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Paper 0 — Geometric Foundations of the LMR Grammar

Status​

Geometric Foundation

Authority​

Paper 0 provides geometric support for the LMR codex grammar.

It is logically prior to Paper I in one sense: it addresses why the grammar has the form it has.

However, Paper I remains the entry point for codex notation, side discipline, and formal reading of the structural arc.

Role in LMR​

Paper 0 derives or motivates the geometric structures that support the LMR grammar.

It provides orientation for:

  • tetrahedral closure
  • face equivalence
  • face-pairing schedules
  • central exclusion
  • involution
  • hourglass grammar
  • quadrant grammar
  • interface-facing structure

What Paper 0 Establishes​

Paper 0 establishes geometric support for the structural grammar used in Arc 1.

It supports the reading of:

  • the hourglass
  • the quadrant grammar
  • mid₁
  • facing multiplicity
  • tetrahedral basin structure
  • structural closure

What Paper 0 Does Not Do​

Paper 0 does not:

  • introduce forces
  • introduce fields
  • introduce dynamics
  • replace Paper I
  • modify the codex
  • establish standard particle geometry
  • assert literal particle shape
  • override the Arc 1 paper sequence

Read This For​

Read Paper 0 for the geometric basis of the LMR grammar.

It is especially useful for understanding why tetrahedral structure, face pairing, and hourglass grammar are not arbitrary visual choices.

Placement in Reading Order​

Readers may follow either path:

Conceptual entry:
Paper I → Paper II → Paper III → Paper IV → Paper V → Paper 0

Geometric entry:
Paper 0 → Paper I → Paper II → Paper III → Paper IV → Paper V