RiskDataScience

⚽♟️🃏 260 sports & games. One shared rules API. 🚀 Building rulesatlas: an open-source Python + R library for game states, legal transitions & outcomes. Fully extensible w custom rules No simulations. Just rules🤖 pip install rulesatlas #RuleAtlas #OpenSource #Python #RStats #AI

15/15 🌌 P12 | Under a mean-energy budget, uniform hyperbolic volume on a ball minimizes worst-direction infinitesimal Lorentz-boost sensitivity over all probability laws. For E→∞, only 1 spatial dimension reaches zero sensitivity. github.com/rds0001/agentic-m…

14/15 📐 P11 | Preserving order pairwise is not the same as using one shared random monotone map. For Lorentz order in dimension d≥2 on a radius-R ball, the latter has an optimal uniform mean-bias and RMS-error floor R(d−2)/d. github.com/rds0001/agentic-m…

13/15 ⚡ P10 | Near a three-level Gibbs state, the first positive work depends on the number-theoretic properties of the energy spectrum. A fixed positive mean yield, however, always requires Θ(δ⁻²) copies. github.com/rds0001/agentic-m…

12/15 📉 P09 | Globally close models can diverge when their conditional transitions are switched locally. For m positive path models at TV diameter ε, the sharp worst-case gap is Θ(Φ(mε)), where Φ(x)=x(1+ln(1/x)) for 0<x<1. github.com/rds0001/agentic-m…

11/15 🎲 P08 | N exactly pairwise independent Bernoulli variables at fixed bias p need log₂N+O_p(1) bits of joint entropy. With fixed pair-correlation tolerance ε for fair signs, the leading scale drops to (1−ε)log₂log₂N. github.com/rds0001/agentic-m…

10/15 🧮 P07 | Proof resources aren't interchangeable. In a specified conservative calculus, polynomial refutations of unary pigeonhole need Θ(n²) fresh definitions in total, yet O(n) simultaneously live names suffice. github.com/rds0001/agentic-m…

9/15 🔋 P06 | Mean excitation E>1 permits exact correction of any prescribed finite number of phase errors. But at fixed positive dephasing noise, every finite E leaves nonzero error. Reaching error ε costs Θ_p(log(1/ε)) mean excitation. github.com/rds0001/agentic-m…

8/15 ⚛️ P05 | Pure global quantum states can have exact product marginals on all sufficiently small subsystems. With mean excitation E≥2 for every logical input, maximum exact one-erasure code dimension grows as Θ_E(N^(⌊E⌋−1)). github.com/rds0001/agentic-m…

7/15 🧩 P04 | For an N-party classical process, validity under N independent copies is equivalent to validity under every number of copies—and to a compatible fixed global order. Correlated extensions follow a different hierarchy. github.com/rds0001/agentic-m…