Universal-substrate reasoning.
The mathematical receipts.
One compiler. Constraint satisfaction, chemistry, circuit equivalence, and symbolic math all solved through orthogonal projection on a Clifford-algebra substrate. Zero learned parameters. Zero training. Reproducible by anyone with an API key.
Closed-world constraint satisfaction (Sudoku, k-coloring, exact cover, scheduling, propositional SAT) — not WalkSAT, not annealing, not learned search.
- Sudoku 100% extreme @ 30.6 ms / puzzle (vs Kona 96.2% @ 313 ms / 36.5M params)
- Same compiler scales N = 4 → 25 (any perfect-square grid)
- Zero training, zero parameters, deterministic
SMILES → multivector fingerprint encoding atomic numbers, positions, bond wedges, and stereochemistry on a rotation-invariant geometric basis. Crosses conformer and framework boundaries.
- MW Pearson 0.998 (exact, by construction)
- logP zero-shot Pearson 0.581 (within ChemBERTa zero-shot band, no training)
- Structural similarity vs Morgan/Tanimoto Spearman 0.492 — competitive with 77M-parameter trained baselines
- 1 ms median encoding latency
Observable-perturbation discipline on ISCAS'85 — gate-level perturbations pre-screened for downstream observability via brute-force random sampling, then verified by orthogonal-projection equivalence.
- ISCAS'85 100% Track A + Track B (11/11 each, observability-screened)
- Includes c6288 32-bit multiplier
Universal pattern across domains: relax constraints into a candidate space → iterate propagation to a fixed point → branch on the most-constrained dimension when propagation plateaus. No learned weights. All parameters derived from the input, not declared as constants.
- Self-derived thresholds (mean + k·σ of the corpus's own distribution)
- Fixed-point contraction with certainty gates — refuses to collapse when support is insufficient
- Deterministic given input + seed; reproducibility hash returned with every result
Frontier-lab discipline: every known failure is listed publicly. If it's not on our list, it works. If it doesn't work and isn't on the list, we want to know.
- · Gradient SAT drops to 90% at N=25
- · Zero-shot logP r=0.581 (ChemBERTa-trained outperforms)
- · TSPLIB 11.8% above optimal
- · Cuprate within-family Jaccard 0.00 (operator-tier failure)
Every result returned by the lab.dydact.io API includes a BibTeX snippet and a permanent reproducibility hash.
@misc{dolas2026,
author = {Ukpeh, Francis and {DOLAS}},
title = {Universal-Substrate Reasoning: Zero-Parameter Geometric Compilation Across Domains},
year = {2026},
url = {https://orthogonalabs.dydact.io}
}