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.

Falsify it on lab.dydact.io Known failure modes

research tracks

Continuous-Superposition CSP

Closed-world constraint satisfaction (Sudoku, k-coloring, exact cover, scheduling, propositional SAT) solved by orthogonal projection on a Cl(6) eigenstate basis — not WalkSAT, not annealing, not search.

Sudoku 100% extreme @ 30.6 ms / puzzle (vs Kona 96.2% @ 313 ms / 36.5M params)
Zero training, zero parameters, deterministic

Geometric Chemistry (Cl(3,0))

SMILES → Cl(3,0) multivector via G0(Z_total) + G1(positions) + G2(bonds as wedges) + G3(stereo). Rotation-invariant 4D fingerprint crosses conformer & framework boundaries.

MW Pearson 0.998 (exact via G0)
logP zero-shot Pearson 0.581 (within ChemBERTa zero-shot band, no training)
Structural similarity vs Morgan/Tanimoto Spearman 0.492 — competitive with 77M-param ChemBERTa
1 ms median encoding latency

Circuit Equivalence

Observable-perturbation discipline on ISCAS'85 — gate-level perturbations pre-screened for downstream observability via brute-force random sampling, then verified via substrate equivalence.

ISCAS'85 100% Track A + Track B (11/11 each, observability-screened)
Includes c6288 32-bit multiplier

Substrate Geometry

Cl(6)/Cl(8) algebra, S^63 manifold, Banach contraction with certainty gates, Thoth margin (63/64), Hawking residual hierarchy. The math behind dydact's cognition.

Decomposed components: IS / COVERAGE / PURPOSE / LOGIC / INVERSION / INFLATION
Triadic FU (KNOW / DO / WITNESS) governs all parameters — no hardcoded constants
Bidirectional persistence: forward-self + backward-self via λ=0.999 operator

What we cannot do.

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)

Full failure dashboard

Citing this work

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 via Cl(6) Topological Relaxation},
  year   = {2026},
  url    = {https://orthogonalabs.dydact.io}
}

Universal-substrate reasoning.The mathematical receipts.

Universal-substrate reasoning.
The mathematical receipts.