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Cohesion Dynamics (CD)

K-LENS-PN — Petri Net / Occurrence Net Lens

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Paper K-LENS-PN maps K-KERN grammar to Petri net semantics (safe Petri nets, occurrence nets, asynchronous transition systems). The lens provides mathematical framework for executable carrier implementations and M-series simulations by representing CD structure in terms of places, transitions, and resource flow.

Key Mappings: Configurations → places (resource locations), resolutions → transitions (state changes), admissibility → enabling (sufficient tokens), histories → reachable markings, irreconcilability → conflict (resource contention). Ontological Status: This lens does not assert that Petri net primitives are ontologically fundamental. Rather, it shows that Cohesion Dynamics’ ontological primitives can be faithfully represented by Petri net structure under appropriate assumptions. The ontological commitments remain those of K-KERN.

Summary

Representational Assumptions: The lens requires resource interpretation, conservation, and boundedness—formalism-specific conditions not required by K-KERN. This positions CD as compatible with executable carriers while avoiding ontological commitment to resource-based reality.

Status

  • Paper ID: K-LENS-PN | Series: K-series (Kernel Architecture) | Status: Staging
  • Dependencies: K-KERN, K-GOV, K-LENS-ES (companion)

Executable Carriers and Simulations

K-LENS-PN provides the foundation for executable CD carriers:

  • Petri nets are directly executable (algorithmic firing rules)
  • Standard implementation strategy for carrier architectures
  • Enables M-series mechanism simulations
  • Underpins E-series empirical testing

Admissibility Branching vs Ontological Branching

Critical distinction: Petri nets admit multiple enabled transitions from a given marking. In K-LENS-PN, this represents non-singular admissibility of resolution pathways, not the existence of multiple realized futures.

  • Enabled ≠ actualized: Multiple transitions may be enabled, but exactly one fires
  • Single-history semantics: No ontological branching or merging of realized outcomes
  • Conflict = exclusive resolution: Firing one transition disables incompatible alternatives
  • Stochasticity in selection: Which resolution fires is not predetermined, but only one occurs

This aligns with Simple Core semantics: non-singular admissibility with single resolution.

Worked Example: Double-Slit Detection

The paper includes a detailed worked example showing how double-slit detection maps to Petri net structure:

  • Photon = obligation (token at initial place)
  • Two detectors = two enabled transitions (conflict)
  • One resolution = exactly one transition fires
  • Interference = enabling conditions, not execution

This demonstrates that PN conflict cleanly captures CD’s single-resolution semantics.

Additional Assumptions

Required for Petri Net Representation

  • Configuration-place bijection (natural)
  • Resolution-transition bijection (natural)
  • Dependency-flow correspondence (natural)
  • Safe marking (natural from global indexing)

Additional Interpretive Commitments

  • Places as resources (semantic commitment)
  • Tokens as resource counts (interpretation)
  • Token conservation (not required by K-KERN)
  • Bounded marking (not required by K-KERN)

Read the Full Paper

Interactive Demo

Explore Simple Core CD semantics with the Petri Net Lens in our interactive demo:

See Also

Relationship to Other Formalisms

Petri Nets vs Event Structures

  • Event structures (K-LENS-ES): Emphasize causality and conflict
  • Petri nets (K-LENS-PN): Emphasize resource and state

Both are K-LENS lenses — neither is privileged.

Formal Connection: Occurrence nets are equivalent to prime event structures (Nielsen-Plotkin-Winskel theorem).

Petri Nets and A-series Carriers

A-series carriers (graph-based, order-theoretic) can be implemented as Petri nets. K-LENS-PN provides the semantic bridge between K-KERN grammar and executable carrier implementations.