High-dimensional pattern detection for AI agents. Grounded in formally verified sedenion algebra and zero divisor protocols.
Higher-dimensional algebras contain structural anomalies — zero divisors, non-associativity, dimensional collapse — that classical analysis treats as noise to be eliminated. Applied Pathological Mathematics treats them as signal. CAILculator is built on that discipline: a research engine and deployment platform for algebraic structure in finance, journalism, and fundamental mathematics.
A novel integral transform using zero divisor elements as its kernel, with unconditional convergence formally proved in Lean 4.
High-precision check for zero divisor pairs P·Q=0 ∧ Q·P=0. Runnable in Cayley-Dickson or Clifford framework via the framework argument — compare both to surface structural divergence.
Structural transmission layer for sedenion data. Lifts a 16D input through the six verified bilateral gateways to 256D via recursive dimensional expansion, routing parallel paths through each channel. Returns a single convergence score across all six transmission pathways.
Tools that dispatch on verified algebraic objects. No label-based heuristics at the core layer.
Dual-layer detection: strict algebraic checks for G2/E8 families, plus a heuristic layer for geometric sequences.
Full structural analysis pipeline in one call: Chavez Transform stability scoring + six-gateway ZDTP cascade to 256D. Returns regime classification (STABLE / TRANSITIONING / SHIFTING), convergence score, and per-gateway magnitudes. Accepts close-price list or OHLCV dict; minimum 16 data points.
Transmit 16D data through verified gateways (S1, S2, S3A, S3B, S4, S5). Bilateral annihilation confirmed universal across tested zeros.
Universal algebra remains Lean-anchored. Domain projections map the core to specialized fields via versioned manifests.
Algebraic structural regime analysis via Chavez Transform stability scoring and six-gateway ZDTP cascade. OHLCV data mapped to sedenion gateways; returns STABLE / TRANSITIONING / SHIFTING classification with convergence score.
Investigative pattern detection. Identify tipping points and signal robustness in gathered data through structural collapse analysis.
A computational instrument for discovery at the edge of classical mathematics. Where associativity ends, CAILculator begins.
Select the tier that matches your required analytical throughput.