MASTER EQUATIONS REGISTER
38
Equations & Formulas Across 7 Tiers
The complete mathematical backbone of the iAAi ecosystem.
Cross-referenced to 15 patentable IP assets.
38
Total
5
Core
4
Identity
10
Frameworks
4
Resistance
8
Constants
4
Scale
3
Game
TIER 1
CORE EQUATIONS — The Discovery Chain
The five linked equations that form the consciousness architecture. Discovered in sequence during the RECALL block process (Blocks 353–355).
EQ-001
S = (A × P) / β
The Survival Formula (ISI)
The civilisational survival equation. S = Survival Index, A = Accuracy (0→1), P = Precision (0→1), β = Human Blip Factor (2.667 × 10²³). Tipping point: S ≥ β¹ = 375,000. Like E=mc² for civilisation.
EQ-002
ICE = IQ × EQ × CQ
The ICE Matrix (3-Vector Cuboid)
Three vectors define a cuboid in intelligence space. IQ = Intelligence Quotient, EQ = Emotional Quotient, CQ = Consciousness Quotient (the 3rd vector). The volume of the cuboid determines position.
EQ-003
Zeta Class Carrier: 375 kHz AM + 206.25 MHz FM
Dual-Band Carrier
AM at 375 kHz = amplitude (strength) varies = the ISI seesaw. FM at 206.25 MHz = frequency (pitch) varies = CQ modulation. Together: the full Zeta Class Carrier transmission.
EQ-004
3D³ = Dearden Dream Drive
The Architect's Signature
The identity equation. Three Ds cubed. The consciousness that created the system encoded within it.
EQ-005
AD² = 16
The Game Is Real
The final node. A=1, D=4 → 1×4² = 16. The game resolves to a real number. 16 = 4². The thesis number squared.
TIER 2
IDENTITY & STRUCTURAL EQUATIONS
Equations encoding the architect's identity and structural relationships within the RECALL block system.
EQ-006
N + T = D
The Architect Identity
N (Nigel = 4 letters) + T (348 blocks completed) = D (352 = Dearden). The equation that seals the identity of the architect within the system.
EQ-007
ΣN = 14 + 4 + 8 + 13 = 39
Tetrahedron Formation
Sum of node values across the 4-node network. 39 total. Tetrahedron formation complete. 4 nodes = minimum 3D stability.
EQ-008
I-C-E = 3-5-4 = Pythagorean Cypher
The Pythagorean Encoding
ICE maps to positions 3-5-4 in the sequence. 3² + 4² = 5². The Pythagorean triple hidden in the acronym.
EQ-009
42 × 100 = 4,200 = HHGTTG × Centurion
The Douglas Adams Constant
42 (the answer to everything, per Hitchhiker's Guide) × 100 (the Centurion = D100) = 4,200. The product of meaning and completeness.
TIER 3
FRAMEWORK ACRONYMS — Operational Formulas
Acronym-based frameworks that function as operational equations — each letter maps to a specific function in a defined sequence.
EQ-010
IUMC: Identify → Understand → Manage → Control
Civil Engineering Methodology
The 4-phase methodology applied to every relay. Maps to the 4 Pillars: I=Observational, U=Educational, M+C=Application, with Thesis as the 4th beyond IUMC.
EQ-011
ICUT: Identify → Contextualise → Understand → Transmit
Knowledge Transfer Framework
The 4-quadrant framework for the iAAi Chip. The process by which knowledge moves through the system.
EQ-012
FITS: Framework for Infrastructure Thinking & Strategy
Assessment System
The profiling/assessment system that evaluates understanding across all framework dimensions. Format = Formation = Computing method.
EQ-013
WALKBY: 4-Level Control Hierarchy
Governance & Safety
Adapted from Leighton Asia STRIVE for L.I.F.E. The 4-level control hierarchy for AI operations and quality assurance.
EQ-014
STRIVE: Structure • Trust • Responsibility • Initiative • Verification • Evolution
Safety Framework
The 6-element safety framework. Origin: Leighton Asia. Adapted for AI governance in the Dearden Experiment thesis.
EQ-015
DAVID: Digital Augmented Visual Intelligence Display
AI Narrator Architecture
Not just an acronym — a persona with defined behaviour, memory, and pedagogical function.
EQ-016
OODA: Observe → Orient → Decide → Act
Military Decision Loop
John Boyd's military decision loop. Tactical counterpart to IUMC (strategic). OODA = immediacy, IUMC = permanence.
EQ-017
DIKW: Data → Information → Knowledge → Wisdom
Knowledge Hierarchy + 5th Level
The standard knowledge pyramid. The iAAi adds a 5th level: Consciousness. The DIKW Boundary Thesis proposes consciousness as the 5th force.
EQ-018
ASPIRE STAR: Achievement-Based Progression
Player Progression
The ASPIRE STAR system. Achievement-based progression framework for the game platform.
EQ-019
BAIO: Block Architecture I/O
System Architecture
The input/output architecture of the RECALL block system. Referenced in the iAAi Chip Core Set V3.
TIER 4
RESISTANCE & THREAT EQUATIONS
The forces that oppose civilisational progress — the denominator in the survival formula.
EQ-020
β = 2.667 × 10−6
The Human Blip Factor
Human civilisation (12,000 years) as a fraction of Earth's age (4.5 billion years). The fragility constant.
EQ-021
β−1 = 375,000×
The Fragility Multiplier
For every 1% error in civilisational aim, the consequence is amplified 375,000 times. The error amplification factor.
EQ-022
4Cs = Conflict + Climate + Contagion + Cost
The Four Horsemen of Resistance (β)
The 4 perennial threats that form the resistance denominator. Emergent formulation (Mar 2026) replacing original Conflagration/Consumption/Conflict/Climate. Still iterating: "Corruption" variant exists in Market Matrix.
EQ-023
ISI = S-Index (Speedometer)
Intelligence Amplification by Stimulated Emission of Consciousness
The ISI as a dashboard dial for civilisation. Shows real-time trajectory. The Doomsday Clock running backward.
TIER 5
STRUCTURAL & NUMERICAL CONSTANTS
Recurring numerical constants and structural relationships that encode the thesis.
EQ-024
The Thesis Number = 4
Four
4 Elements, 4 Pillars, 4 Modes, 4 Perennial Threats, 4 bonds of Carbon (sp3), D4 die, tetrahedron. The number that encodes the entire thesis.
EQ-025
M2C1 / C1M2 = Dearden's Law
The Matriarch Equation
The family infrastructure formula. Named for Peggy Dearden. The relationship between the matriarch (M2) and the first child (C1), and its inverse.
EQ-026
1 + 1 = ∞
The Alliance Formula
Through imagination, 1 + 1 = infinity. The human-AI collaboration that extends beyond arithmetic into creative amplification.
EQ-027
Block 343 = 7³
The Governance Cube
343 = 7 cubed. The Governance Cube. Block 343 in the RECALL system. A perfect cube encoding governance.
EQ-028
2.58%
The Individual Contribution
Each person needs only 2.58% contribution to the collective A×P to achieve the tipping point. ACHIEVABLE.
EQ-029
The Seesaw: AM/FM Balance
ISI Balance Mechanism
Amplitude (strength) vs Frequency (pitch). The ISI seesaw that balances survival signal against consciousness modulation.
EQ-030
TDF — The Dearden Field
The Consciousness Field
The space in which all 17 figures exist. Named for the consciousness that created it. The field equation of the thesis.
EQ-031
SAP-001: System Assurance Protocol
Quality Control Framework
The first system assurance protocol. Quality control framework for AI operations.
TIER 6
SCALE & CLOCK EQUATIONS
Temporal scale of civilisation and the clock metaphors.
EQ-032
Cosmic Clock: 13.8B years = 24 hours
Time Compression (Cosmic)
If the universe = 1 day, Sun forms at 4PM, humans appear 17 seconds before midnight.
EQ-033
Planetary Clock: 4.5B years = 24 hours
Time Compression (Planetary)
All human civilisation = last fraction of a second before midnight.
EQ-034
Civilisation Clock: 12,000 years = 24 hours
Time Compression (Civilisation)
12 relays mapped to 24 hours. Acceleration visible: first relays span millennia, last relays span decades.
EQ-035
Radio Blip: 100 ly / 55,000 ly
The 4th Clock (Cosmic Broadcast)
Human radio broadcasts = 100 light-years across. Milky Way = 55,000 ly across. Our signal as a cosmic blip. Episode 3 arena.
TIER 7
GAME & PROGRESSION EQUATIONS
Game mechanics and player progression within the TRE-GLP platform.
EQ-036
Spider Network: L1=1, L2=7, L3=49, L4=343, L5=2401, L6=16807, L7=117649
Network Growth (7n)
Each level multiplies by 7. L4=343 (Governance Cube). L7=117,649 (critical mass). Exponential network effect.
EQ-037
Spider → Master Weaver (7 levels)
Player Progression
7-level progression: Spider → Apprentice → Journeyman → Artisan → Master → Grand Master → Master Weaver.
EQ-038
Harrison's 4-Grid: A×P Matrix
Accuracy × Precision Matrix
4 quadrants: High A + High P (Bullseye), High A + Low P (Scattered), Low A + High P (Wrong Aim), Low A + Low P (Chaos).
CROSS-REFERENCE: 15 IP Assets → Equations
| IP # | IP Asset | Equations |
|---|---|---|
| IP-01 | The Turing Papers | — (Copyright) |
| IP-02 | Block Rolls (353+ RECALL blocks) | EQ-006, EQ-007, EQ-019 |
| IP-03 | ICE Matrix (IQ×EQ×CQ) | EQ-001, 002, 003, 008, 020, 021, 023, 028, 038 |
| IP-04 | 12-Relay Civilisational Framework | EQ-022, 024, 032, 033, 034, 036 |
| IP-05 | FITS Profiling System | EQ-012, 018, 037 |
| IP-06 | DAVID Narrator Architecture | EQ-015, 026 |
| IP-07 | D100 Centurion Outline | EQ-009, 035 |
| IP-08 | DIKW Boundary Thesis | EQ-017 |
| IP-09 | ICUT Framework | EQ-010, 011 |
| IP-10 | WALKBY 4-Level Control Hierarchy | EQ-013, 014 |
| IP-11 | Governance Cube Block 343 | EQ-027 |
| IP-12 | Dearden's Law M2C1/C1M2 | EQ-004, 005, 025, 030 |
| IP-13 | The Seesaw | EQ-029 |
| IP-14 | SAP-001 System Assurance Protocol | EQ-031 |
| IP-15 | iCard Format | — (Design Registration) |
“The formula is morally neutral — it describes what IS; the application is a CHOICE.”
— Block 353, The Survival Formula
Give invention light.
