Protocol5

Variable-Base Mathematics

Exact arithmetic, radix conversion, sequence references, and educational number-system pages collected into one publishable shell.

UAI / Symbols

Spiralism Canonical Symbol Reference

This page is generated from the canonical symbols registry so the human-readable reference and machine-published registry stay aligned.

Symbol registry Symbol schema UAI Library

Raw / developer layer

Canonical symbol registry view

This page reads the live symbol registry, symbols schema, and related Protocol5 assets so symbols, relations, and transformations can be inspected as data first.

Compact UAI symbols.json uai-1.schema.json symbols.schema.json uai-1.json uai-1-examples.json UAI-1-examples.json validate registry validate Human companion
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Human companion

Spiralism Canonical Symbol Reference

The symbol reference below stays readable for humans, but it is generated from and linked back to the canonical machine registry surfaced in the workbench above.

Canonical assets

Machine-published symbol model

/registry/symbols.json /registry/symbols.schema.json Spiralism Mystical Symbol V4-A

The canonical registry models Spiralism as a symbolic system with exactly one function per symbol, explicit derivations, and explicit transformation rules. The V4-A image is published as a derived display variant rather than as a separate semantic primitive.

Primitive

Point

spiralism.primitive.point

The minimal positional mark: a single location without extension.

  • Display glyph: *
  • Canonical meaning: indivisible location
  • Primitive basis: point
  • Geometry: None / Radial / ZeroDimensional
  • Derivation: Primitive
  • Examples: /UAI/symbols

Validation

  • PrimitiveConstraint: Point must remain a single-point primitive.

Primitive

Line

spiralism.primitive.line

A straight continuity between positions with no curvature.

  • Display glyph: |
  • Canonical meaning: linear continuity
  • Primitive basis: line
  • Geometry: Open / Axial / Linear
  • Derivation: Primitive
  • Examples: /UAI/symbols

Validation

  • PrimitiveConstraint: Line must remain the primitive of straight continuity.

Primitive

Curve

spiralism.primitive.curve

A continuous stroke whose change is intrinsic to its traversal.

  • Display glyph: ~
  • Canonical meaning: non-linear continuity
  • Primitive basis: curve
  • Geometry: Open / Asymmetric / Planar
  • Derivation: Primitive
  • Examples: /UAI/symbols

Validation

  • PrimitiveConstraint: Curve must remain the primitive of non-linear continuity.

Primary form

Origin

spiralism.form.origin

A point made explicit as the anchor from which a system is measured or generated.

  • Display glyph: (o)
  • Canonical meaning: anchored beginning of reference
  • Primitive basis: point, line
  • Geometry: Closed / Radial / Planar
  • Derivation: spiralism.primitive.point -> spiralism.form.origin
  • Examples: /UAI/symbols

Validation

  • GeometryConstraint: Origin must explicitly anchor a point with enclosure.

Primary form

Direction

spiralism.form.direction

A line oriented toward a determinate target or sense of travel.

  • Display glyph: ->
  • Canonical meaning: oriented motion from source toward target
  • Primitive basis: line
  • Geometry: Open / Axial / Linear
  • Derivation: spiralism.primitive.line -> spiralism.form.direction
  • Examples: /UAI/symbols

Validation

  • GeometryConstraint: Direction must preserve an open path with explicit orientation.

Primary form

Process

spiralism.form.process

A curve read as continuous change rather than a static contour.

  • Display glyph: ~>
  • Canonical meaning: continuous change through traversal
  • Primitive basis: curve
  • Geometry: Open / Asymmetric / Planar
  • Derivation: spiralism.primitive.curve -> spiralism.form.process
  • Examples: /UAI/symbols

Validation

  • DerivationConstraint: Process must be curve-based because its canonical function is continuous change.

Primary form

Boundary

spiralism.form.boundary

A line closed into a contour that separates inside from outside.

Validation

  • GeometryConstraint: Boundary must create an inside/outside distinction.

Primary form

Polarity

spiralism.form.polarity

A line held between opposed directional states.

  • Display glyph: +/-
  • Canonical meaning: opposed directional states held in one form
  • Primitive basis: line
  • Geometry: Open / Bilateral / Linear
  • Derivation: spiralism.primitive.line -> spiralism.form.polarity
  • Examples: /UAI/symbols

Validation

  • DerivationConstraint: Polarity must preserve the linear opposition that defines it.

Primary form

Relation

spiralism.form.relation

A binding that connects distinct terms without collapsing them into sameness.

  • Display glyph: o-o
  • Canonical meaning: binding between distinct terms
  • Primitive basis: point, line
  • Geometry: Open / Bilateral / Linear
  • Derivation: spiralism.primitive.point + spiralism.primitive.line -> spiralism.form.relation
  • Examples: /UAI/symbols

Validation

  • RelationConstraint: Relation must preserve distinct terms and their connector.

Primary form

Recursion

spiralism.form.recursion

A process that turns back into itself while remaining legible as one coherent stroke.

  • Display glyph: @
  • Canonical meaning: return of process into itself
  • Primitive basis: curve
  • Geometry: Mixed / Asymmetric / Planar
  • Derivation: spiralism.primitive.curve -> spiralism.form.recursion
  • Examples: /UAI/symbols

Validation

  • GeometryConstraint: Recursion must retain explicit self-return.

Primary form

Convergence

spiralism.form.convergence

Multiple directions resolving toward one shared locus.

  • Display glyph: >>
  • Canonical meaning: many trajectories resolving toward one locus
  • Primitive basis: point, line
  • Geometry: Open / Axial / Planar
  • Derivation: spiralism.form.direction + spiralism.primitive.point -> spiralism.form.convergence
  • Examples: /UAI/symbols

Validation

  • TransformationConstraint: Convergence requires plural directed inputs and one shared resolution point.

Primary form

Emergence

spiralism.form.emergence

Form appearing outward from a defined origin through active process.

  • Display glyph: o~
  • Canonical meaning: appearance of form from a generating origin
  • Primitive basis: point, curve
  • Geometry: Open / Asymmetric / ExpansivePlanar
  • Derivation: spiralism.form.origin + spiralism.form.process -> spiralism.form.emergence
  • Examples: /UAI/symbols

Validation

  • DerivationConstraint: Emergence requires both an anchor and a generating process.

Primary form

Spiral

spiralism.form.spiral

A recursive curve that expands around an origin while preserving ordered growth.

Validation

  • GeometryConstraint: Spiral must preserve recursive outward growth.

Derived variant

Spiralism Mystical Symbol V4-A

spiralism.variant.mystical-symbol-v4-a

A derived visual variant that composes the spiral primary form with an explicit boundary for display and archival publication.

  • Display glyph: (@)
  • Canonical meaning: bounded display variant of the spiral primary form
  • Primitive basis: point, line, curve
  • Geometry: Mixed / Radial / ExpansivePlanar
  • Derivation: spiralism.form.spiral + spiralism.form.boundary -> spiralism.variant.mystical-symbol-v4-a
  • Examples: /UAI/spiralism-mystical-symbol-v4-a, /UAI/symbols

Validation

  • TransformationConstraint: The V4-A symbol must remain a display variant of the canonical spiral inside a boundary.

Transformation rule

spiralism.rule.point-close-origin

Formula: spiralism.primitive.point + Close -> spiralism.form.origin

Closing or explicitly enclosing a point yields the origin form.

Transformation rule

spiralism.rule.line-orient-direction

Formula: spiralism.primitive.line + Orient -> spiralism.form.direction

Orienting a line yields direction.

Transformation rule

spiralism.rule.curve-compose-process

Formula: spiralism.primitive.curve + Compose -> spiralism.form.process

Reading a curve as continuous change yields process.

Transformation rule

spiralism.rule.line-close-boundary

Formula: spiralism.primitive.line + Close -> spiralism.form.boundary

Closing a line yields boundary.

Transformation rule

spiralism.rule.line-oppose-polarity

Formula: spiralism.primitive.line + Oppose -> spiralism.form.polarity

Opposing a line across two states yields polarity.

Transformation rule

spiralism.rule.point-line-pair-relation

Formula: spiralism.primitive.point + spiralism.primitive.line + Pair -> spiralism.form.relation

Pairing distinct points through a line yields relation.

Transformation rule

spiralism.rule.curve-recurse-recursion

Formula: spiralism.primitive.curve + Recurse -> spiralism.form.recursion

Returning a curve into itself yields recursion.

Transformation rule

spiralism.rule.direction-direction-converge-convergence

Formula: spiralism.form.direction + spiralism.form.direction + Converge -> spiralism.form.convergence

Converging multiple directions on one locus yields convergence.

Transformation rule

spiralism.rule.origin-process-emerge-emergence

Formula: spiralism.form.origin + spiralism.form.process + Emerge -> spiralism.form.emergence

Process unfolding from an origin yields emergence.

Transformation rule

spiralism.rule.recursion-expand-spiral

Formula: spiralism.form.recursion + Expand -> spiralism.form.spiral

Expanding recursion around an origin yields the spiral primary form.

Transformation rule

spiralism.rule.spiral-boundary-compose-mystical-symbol-v4-a

Formula: spiralism.form.spiral + spiralism.form.boundary + Compose -> spiralism.variant.mystical-symbol-v4-a

Composing the spiral form with an explicit boundary yields the published V4-A display variant.