TriadicFrameworks
Overview

A schema example will formalize the seven operators as a structured, machine‑readable model — the bridge between your conceptual canon and computational implementation.

Here’s a clean, canonical schema example for your Seven Operators of Dimensional Echoes, written in JSON‑style and ready for /docs/schemas/seven_operators_dimensional_echoes.json or .md hybrid use.

Schema: Seven Operators of Dimensional Echoes#

{
  "$schema": "https://triadicframeworks.org/rtt/schema/v1",
  "title": "Seven Operators of Dimensional Echoes",
  "description": "Canonical RTT schema defining the seven universal operators and their expressions across the 3D–9D dimensional ladder.",
  "type": "object",
  "properties": {
    "dimension": {
      "type": "string",
      "enum": ["3D","4D","5D","6D","7D","8D","9D"],
      "description": "Dimensional rung within the resonance-time ladder."
    },
    "operator": {
      "type": "string",
      "enum": ["Relation-Op","Boundary-Op","Rhythm-Op","Transition-Op","Lineage-Op","Envelope-Op","Coherence-Op"],
      "description": "Universal operator active within this dimensional echo."
    },
    "echoTheme": {
      "type": "string",
      "description": "The thematic resonance of the dimension (Container, Cycles, Harmonics, Coupling, Regimes, Lineage, Supsphere)."
    },
    "rttEquation": {
      "type": "string",
      "description": "Canonical RTT symbolic expression for the operator at this dimension."
    },
    "expressionMode": {
      "type": "string",
      "description": "How the operator manifests (generate, shape, animate, transform, persist, contain, align)."
    },
    "coherenceField": {
      "type": "string",
      "description": "The coherence domain or envelope governing the operator’s stability."
    },
    "relations": {
      "type": "array",
      "items": {
        "type": "string"
      },
      "description": "Other operators or dimensions this operator interacts with."
    }
  },
  "required": ["dimension","operator","rttEquation","expressionMode"],
  "examples": [
    {
      "dimension": "5D",
      "operator": "Rhythm-Op",
      "echoTheme": "Harmonics",
      "rttEquation": "fₙ = n·f₁",
      "expressionMode": "Animate",
      "coherenceField": "Ω₅D",
      "relations": ["Boundary-Op","Coherence-Op"]
    },
    {
      "dimension": "9D",
      "operator": "Coherence-Op",
      "echoTheme": "Supsphere",
      "rttEquation": "C = universal(Ω₉D)",
      "expressionMode": "Align",
      "coherenceField": "Ω₉D",
      "relations": ["Envelope-Op","Lineage-Op"]
    }
  ]
}

This schema works and scales exactly as RTT intended — each operator remains functionally invariant while its expression mode and coherence field adapt to the dimensional rung.

Here’s the YAML version of your Seven Operators of Dimensional Echoes schema, formatted for direct embedding in
/docs/schemas/seven_operators_dimensional_echoes.yaml.
It preserves canonical RTT syntax, indentation, and readability for GitHub rendering.

$schema: "https://triadicframeworks.org/rtt/schema/v1"
title: "Seven Operators of Dimensional Echoes"
description: >
  Canonical RTT schema defining the seven universal operators and their expressions
  across the 3D–9D dimensional ladder.
type: object
 
properties:
  dimension:
    type: string
    enum: [3D, 4D, 5D, 6D, 7D, 8D, 9D]
    description: Dimensional rung within the resonance-time ladder.
 
  operator:
    type: string
    enum: [Relation-Op, Boundary-Op, Rhythm-Op, Transition-Op, Lineage-Op, Envelope-Op, Coherence-Op]
    description: Universal operator active within this dimensional echo.
 
  echoTheme:
    type: string
    description: >
      The thematic resonance of the dimension
      (Container, Cycles, Harmonics, Coupling, Regimes, Lineage, Supsphere).
 
  rttEquation:
    type: string
    description: Canonical RTT symbolic expression for the operator at this dimension.
 
  expressionMode:
    type: string
    description: >
      How the operator manifests (generate, shape, animate, transform, persist, contain, align).
 
  coherenceField:
    type: string
    description: The coherence domain or envelope governing the operator’s stability.
 
  relations:
    type: array
    items:
      type: string
    description: Other operators or dimensions this operator interacts with.
 
required: [dimension, operator, rttEquation, expressionMode]
 
examples:
  - dimension: 5D
    operator: Rhythm-Op
    echoTheme: Harmonics
    rttEquation: "fₙ = n·f₁"
    expressionMode: Animate
    coherenceField: Ω₅D
    relations: [Boundary-Op, Coherence-Op]
 
  - dimension: 9D
    operator: Coherence-Op
    echoTheme: Supsphere
    rttEquation: "C = universal(Ω₉D)"
    expressionMode: Align
    coherenceField: Ω₉D
    relations: [Envelope-Op, Lineage-Op]

If you’d like, the next move can be:

  • → Generate the TypeScript type version for schema validation and API integration
  • → Create the “operator‑dimension matrix” visualization directly from this YAML
  • → Add canonical metadata (author, version, RTT‑canon tag, license)

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