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Cohesion Dynamics (CD)

R-DCC — Derived Capability Classes

Purpose

This document introduces Derived Capability Classes (DCCs) — named bundles of substrate axioms and capabilities that are frequently assumed together in research papers.

R-DCC is a non-normative reference document; it introduces no new axioms, mechanisms, or theoretical claims.

The goal of DCCs is to:

  • Eliminate repeated axiom enumeration in B-series and other papers
  • Make capability assumptions explicit, named, and reviewable
  • Preserve axiomatic traceability without polluting representational derivations
  • Strengthen programme coherence and scalability

DCCs are semantic conveniences for grouping axioms that naturally co-occur. They do not replace granular axiom references where those axioms play an active operational role in a derivation.

What is a Derived Capability Class?

A Derived Capability Class (DCC) is a named collection of axioms that together define a substrate capability envelope.

Structure of a DCC:

  • Name: A short identifier (e.g., DCC-QM)
  • Capability description: What substrate behaviors this class supports
  • Axiom bundle: The complete list of axioms entailed by this class
  • R-CCC mapping: Which capability class from R-CCC this corresponds to
  • Usage guidance: When to reference this DCC vs. explicit axioms

What DCCs are:

  • Named capability bundles for convenience
  • Synthesis of existing axioms
  • Reference material for consistent capability assumptions

What DCCs are NOT:

  • New axioms or primitives
  • Normative requirements (always non-normative)
  • Replacements for explicit axiom references in derivations
  • Mechanisms or theoretical claims

Relationship to R-CCC

DCCs operate at the axiom-bundle level, while R-CCC (Continuum Capability Classification) operates at the phenomenological capability level.

Correspondence:

  • R-CCC classes (C0–C6) describe what continua can stably support based on empirical and formal results
  • DCCs bundle the axioms required to support those capabilities
  • Each DCC typically maps to one or more R-CCC classes

DCCs make the axiomatic foundation of R-CCC classes explicit and referenceable.

DCC-QM — Quantum-Capable Substrate

Full name: Quantum-Capable Substrate
R-CCC correspondence: Class C6 (Quantum-Emergent Continua)

Capability Description

DCC-QM describes the minimal substrate capability envelope required to support quantum-mechanical structure, including:

  • Interference: Preserved route identity and phase-dependent recombination
  • Non-factorisable joint admissibility: Composite configurations evaluated jointly, preventing subsystem separability (substrate origin of entanglement)
  • Stable discrete spectra: Mode families with invariant basins under precedence dynamics
  • Commit-based resolution: Deterministic branching pre-commit with deterministic resolution at commit
  • Finite tolerance-bounded coherence: Coherence boundaries governed by tolerance parameter WW

Required Axioms

A quantum-capable substrate satisfies all relational axioms and all capability axioms:

Relational Axioms (R-axioms):

  • AX-REL — Relational Evolution: States evolve via relations to other states
  • AX-CON — Global Constraint Invariance: Constraints remain invariant
  • AX-MIS — Mismatch: Constraint incompatibility measure exists
  • AX-TOL — Tolerance: Finite tolerance window WW exists
  • AX-COH — Cohesion: States within WW form cohesive units (CIUs)
  • AX-CONT — Continuum: CIUs co-evolve preserving mutual tolerance
  • AX-PAR — Partition: Mismatch exceeding WW causes partition
  • AX-LOC — Locality: Evolution proceeds locally

Capability Axioms (C-axioms):

  • AX-ADM — Admissible Moves: Non-empty set of mismatch-reducing transitions
  • AX-SEL — Precedence: Deterministic selection minimizing mismatch
  • AX-MEM — Persistence: State retention across interactions
  • AX-TPL — Template Influence: Structures constrain nearby admissible transitions
  • AX-META — Meta-Cohesion: Structures participate as units in higher-order relations

Emergent Structure (No New Axioms)

As established by the Quantum Emergence Program (E2, Phases Q0–Q6), quantum structure emerges from these axioms without requiring additional substrate primitives.

Key result from R-CCC:

Quantum capabilities arise from applying the same operational primitives established in E0 (mismatch, height, tolerance WW, closure cycles, commit-based execution) under stricter admissibility and compatibility regimes.

Emergent quantum features (from existing axioms):

  • Route topology from divergence and recombination
  • Phase as accumulated mismatch along paths
  • Interference from precedence-based recombination
  • Commit-based branch weighting (quadratic measure over branches)
  • Divergent compatible histories (multiple paths pre-commit when joint mismatch within WW)
  • Joint admissibility constraints (substrate origin of entanglement)
  • Discrete modes from hierarchical stabilisation and invariant basins

Normativity and Usage

DCC-QM is always non-normative.

When to reference DCC-QM:

  • Papers that assume a quantum-capable substrate as background capability
  • Papers working at the effective physics level (B-series)
  • When stating scope: “This derivation assumes DCC-QM”

When NOT to reference DCC-QM:

  • When individual axioms are being derived, refined, or stressed
  • When axioms play an active operational role in the argument
  • When the paper is establishing what makes a substrate quantum-capable

Dependency declaration pattern:

deps: R-DCC?>informs

DCC-QM informs papers by making capability assumptions explicit. It does not create normative constraints.

Future DCCs

Additional DCCs may be introduced as programme needs emerge. Potential candidates include:

DCC-CONS — Constructor-Capable Substrate (R-CCC Class C2)

  • All R-axioms + AX-ADM, AX-SEL, AX-MEM
  • Minimum required for constructors

DCC-MODE — Mode-Bearing Substrate (R-CCC Class C4)

  • All R-axioms + all C-axioms
  • Supports discrete stable modes and degeneracy
  • Note: Same axiom set as DCC-QM but operates at a lower capability level; DCC-MODE substrates have not yet developed interferometric or quantum capabilities

DCC-INT — Interferometric Substrate (R-CCC Class C5)

  • All R-axioms + all C-axioms
  • Emergent route structure enables interference
  • Pre-quantum: interference without full quantum-mechanical structure
  • Note: “Emergent route structure” is not an axiom but a capability that arises from the axiom combination; it enables phase-dependent recombination

DCCs should be introduced only when:

  • Multiple papers assume the same axiom bundle repeatedly
  • The capability envelope is well-defined and stable
  • Empirical or formal results (E-series, M-series) have established the bundle

Normativity Rules

Critical: DCCs are always non-normative.

  1. DCCs do not create requirements: Referencing a DCC does not make a paper dependent on R-DCC
  2. DCCs are informative: They clarify what capability envelope is assumed
  3. Granular axioms remain primary: When axioms do work, reference them explicitly
  4. DCCs are semantic shortcuts: They reduce repetitive axiom enumeration

Dependency patterns:

  • ✅ Correct: R-DCC?>informs (non-normative)
  • ❌ Incorrect: R-DCC!>depends (normative — never use this)

When papers change:

  • If R-DCC updates, papers referencing it do not require revision
  • If a paper’s capability assumptions change, update or remove the DCC reference
  • DCCs track capability envelopes, not paper logic

Usage Guidelines

For Paper Authors

When writing papers that assume a quantum-capable substrate:

DO:

  • State clearly which DCC you assume (e.g., “This paper assumes DCC-QM”)
  • Add R-DCC?>informs to dependency metadata
  • Reference specific axioms when they play operational roles in derivations

DON’T:

  • Replace explicit axiom derivations with DCC references
  • Use DCCs as normative dependencies
  • Assume DCC references carry theoretical weight

For Reviewers

When evaluating papers that reference DCCs:

CHECK:

  • Is the DCC reference appropriate for the paper’s scope?
  • Are granular axioms still referenced where they do active work?
  • Is the DCC used as a convenience, not a theoretical claim?

FLAG:

  • Normative DCC dependencies (always incorrect)
  • Missing explicit axiom references where axioms are central
  • DCC references in papers that derive those capabilities

What This Paper Does Not Do

To maintain clarity about scope and role, this document explicitly does not:

Does Not Introduce New Axioms

R-DCC bundles existing axioms. It does not:

  • Add new substrate primitives
  • Extend the axiom set
  • Introduce new mechanisms
  • Make theoretical claims

Does Not Alter Existing Axioms

R-DCC does not:

  • Redefine axiom semantics
  • Change axiom requirements
  • Create new interpretations
  • Modify formal structure

Does Not Derive New Results

R-DCC does not:

  • Prove theorems about capability bundles
  • Establish new emergence results
  • Derive effective physics
  • Make empirical predictions

All results referenced here are established in other papers (A-series, M-series, E-series, B-series).

Does Not Create Normative Requirements

R-DCC does not:

  • Require papers to use DCCs
  • Constrain how axioms are referenced
  • Replace granular axiom usage
  • Create dependencies

Summary

Derived Capability Classes (DCCs) are named axiom bundles that:

Purpose:

  • Eliminate repeated axiom enumeration
  • Make capability assumptions explicit
  • Preserve axiomatic traceability
  • Strengthen programme coherence

Structure:

  • Named capability envelopes (e.g., DCC-QM)
  • Complete axiom lists
  • R-CCC correspondence
  • Usage guidance

Current DCCs:

  • DCC-QM: Quantum-capable substrate (R-CCC Class C6)

Normativity:

  • Always non-normative
  • Reference as R-DCC?>informs
  • Never creates requirements
  • Semantic convenience only

Usage:

  • State capability assumptions clearly
  • Reference when assuming capability envelope
  • Use explicit axioms when they do operational work
  • Do not replace derivations with DCC references

Key principle: DCCs are reference material making implicit capability assumptions explicit. They organize existing axioms without introducing new theory.

References

  • R-CCC: Continuum Capability Classification (capability class definitions)
  • Axioms: R-axioms and C-axioms (see Reference: Axioms)
  • E2: Quantum Emergence Program (empirical basis for DCC-QM)
  • M1–M5: Formal Mechanism Papers (mechanisms underlying capabilities)
  • Paper A: Substrate Mechanics (formal mathematical substrate)
  • B-series: Derived Physics (applications of capability assumptions)

Status: Reference framework established
Epistemic Role: Non-normative synthesis and reference
Primary Value: Explicit, named capability bundles reducing axiom enumeration
Usage: Reference for B-series and other papers assuming capability envelopes