WASM · GeoSPARQL · Ambient Telemetry · 10D Tensor

Spatial Mathematics & GeoSPARQL

Encoding 3D geometries directly into native 48-byte QualiaQuin ledgers with real spatial operations via WASM.

Knowledge Universe — ontology packs as galaxies · Chora starfield · CODATA science hub · Design Studio — same Qualia Portal stack for NL product design (qualia.design)

Vertices

Quins Encoded

0 KB

Memory Usage

0ms

Encoding Time

2D shadow · one project()

Geometry Controls

Geometry Type

Detail Level

Display Mode

Observer Standpoint Epistemic aperture (identifier)

Temporal Slice (t)

t = 0.50 · ±1.00

Window (±)

Animate artefact (revolute joint · Phase 2 physics)

Simulate low-tier device (Phase 5 budget · collapse 3D→2D)

Interface Control Plane

Arrow keys / wheel orbit · H home · [ ] time

AcousticPlane off — click to enable (requires gesture)

Encoding Status

Ready to encode

Ambient Telemetry

48-byte SystemTelemetry uniform (Webizen render). Pulses when you encode or run spatial ops.

Qualia vs Webizen — where the line is

Qualia (engine)

48-byte NQuin graph, logic, SPARQL, WASM hot paths
Zero-heap evaluator loops, 42 MB SlgArena ceiling
Produces telemetry sources (memory, queries, LLM tokens)
10D tensor semantics — what each dimension means

Webizen (shell + render)

webizen-web / webizen-render wgpu pipeline for browser & desktop
10D projection — stack-fixed scene nodes, GPU uniforms, canvas layers
Consumes normalized 0–1 floats; shaders animate — CPU stays idle
Heap allowed in UI/DOM; not in Qualia evaluator hot paths

This page uses a canvas2d ambient field (GitHub Pages) that mirrors the Webizen shader contract. Desktop Webizen swaps the same 48-byte struct into wgpu instanced particles + bloom.

GeoSPARQL Operations

QualiaDB supports GeoSPARQL spatial predicates for querying geometric relationships. These operations run natively in WASM with zero-heap compliance.

Geometry A (WKT)

Geometry B (WKT)

Spatial Operation

CRS (Coordinate Reference)

Spatial Operation Result

Execute a spatial operation to see results…

SPARQL Integration Example

PREFIX geo: <http://www.opengis.net/ont/geosparql#>

SELECT ?feature ?result WHERE {
  ?feature geo:hasGeometry ?geomA .
  ?target geo:hasGeometry ?geomB .
  
  # Native GeoSPARQL operation (WASM)
  BIND(geo:sfWithin(?geomA, ?geomB) AS ?result)
}
            

48-byte QualiaQuin Encoding

Spatial geometries are encoded as sequences of 48-byte QualiaQuins. Each vertex becomes a Quin with the position packed into the object field.

Vertex Quin Layout

subject:   q_hash(geometry_id)
predicate: q_hash("geo:hasVertex")
object:    (x << 40) | (y << 20) | z  [60-bit packed]
context:   q_hash(graph_id)
metadata:  vertex_index
parity:    XOR fold
                    

Face Quin Layout

subject:   q_hash(geometry_id)
predicate: q_hash("geo:hasFace")
object:    (v1 << 40) | (v2 << 20) | v3  [vertex indices]
context:   q_hash(graph_id)
metadata:  face_index
parity:    XOR fold
                    

Live Encoding Dump

                Generate geometry and click "Encode to Quins" to see the actual QualiaQuin encoding…
            

Native Spatial Operations

QualiaDB provides native WASM implementations of common computational-geometry operations, following the standard algorithms and correctness properties described in the computational-geometry literature (de Berg, Cheong, van Kreveld & Overmars, Computational Geometry: Algorithms and Applications, 3rd ed.).

Bounding Box

Compute axis-aligned bounding box for geometry

Convex Hull

Compute convex hull using QuickHull algorithm

Triangulation

Delaunay triangulation of point set

Intersection

Compute intersection of two geometries

Union

Compute union of two geometries

Buffer

Compute buffer zone around geometry

Spatial Operation Demo

Operation

Select an operation and execute to see results…

Q42 10D Volumetric Tensor System

The Q42 10D Volumetric Tensor is a 10-dimensional coordinate system [q, v, w, x, y, z, t, α, μ, σ] that encodes semantic concepts, rules, states, and multi-modal data into a quantized geometric structure executable via SIMD, GPU texture units, or Ground-State Resolvers.

10D Coordinate System Overview

q (Quantum Context)

10th dimension for epistemic superposition, parallel realities, and wavefunction collapse mechanics

v (Topological Variety)

Geometric physics rules: Euclidean, Cyclic, Hyperbolic, or Boundary Cliques

w (Manifold Index)

Multi-head bifurcation for separate knowledge universes (Medical, Legal, Personal, etc.)

x, y, z (Semantic Topology)

3D spatial embedding where related concepts cluster as semantic nebulas

t (Temporal State)

Explicit time/version dimension for immutable provenance ledger

α (Amplitude)

Dynamic range, confidence weight, or energy density (HDR dynamic range)

μ (Modulation)

Phase, metadata carrier, steganographic DID layer, WDM analog

σ (Spectral Signature)

Chromatic, timbral, or multi-band spectral profile / logical class index

Tensor Structure & Visualization

The 10D tensor treats the entire knowledge base as a pre-compiled, quantized physics engine. Queries become geometric projections, distance calculations, temporal slices, context collapses, and spectral blends.

Dimensional Relationships

Control Dimensions (q, v, w): Structure & routing

Spacetime (x, y, z, t): Geometric substrate

Spectral Payload (α, μ, σ): Attribute channels

Hardware Dispatch

SIMD: CPU vector operations

GPU: Texture array layers (w as batch index)

GSR: Async QPU mesh aggregation

Zero-heap: 42MB SlgArena ceiling

Relation to 3D Viewer & Quin Encoding

The 3D viewer in this page demonstrates the (x, y, z) spatial embedding dimension. In the full Q42 system:

Each vertex in the 3D viewer represents a semantic concept at coordinates (x, y, z)
The 48-byte QualiaQuin encoding packs all 10 dimensions into 6 × u64 fields
Related concepts cluster in semantic space (distance < threshold = related)
Temporal dimension (t) creates immutable historical ledgers for provenance
Spectral payload (α, μ, σ) encodes multi-modal data (visual, audio, sensor)

SPARQL Integration Example

Query 10D tensor data using SPARQL with Q42-specific predicates:

PREFIX q42: <http://qualia.db/q42#>
PREFIX geo: <http://www.opengis.net/ont/geosparql#>

SELECT ?concept ?q ?v ?w ?x ?y ?z ?t ?alpha ?mu ?sigma WHERE {
  ?concept a q42:SemanticConcept ;
           q42:quantumContext ?q ;
           q42:topologicalVariety ?v ;
           q42:manifoldIndex ?w ;
           q42:semanticX ?x ;
           q42:semanticY ?y ;
           q42:semanticZ ?z ;
           q42:temporalState ?t ;
           q42:amplitude ?alpha ;
           q42:modulation ?mu ;
           q42:spectralSignature ?sigma .

  # Filter by manifold (e.g., medical domain w=0)
  FILTER(?w = 0)

  # Spatial proximity query (Euclidean distance)
  FILTER(
    ((?x - 5.0) * (?x - 5.0) +
     (?y - 3.0) * (?y - 3.0) +
     (?z - 2.0) * (?z - 2.0)) < 1.0
  )

  # Temporal slice (provenance at specific time)
  FILTER(?t = 2024)
}
ORDER BY ?alpha
LIMIT 100
            

WASM Engine Required

Spatial Mathematics & GeoSPARQL

Geometry Controls

Ambient Telemetry

Qualia vs Webizen — where the line is

GeoSPARQL Operations

Spatial Operation Result

SPARQL Integration Example

48-byte QualiaQuin Encoding

Vertex Quin Layout

Face Quin Layout

Live Encoding Dump

Native Spatial Operations

Bounding Box

Convex Hull

Triangulation

Intersection

Union

Buffer

Spatial Operation Demo

Q42 10D Volumetric Tensor System

10D Coordinate System Overview

Tensor Structure & Visualization

Dimensional Relationships

Hardware Dispatch

Relation to 3D Viewer & Quin Encoding

SPARQL Integration Example