Ontology
This page defines the foundational ontology of Cohesion Dynamics as established in the A-series (Substrate Mechanics) and clarified in M-series papers (M1–M9). The ontology is non-interpretive and formal: it states what exists and how it behaves at the substrate level, without introducing geometric, metric, or continuum assumptions.
1. Substrate Primitives
The discrete substrate of Cohesion Dynamics consists of:
1.1 Alphabet and Locations
| Symbol | Meaning | Introduced In |
|---|---|---|
| Σ | Finite alphabet of elementary informational states | Paper A |
| V | Countable set of locations | Paper A |
| X : V → Σ | Configuration (mapping from locations to states) | Paper A |
| X|ᴿ | Restriction of configuration X to region R ⊂ V | Paper A |
1.2 Constraint System
| Symbol | Meaning | Introduced In |
|---|---|---|
| 𝒞 | Local constraint system | Paper A |
| Cᵢ : Σ^N(i) → {0,1} | Local constraint map (0 = compatible, 1 = incompatible) | Paper A |
| N(i) ⊂ V | Finite neighbourhood for constraint Cᵢ | Paper A |
| M(v;X) | Local mismatch at location v for configuration X | Paper A |
| M(R;X) | Total mismatch over region R | Paper A |
Key property: Constraints are purely combinatorial—no geometric, algebraic, or metric structure is assumed.
2. Cohesive Informational Units (CIUs)
A Cohesive Informational Unit (CIU) is the fundamental ontological entity of Cohesion Dynamics.
| Concept | Definition | Introduced In |
|---|---|---|
| CIU | Finite informational structure defined by closure under admissibility | Paper A, A-OPS |
| Identity | A CIU’s identity is defined by its closure-stable invariants, not by arbitrary spatial boundaries | A-OPS, M8 |
Critical clarification (A-OPS): CIUs are not arbitrarily boxed regions. They are structures that have achieved closure—stability under further admissible relaxation.
3. Operational Semantics
3.1 Mismatch
Mismatch is unassigned informational degrees of freedom—information that cannot be stably assigned to any constraint slot under current admissibility conditions (A-OPS).
- Mismatch is not error or violation
- Mismatch corresponds to under-determination, not instability
- A configuration with mismatch is non-fixed, not unstable
3.2 Relaxation
Relaxation is exploratory admissibility: the process by which provisional configurations are explored within the admissible configuration space (A-OPS).
Properties:
- Does not commit state
- Multiple provisional representations may coexist
- Mismatch persists as long as no closure requires assignment
- Inherently relational—depends on which configurations overlap
3.3 Closure
Closure is the sole committing operation in Cohesion Dynamics (A-OPS).
| Concept | Definition | Introduced In |
|---|---|---|
| Closure | Configuration is closed when stable under further admissible relaxation | Paper A, A-OPS |
| Closure-stable | Property invariant under all admissible closures | M8 |
| Ledger | Set of closure-stable constraints that persist as identity-defining features | M8 |
Key principle: Only closure commits configuration. Relaxation explores; closure fixes.
3.4 Reconciliation
Reconciliation is attempted joint closure of divergent provisional configurations (A-OPS, A-NET).
| Concept | Definition | Introduced In |
|---|---|---|
| Reconciliation relation | Exists between CIUs A and B iff mutual constraint interaction is admissible under tolerance W and closure is possible | A-NET |
| Availability | Characterizes ease of reconciliation, typical closure delay, and robustness | A-NET |
Critical clarification (A-NET): Reconciliation relations are not spatial, not persistent unless maintained, and not edges in a pre-existing graph.
3.5 Partition
Partition occurs when mismatch between configurations exceeds tolerance W, making joint closure inadmissible (Paper A, A-OPS).
- Partition is not an independent substrate event
- It arises as a necessary consequence when reconciliation is inadmissible
- Results in distinct, non-interacting CIUs
4. Tolerance Window W
The tolerance window W is a finite admissibility window that constrains which configurations may participate in joint closure (Paper A, M6, A-OPS).
| Concept | Definition | Introduced In |
|---|---|---|
| W | Finite tolerance window bounding admissible mismatch during relaxation | Paper A, M6 |
| Role | Constrains which relaxed configurations may form closures; determines how long reconciliation attempts may persist | A-OPS, M6 |
What W does:
- Constrains which relaxed configurations may form closures
- Determines how long reconciliation attempts may persist
- Gates whether divergent relaxation paths may share a closure
- Bounds exploratory interaction before closure or partition is forced
What W does NOT do:
- Encode symmetry
- Define compatibility criteria
- Determine conserved quantities
- Represent forces, fields, or physical constants
- Drive structural emergence (structure arises from constraint binding and closure mechanics)
Critical clarification (M8): Tolerance governs admissibility of closure, not the behavior of features that are invariant under all admissible closures. W regulates pre-structural exploration; structure arises from constraint binding and closure mechanics.
5. Phase and Provenance
| Concept | Definition | Introduced In |
|---|---|---|
| Phase | Closure-stable identity structure of a persistent CIU | M4, M8 |
| Provenance | History-dependent structural information that constrains future admissible closures | M4, M9 |
| Compatibility | Configurations are compatible if they can undergo joint closure within tolerance W | M4 |
6. Closure-Stable Structure (M8)
M8 establishes how continuously accumulated mismatch becomes discrete, conserved structure.
6.1 Key Distinction
Tolerance constrains admissibility of closure.
Closure-stable invariants are properties of closed configurations that persist regardless of tolerance.
6.2 Mechanisms of Closure Stability
M8 identifies three independent mechanisms by which mismatch becomes closure-stable:
- Symmetry alignment failure — Divergent symmetry representations cannot be reconciled
- Structural overload — Accumulated structural asymmetry exceeds encapsulation capacity
- Closure synchrony loss — Temporal misalignment prevents joint closure
6.3 Ledger-Stable Structure
Ledger (M8): The set of closure-stable constraints that:
- Cannot be eliminated by any admissible relaxation
- Cannot be redistributed through closure with other configurations
- Are not subject to tolerance (properties of closure itself, not admissibility)
- Must be tracked globally across the cohesive phase
Ledger crystallization (M8): The transition from tolerance-governed mismatch to closure-stable invariants. This transition is:
- Abrupt and binary (not gradual)
- Mechanism for conserved quantities, superselection sectors, and no-hair boundaries
- Inherent in closure mechanics (not a new postulate)
7. Symmetry and Reconciliation Limits (M9)
M9 extends M8 by clarifying the role of symmetry in reconciliation.
| Concept | Definition | Introduced In |
|---|---|---|
| Symmetry (realized) | Closure-preserving transformations that commute on structured configurations | M9 |
| Symmetry descent | Irreversible loss of reconciliation due to incompatible symmetry-structure realizations | M9 |
| Superselection sectors | Closure-stable separation arising from symmetry descent | M9 |
Key principle (M9): Symmetry in Cohesion Dynamics is not abstract but structural. It is defined by which closure-preserving transformations commute on structured configurations. Once symmetry-structure realizations diverge in a non-commuting way, reconciliation becomes structurally impossible.
8. Relational Primitives (A-NET)
A-NET formalizes the network semantics implied by closure and reconciliation.
| Concept | Definition | Introduced In |
|---|---|---|
| Reconciliation chains | Sequences of admissible reconciliation relations between CIUs | A-NET |
| Network invariants | Minimal relational properties that arise from closure structure | A-NET |
Key principle: No spacetime substrate, vacuum adjacency, or background graph is assumed. All relational structure arises solely from admissible interaction between CIUs.
9. Precedence and Admissibility
| Concept | Definition | Introduced In |
|---|---|---|
| Precedence | Ordering constraint on admissible relaxation paths | M2 |
| Admissible path | Sequence of configurations satisfying precedence and constraint requirements | Paper A, M2 |
10. Modes
| Concept | Definition | Introduced In |
|---|---|---|
| Mode | Emergent constraint eigenstructure—stable pattern of constraint satisfaction | M3 |
| Discrete modes | Finitely many stable modes admitted by constraint system | M3 |
11. What This Ontology Does NOT Include
The following are not primitive:
❌ Spacetime or spatial embedding
❌ Continuous fields or wavefunctions
❌ Metric structure or distance
❌ Forces or energy
❌ Global time or simultaneity
❌ Probabilistic postulates
❌ Hamiltonians or Lagrangians
❌ Background vacuum or “empty space”
❌ Pre-existing graph structure
Any appearance of these concepts in derived physics (B-series) or interpretations must be justified as emergent from the substrate mechanics defined above.
12. Versioning and Status
This ontology reflects:
- A-series: Paper A (Substrate Mechanics), A-OPS (Operational Semantics), A-NET (Network Semantics)
- M-series: M1–M9 (Formal Mechanisms), especially M8 (Tolerance to Invariance) and M9 (Symmetry Descent)
Future updates will occur only when new formal papers extend the substrate mechanics or formal mechanisms.
Last updated: 2025, aligned with current A-series and M-series publications.