Table of Contents — Shunyaya Symbolic Mathematical AI (SSM-AI)

Executive Summary

SECTION 0 — Introduction

SECTION 1 — What SSM-AI Is (Positioning & Promise)

SECTION 2 — SSM-AI Canon (Bounded Numerals → Streaming Fuse)

• 2.1 Two-Lane Numeral and Collapse
• 2.2 Clamp & Rapidity
• 2.3 Order-Invariant Streaming Fuse (U/W mean in u-space)
• 2.4 Lane Mul/Div (M2) and Division Policy

SECTION 3 — Lens → Align → RSI Pipeline

• 3.0 Lens → Align → RSI (Overview)
• 3.1 Contrasts e (Designing Lenses for Different AI Aspects)
• 3.2 Symmetric Maps → Alignment
• 3.3 Chooser — RSI (Bounded Selection Index)
• 3.4 Bands (A++/A+/A0/A-/A–) and Thresholds
• 3.5 Lens Calibration Quickstart
• 3.6 Ready-to-Paste Manifest Snippet

SECTION 4 — Calm Gate and Governance

• 4.1 Telemetry Lanes (Inputs to the Gate)
• 4.2 Gate Formula & Modes
• 4.3 Gate Knobs & Purity
• 4.4 Ready-Made Gate Presets
• 4.5 Two-Minute Gate Calibration
• 4.6 Gate Stamp Fields

SECTION 5 — Step → Path → Plan Scoring Pipeline

• 5.1 Step Scores & Priors in u-Space
• 5.2 Path Pooling & Reporting
• 5.3 Failure Containment & Rollback
• 5.4 Plan-Level Priors & Gates
• 5.5 Developer Hooks

SECTION 6 — Empirical Validation & Mini Benchmarks

• 6.1 Task Suite & Protocol (tiny A/B replay tasks)
• 6.2 Metrics (calculator-fast; no retraining)
• 6.3 Ablations (small knobs, big clarity)
• 6.4 Results (tiny tables; reproduce from stamps)
• 6.5 Reproducibility (five-step replay from stamps)

SECTION 7 — Scalability & Numerical Precision

• 7.1 Long-Path Guidance (agents, streams, shards)
• 7.2 Dtype & Epsilon (defaults and guards)
• 7.3 Stability Near Edges (a → ±1)
• 7.4 Software–Hardware Parity (fixed-point notes)
• 7.5 Performance (O(N) time / O(1) memory)
• 7.6 Robustness (quick checks and acceptance)
• 7.7 Troubleshooting (symptoms → fixes)

SECTION 8 — Integration Quickstarts

• 8.1 LLM Decoding Hooks (bounded chooser in logit space)
• 8.2 RAG Pipeline Hook (bounded doc ranking)
• 8.3 Agents/Tools Middleware (bounded steps & rollback)
• 8.4 CI / Golden Tests (parity & invariance verification)

Appendix A — Calm Gate & Bands (A1–A7)

Appendix B — Symbolic Search Lens (B1–B10)

Appendix C — Stamp & Ledger Schema (C1–C7)

Appendix D — Starter SDK & Reference (D1–D6)

Appendix E — Vendor Bake-off Protocol (E1–E9)

Appendix F — SSM-Audit CFO Pack (F1–F9)

Appendix G — SSMH Acceleration Parity

(Hardware lane: deterministic parity, stamp-ready)

Appendix H — Comparisons & Synergies

(How confidence methods become lenses into the lane)

Appendix I — Lens Builder

(Derive Unit, c, and weights from logs)

Appendix J — SDK Packaging & Golden Tests

(PyPI-ready structure, reproducibility, quickstart)

Appendix K — SSM-Search

(Lane-native ranking with classical retrieval preserved)

Appendix L — Governance Quick Reference

(Manifests-as-contract, privacy, auditability)

Appendix M — Interop & Wire Protocol

(JSON/CSV lane mapping, versioning, replay)

• M1 Data model (lane JSON schema)
• M2 CSV schema (headers, units, and reproducibility)
• M3 Wire serialization (key order and precision)
• M4 Replay and audit workflow
• M5 Schema versioning and validation
• M6 Integration examples (decode, tool, evaluation)
• M7 Error recovery and reconciliation
• M8 Hash stamping and consistency
• M9 Wire replay pseudocode
• M10 Acceptance checklist

Appendix N — CFO Pack & Procurement Snap-Line

(Structured lane for value, audit, and financial reproducibility)

• N1 Purpose and scope
• N2 Symbolic view of cost, savings, and risk
• N3 Procurement alignment and vendor manifesting
• N4 CFO gate (value vs. variance control)
• N5 Ledger stamping and verification
• N6 Manifest alignment for procurement
• N7 ROI reconstruction using (U,W) lanes
• N8 Reporting schema (ASCII + JSON parity)
• N9 Governance hooks for finance

Appendix O — Glossary

(Compact reference of all bounded terms and invariants)

• O1 Core invariants (phi((m,a)) = m, boundedness)
• O2 Key functions (tanh/atanh, clamp, fuse)
• O3 Manifest and hash terminology
• O4 Alignment lane variables and roles
• O5 RSI, RSI_env, and gating mechanics
• O6 Band thresholds and hysteresis
• O7 Ledger, stamp, and manifest vocabulary
• O8 Interop definitions
• O9 Cross-domain symbolic terms

Appendix P — FAQ & Troubleshooting

(Field questions, diagnostics, and validation recipes)

• P1 Quick FAQ (top 10)
• P2 Troubleshooting (symptom → fix)
• P3 Minimal acceptance battery
• P4 Quick numeric recipes
• P5 Priors, bias, and gate discipline
• P6 Priors & bias control (tiny, transparent)
• P7 Performance & scaling (mixed precision, streaming)
• P8 Common misconceptions
• P9 End-to-end worked mini example
• P10 One-minute acceptance checklist

Appendix Q — Release Notes & Manifest Map

(Versioning, hashing, and deterministic reproducibility)

• Q1 Manifest map (top-level keys & meaning)
• Q2 Versioning & compatibility
• Q3 Release notes (current cycle)
• Q4 Migration checklist
• Q5 Canonicalization & hashing
• Q6 Deprecations & reserved fields
• Q7 Interop tests
• Q8 Zero-risk patches
• Q9 Example manifest & diff
• Q10 Repro checklist

Appendix R — Domain Adapters

(Universal integration layer for any scientific or business vertical)

• R1 Domain adapter contract (universal template)
• R2 Example domain — SSM-Chem (reaction stability)
• R3 Worked minis (calculator-fast reproducibility)
• R4 Minimal manifest stub
• R5 API sketch (drop-in reference)
• R6 Wire envelope (JSON serialization)
• R7 Governance hooks (determinism & privacy)
• R8 Acceptance checklist
• R9 Stamp example & one-line takeaway

Explore Further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-AI

Disclaimer
Research/observation only. Not for operational, safety-critical, or legal decision-making. Numbers remain identical by construction: phi((m,a)) = m. Lanes are bounded in (-1,+1) and composed with order-invariant rules as declared.