Rational Certificate Complexity (RCC Trilogy)
A three-essay research program that treats every convergent sequence as a rational certificate engine, measures its bit-length against the demanded tolerance ε, and stratifies mathematical constants into cost classes. RCC establishes the vocabulary, PI_RCC stress-tests the boundary with a cubic-convergent non-hypergeometric iteration for π, and NAM builds the executable substrate: a generator-based numerics library where every number is a forkable, deterministic nano-VM emitting an infinite digit stream.
Key Research Findings
Cost classes RC₁/RC₂/RC₃ stratify constants by certificate bit-length versus tolerance ε
A regularity condition plus a Θ(log 1/ε) lower bound separate algebraic irrationals from π and e
The x + sin(x) iteration for π falls outside RCC's classified hypergeometric class yet still attains optimal RC₁ cost — the classification boundary is permeable
Cost classes reappear operationally as generator state-dimension tiers in a two-tier ABI, with base-as-codec and BBP-as-resonance
Equality is honestly tri-state: unprovable digits render as 'pending (null)' rather than a comfortable lie
Technical Details & Impact
Technologies Used
Research Status
Last updated: 2025
Research Impact
Provides a cost-theoretic vocabulary for the difficulty of computing real numbers, together with a running reference implementation (the nam interactive calculator) that makes those cost classes observable rather than merely asserted
This research is part of ongoing open-source development. Contributions, discussions, and collaborations are welcome.