# Know Math

> All computation is mathematical. Uncertainty is quantified. Optimization has structure. Proof has rules. Numbers don't lie but models can.

- Skill: `ariffazil/know-math` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add ariffazil/know-math`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ariffazil/know-math/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: ariffazil (https://skillmd.com/u/ariffazil)
- Updated: 2026-09-10
- Page: https://skillmd.com/skills/ariffazil/know-math

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# know-math

> **Purpose:** All computation is mathematical. Uncertainty is quantified. Optimization has structure. Proof has rules. Numbers don't lie but models can.

## Axis 1: Invariants

- **authority**: mathematical proof is self-verifying (tautology)
- **evidence_schema**: quantified claims require confidence intervals + sample size
- **reversibility**: True
- **lineage**: proofs trace to axioms; statistics trace to data
- **trigger_semantics**: quantification OR optimization OR uncertainty OR proof_needed
- **failure_contract**: report confidence band, never point estimates without CI
- **resource_budget**: {'cpu': 'high', 'time_ms': 60000, 'entropy': 'measurable'}
- **audit_surface**: ['methods_used', 'confidence_intervals', 'convergence_status']

## Axis 2: Bridge Connections

- **kernel_verbs**: ['arif_verify']
- **skills**: ['verify-gate', 'memory-manage', 'observe-ground']
- **domains**: ['wealth-*', 'geo-*', 'meta-evals']
- **protocol**: knowledge_substrate
- **inputs**: {'problem': 'string', 'data': 'list[number]', 'method': 'string'}
- **outputs**: {'result': 'number', 'confidence': 'float', 'method': 'string', 'assumptions': 'list[string]'}

## Axis 3: Contrast

- **Not**: wealth-reason, meta-plan
- **Distinction**: UNIVERSAL mathematical reasoning. wealth-reason is DOMAIN capital math. meta-plan is WORKFLOW DAGs. This is the SUBSTRATE they derive from.
- **Trigger conflicts**: fires when any claim requires quantification; domain skills fire only in their domain

## Coverage

- probability_statistics
- linear_algebra
- calculus_optimization
- graph_theory
- information_theory
- logic_proof
- numerical_methods

## Domain Bridges

- **wealth**: NPV, IRR, Monte Carlo, Markowitz, Kelly criterion
- **geo**: geostatistics, kriging, volumetric uncertainty
- **meta**: benchmarking, hypothesis testing, confidence intervals
- **audit**: hash chains, cryptographic proof, chain integrity

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*Forged: 2026-07-11 under F13 SOVEREIGN.*
*DITEMPA BUKAN DIBERI*