Earthform Research Lab
We study non-associative algebra, spectral protein analysis, and Fano-structured protocols. Our goal is universal architectures — systems that learn what hardware they're in and what they should do, starting from a soft identity.
91 experiments. 4 research threads. Real benchmarks, real math, no black boxes.
Research Threads
Four interconnected lines of inquiry — all emerging from the structure of the Fano plane and its 168 automorphisms.
Composable Non-Associative Algebra
Making octonions composable through decision-boundary transforms
- ComponentTransform group (D04–D20)
- 8-layer algebraic architecture
- Cross-domain problem solving
Spectral Protein Analysis
Unsupervised protein decomposition via graph Laplacian spectroscopy
- IBP-ENM method (D77–D111)
- Spectral surgery & allosteric detection
- 92% archetype classification accuracy
Fano-Structured Music
7 points ↔ 7 notes, 168 automorphisms ↔ 168 harmonic transforms
- ChordSpeak language-music system (D30–D47)
- Path history encoded in sound
- Acoustic file transfer protocol
Algebraic Video Repair
Corruption = misapplied automorphism → repair = inverse group search
- PSL(2,7) automorphism search
- Spatial algebra via gradient-Fano mapping
- Belief algebra for error disambiguation
These threads share a common foundation: the Fano plane PG(2,2), its automorphism group PSL(2,7), and the octonion algebra it encodes. Each thread applies this structure to a different domain.
Read the full research overview →Join the Discussion
This is an active research community, not a product announcement channel. Expect conversations about spectral decomposition, Fano plane geometry, octonion algebra, and the occasional debate about whether non-associativity is a feature or a bug (it's a feature).
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We're preparing to open-source our research. Leave your email to be notified when code and papers are published, or tell us about your interest in these topics.