A-Series: Substrate Mechanics
The A-series provides the formal mathematical specification of the discrete substrate consistent with earlier conceptual and empirical constraints.
These papers define the substrate purely combinatorially. No geometry, metric, or continuum concepts appear at this level.
What the A-Series Establishes
The A-series formalizes:
- Finite alphabet Σ and discrete locations V
- Local constraint system 𝒞 defining admissibility
- Mismatch measure M(v;X) for configurations
- Commit semantics: how configurations may diverge through admissible alternatives
- Operational semantics of mismatch, closure, and tolerance
- Relational closure and network semantics
This is the foundational layer on which all other series (M, B, G) build.
Papers
A — Formal Substrate Mechanics
Core substrate primitives and mechanics
Formalizes the discrete substrate assumed in the Cohesion Dynamics framework. Refines and operationalizes the conceptual primitives introduced in Paper F: Conceptual Foundations.
Defines alphabet, locations, configurations, local constraint systems, mismatch measures, and the basic operations that govern substrate evolution.
Key concepts: Alphabet Σ, locations V, constraints 𝒞, mismatch M, relaxation, closure, tolerance W, partition
Status: v0.8
A-OPS — Operational Semantics of Mismatch, Closure, and Tolerance
Clarifies substrate-level behavior
Provides precise operational semantics for how mismatch, closure operations, and tolerance windows function at the substrate level. Essential for understanding how the substrate actually behaves in practice.
Status: Published
A-NET — Relational Closure and Network Semantics
Network semantics and relational primitives
Establishes the network semantics and relational primitives that govern how substrate elements interact. Shows how relational closure emerges from the constraint structure.
Status: Published
Who Should Read This Series?
This series is for you if:
- You want the precise mathematical foundations of Cohesion Dynamics
- You need to understand substrate mechanics to evaluate B-series or G-series derivations
- You are comfortable with formal mathematical definitions
- You want to verify claims about what is assumed vs. derived
This series is not:
- A conceptual introduction (see F-series for that)
- An interpretation or application (see B-series and G-series)
- Concerned with effective physics (that comes in later series)
Additional Resources
For context on how the A-series fits into the broader research programme, see the Research Programme page.
To understand what builds on substrate mechanics, see the M-Series, B-Series, and G-Series pages.