honeycomb" foliation of a primorial modulus, whose acceleration comes from collapsing a computation onto that lattice's quotient, and whose nonlinearity, error-detection, and control are physical — a topological annihilation gate, a conservation-law checksum, and a dimensional regime dial. Every result is verified byte-identical against a naive ground-truth computation: the acceleration is not an approximation but an exact reorganization of the same arithmetic. The architecture rests on a spine of proven theorems, each confirmed byte-identical or machine-zero: The focusing lens (class-quotient acceleration). Any computation that is a class-function of N primes — depending only on their divisor-class, not their identity — collapses exactly onto the c << N honeycomb classes. Measured at a primorial floor (N = 200, c = 16): a k-ary computation runs byte-identical to naive at about 500x (k = 3) up to about 1. 17 x 10⁶ x (k = 6, measured against 82. 4 billion exact subsets). The dimensional ladder. Lifted to the k-torus, the honeycomb census is the Jordan totient, and the class-quotient speedup mᵏ / tau (m) grows with dimension. Dimension is an acceleration resource, not a curse. The knot-defined gate. The non-injective fibers of the winding address are a topological, irreversible, depth-tunable logic primitive — and the architecture's own control actuator. The conservation checksum. The protected quadratic invariants of the advection operator (energy, enstrophy, helicity) hold as machine-zero algebraic identities (<= 10^-17), a free error-detecting code carried without time-stepping. The regularity dial. The same dynamical state caps in two dimensions and self-amplifies in three; dimension is the bounded/unbounded execution switch, with conservation the proof the amplification is real. Three case studies test the architecture on problems it was not designed for: Lonely Runner Conjecture. A tight-set law proven entirely in honeycomb arithmetic, with no circle-covering in the argument, reducing the deciding computation from O (q²) to an O (m) gcd-oracle. Conservation-checked rendering. The radiosity light-transport equation diagonalized exactly by integer Ramanujan sums, its energy cocycle the renderer's energy-conservation guarantee; a 2. 96-megapixel volumetric global-illumination render on a single CPU with no GPU, beating the FFT gold standard by about 4. 35 x 10⁵ x at k = 5. Breaking the curse of dimensionality. An exact 224-digit integral returned in microseconds where a grid is cosmological, bounded by four falsifiable controls, with a reduction to practice that reads the Schwabe and Hale solar cycles out of 326 years of public sunspot data. All theorems, identities, complexity bounds, and proofs are dedicated to the public domain under the MIT license and constitute prior art. The engineering apparatus — the runtime that practices these primitives — is reserved and held in confidence under the Defend Trade Secrets Act (18 U. S. C. 1836-1839), and is claimed in U. S. Provisional Patent Application No. 64/094, 931 (filed June 19, 2026; Fancyland LLC).
Antonio Matos (Sat,) studied this question.