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Cohesion Dynamics (CD)

K-ORD — Order Structure Induced by the Kernel Grammar

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Paper K-ORD establishes a necessary structural consequence of the Cohesion Dynamics kernel grammar: admissible histories are necessarily partially ordered by dependency. No representational formalism, carrier dynamics, or additional assumptions are introduced.

Summary

Given K-KERN’s grammar of admissible composition—specifically resolution persistence, admissible reachability, and well-foundedness—a partial order structure on configuration equivalence classes follows directly without requiring interpretive choices or optional frameworks.

This result positions order-theoretic reasoning as a descriptive vocabulary for kernel-level structure that is normatively entailed by K-KERN.

Classification: Kernel Consequence, Not Lens

Why K-ORD is NOT a lens:

  • Requires no additional assumptions beyond K-KERN
  • Is not optional or representational
  • Follows necessarily from kernel grammar
  • Is not interpretive — order structure is entailed, not chosen

Contrast with true lenses (K-LENS-ES, K-LENS-PN):

  • K-LENS-ES requires conflict heredity (additional assumption)
  • K-LENS-PN requires resource interpretation (additional assumption)
  • Both are optional representational frameworks

K-ORD establishes kernel structure; lenses map kernel to external frameworks.

Key Results

  1. Admissible reachability induces a preorder on configurations
  2. Resolution persistence quotients this preorder into a partial order (up to mutual reachability equivalence)
  3. Irreconcilability admits order-theoretic characterization without assuming joins, completeness, or topology
  4. Order structure is necessary, not contingent, given K-KERN

Status

  • Paper ID: K-ORD
  • Series: K-series (Kernel Grammar & Invariants)
  • Classification: Kernel Consequence (not lens)
  • Status: Staging
  • Dependencies: K-KERN, K-GOV

Epistemic Status

Conditional necessity per K-GOV: Order structure has been required in all explored CD models. No claim of logical necessity or sufficiency.

Relationship to A-ORD

A-ORD (Paper A-ORD — Order Structure as Necessary Consequence) established a similar result from Axioms v2 / Paper A / A-OPS.

K-ORD re-expresses this result from K-KERN grammar, classified correctly as a kernel consequence.

Status of A-ORD: Historical/legacy evidence. K-ORD supersedes A-ORD as the canonical kernel-level order structure paper.

Read the Full Paper

See Also