Earthform Research Lab
We build algebraic AI that learns, teaches, and proves what it knows. Research in non-associative algebra, spectral proteins, and Fano-structured protocols — becoming systems that educate.
90+ experiments. A trained model. Research that teaches.
Research
Non-associative algebra, spectral proteins, music, error correction
90+ experiments across four interconnected threads. The Fano plane PG(2,2) and its 168 automorphisms, applied to real domains.
Learn
Verifiable education. Games. Real knowledge. $1/day → $1/month.
AI tutoring powered by our Fano-7 architecture. Crystallized intelligence means costs go down as the system gets better.
Build
Distributed compute. Contribute cycles, get routing done.
The beacon network connects spare compute into a shared resource. Contribute → earn credits → learn for less.
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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