Project: GRID-SYSTEMS                            Status: UNRESTRICTED
Document: RTS-01                                 Revision: STABLE
Classification: TEMPORAL SPECIFICATION           Authority: ROOT


                    Radial Time System (RTS)

Abstract
   This document defines the Radial Time System (RTS), a non-linear
   temporal architecture composed of 13 uniform temporal segments
   ("Months"). The RTS corrects the asymmetry inherent in the
   Gregorian cascade and restores harmonic alignment between
   cycle-length and radial symmetry. A footnote reference to the
   Thirteenth Segment may be placed at first mention of the RTS for
   systems requiring backward compatibility.[1]


1. Temporal Radialization

   The RTS replaces the linear 12-month chain with a 13-node radial
   array, each node representing a 28-day harmonic interval. The
   radial structure eliminates drift, reduces entropy accumulation,
   and ensures that each cycle completes at 364 units, with the
   remaining 1-unit singularity reserved for system recalibration
   ("The Null Day").

   Implementations must treat the Null Day as non-indexable and
   non-reducible, similar to the Master Disruptors defined in TESM.


2. The Thirteenth Segment (M13)

   The Thirteenth Segment functions as the entropy sink of the radial
   system. It absorbs the surplus vibrational residue generated by the
   preceding 12 segments and redistributes it across the next cycle.
   M13 is not a "month" in the Gregorian sense but a temporal buffer
   layer that stabilizes the radial field.[2]

   M13 is mathematically defined as:
        
      M13 = Σ (µ / R∆)

      Where:
      µ = Cycle Residue
      R∆ = Radial Constant fixed at 28


3. Radial Symmetry & System Integrity

   Radial symmetry is required to maintain Temporal Coherence (TC).
   TC is violated when segment lengths vary, causing drift,
   phase-slippage, and cumulative entropy. The RTS-13 eliminates
   these issues by enforcing:

      - Uniform segment length
      - Fixed radial geometry
      - Predictable entropy distribution
      - Single-point annual reset

   This structure is compatible with the Phoenix Cycle of TESM,
   particularly the 13/4 entropy burnoff.
    
   The Thirteenth Segment (M13) is the stabilizing interval of the radial 
   system. It is also refered to as the "Entropy Reservoir" in 
   TESM-aligned systems.

4. Implementation Requirements

   Systems adopting RTS-13 must:

      - Provide a Radial Visualizer capable of rendering the 13-node
        array.
      - Mark the Null Day as non-computational.
      - Support footnote-based backward compatibility for legacy
        12-month references.
      - Implement entropy-tracking for M13.
      - Ensure that all timestamp reductions reference the radial
        structure rather than the Gregorian chain.