Q42 10D Volumetric Tensor Standard

Version: 1.2
Date: 2026-06-21 (rev; was 1.1 2026-06-17)
Status: Draft Standard
Repository: https://github.com/mediaprophet/qualiaDB/tree/0.0.28

Changelog (1.2): §4 made normative — the volume-search metric is selected by the query’s v topology class, with an exact euclidean formula and a GPU/CPU determinism requirement (the GPU compute path MUST compute the identical metric as the CPU reference). Implements the metric-unification work in ALGEBRA_MANIFOLD_PLAN.md §4.

Abstract

This standard defines the 10-dimensional volumetric tensor coordinate system [q, v, w, x, y, z, t, α, μ, σ] for the Q42 volumetric tensor system. The system provides absolute mechanical sympathy across heterogeneous hardware (edge phones to A2000 GPUs to scarce QPUs) by mapping neuro-symbolic human-centric logic into raw geometric physics simulations executable via SIMD, GPU texture units, or asynchronous Ground-State Resolvers.

1. Coordinate System Definition

1.1 Tensor10D Structure

The Tensor10D structure is a 40-byte, zero-heap compatible, stack-allocated structure using fixed-size f32 values for GPU/SIMD compatibility and quantization.

#[repr(C)]
pub struct Tensor10D {
    pub q: f32,      // Quantum Context / Superposition Index
    pub v: f32,      // Topological / Algebraic Variety Class
    pub w: f32,      // Manifold / Domain Index
    pub x: f32,      // Semantic Topology X coordinate
    pub y: f32,      // Semantic Topology Y coordinate
    pub z: f32,      // Semantic Topology Z coordinate
    pub t: f32,      // Temporal State / Provenance Ledger
    pub alpha: f32,  // Spectral Amplitude / Dynamic Range / Confidence Weight
    pub mu: f32,     // Spectral Modulation / Phase / Metadata Carrier
    pub sigma: f32,  // Spectral Signature / Logical Class Index
}

1.2 Dimension Semantics

Structural & Quantum Identifiers:

Spacetime Dimensions:

Spectral-Logical Payload:

1.3 Phenomenal multi-modal σ projection (U2 + U3)

The Qualia WASM portal projects the same σ field into two last-mile modalities without duplicating storage:

Modality Universe Projection Reference
Visual U2 Viewport λ_nm = 400 + fract(σ)×300 → CIE 1931 XYZ → linear sRGB portal_spectral.rs, spectral.wgsl
Auditory U3 AcousticPlane same λ_nm → f_hz = lerp(1760, 110, t) where t = (λ_nm−400)/300 portal_acoustic.rs

Where fract(σ) = σ - floor(σ). Integer wraps on σ must not change either projection.

High-density sheets: Full SPD (vision) and STFT/CQT (audio) live in mmap sidecars linked at bake time — not inlined in the 40-byte Tensor10D stride. Each node carries a 64-bin preview derived from σ for hot-path parametric synthesis (SPECTRAL_PREVIEW_BINS = 64). Normative audio layouts: q42-acoustic-plane-draft.md.

α and μ in audio:

2. Hardware Capability Tiers

2.1 Tier Classification

Tier 0: Strict Edge / Battery Reserve

Tier 1: Mainstream Native

Tier 2: High-Performance Local / Solar Surplus

Tier 3: Ground-State Resolver / QPU Escrow

2.2 Telemetry-Aware Dispatching

The HardwareTierDispatcher must dynamically route execution based on:

2.3 Execution Strategies

3. Zero-Heap Execution Constraints

3.1 Hot Path Requirements

3.2 Buffer Management Pattern

// Zero-heap function signature
pub fn process_tensor(
    input: &[Tensor10D],
    output: &mut [f32],  // Caller-supplied buffer
    count: usize,
) -> Result<usize, ProcessingError>

3.3 Memory Constraints

4. Topological Distance Metrics

4.1 Metric selection (NORMATIVE)

The volume-search distance between a query tensor Q and a node tensor N is selected by the query’s topological class ⌊Q.v⌋ (the same class applies to every node in a given search — it is a property of the query, not of each node):

⌊Q.v⌋ Metric Fields used
0 Euclidean x, y, z, t, α, μ, σ
1 Cyclic / toroidal x, y, z (mod 1)
2 Hyperbolic x, y, z
≥ 3 Boundary clique v

This mirrors Tensor10D::full_distance (crates/qualia-core-db/src/tensor/mod.rs).

Euclidean (v = 0) — the full 7-dimensional form (note: q, v, w are NOT part of the metric):

d = √( (Δx)² + (Δy)² + (Δz)² + (Δt)² + (Δα)² + (Δμ)² + (Δσ)² )

Cyclic (v = 1) — toroidal wrap on each spatial axis:

d = √( c(Δx)² + c(Δy)² + c(Δz)² ),   c(δ) = min(|δ|, 1 − |δ|)

Hyperbolic (v = 2) — exponential hierarchy over the spatial axes:

d = ln( e^|Δx| + e^|Δy| + e^|Δz| )

Boundary (v ≥ 3) — clique membership:

d = 0 if Q.v == N.v else 1

A node N is a hit iff d(Q, N) ≤ max_distance.

4.2 GPU/CPU determinism (NORMATIVE)

A conforming implementation MUST compute the identical metric (§4.1) on every execution path — CPU SIMD, GPU, and any fallback — so a volume search returns the same hit set regardless of the hardware that runs it. In particular the GPU compute kernel MUST implement all four metrics and dispatch on ⌊Q.v⌋; it MUST NOT silently restrict to euclidean.

Reference implementation:

Earlier revisions only implemented the euclidean branch on the GPU, so results diverged from the CPU path for v ≠ 0; v1.2 closes this. (See ALGEBRA_MANIFOLD_PLAN.md §4.1 and the cpu_tensor_search_honors_topology_class test.)

4.3 Topological Bifurcation

Combined with manifold identifier (w), topological class (v) enables structural “wormholes” for cross-domain correlation:

5. Ground-State Resolver (GSR) Integration

5.1 QUBO Problem Format

pub struct QuboProblem {
    pub problem_id: String,
    pub coefficients: Vec<(usize, usize, f32)>,
    pub linear_terms: Vec<(usize, f32)>,
    pub size: usize,
    pub context_id: u64,
}

5.2 Resolution Process

  1. QPU Resolution: Async mesh aggregation for quantum context resolution
  2. Classical Fallback: Exhaustive search (n≤16) or greedy approximation (n>16)
  3. Axiom Caching: Store winning contexts for future reference
  4. Epistemic Frame Evolution: Create new t slices when contexts resolve

5.3 Result Format

pub struct GsrResult {
    pub problem_id: String,
    pub winning_context: f32,
    pub confidence: f32,
    pub resolved_at: u64,
    pub compute_time_ms: u64,
    pub classical_fallback: bool,
}

6. Q42 Volume Integration

6.1 NQuin to Tensor10D Mapping

The bridge layer converts between the 48-byte NQuin structure and the 40-byte Tensor10D structure:

6.2 Tensor Metadata

pub struct TensorMetadata {
    pub tensor: Tensor10D,
    pub has_tensor: bool,
    pub tensor_version: u32,
}

6.3 Query Operations

7. Cryptographic Integration

7.1 Sanctuary Lane Cryptography

7.2 Zero-Heap Cryptographic API

pub fn encrypt_sanctuary_chunk(
    cipher_key: &[u8; 32],
    volume_tweak: &[u8; 16],
    chunk_index: u64,
    plaintext: &[u8],
    ciphertext_out: &mut [u8],  // Caller-supplied
    tag_out: &mut [u8],          // Caller-supplied
    additional_data: Option<&[u8]>,
) -> Result<usize, String>

8. Feature Flags

8.1 Tensor Features

8.2 Build Configuration

# Enable all tensor features
cargo build --features tensor-10d,tensor-gpu,tensor-npu,sanctuary-crypto

# Enable only CPU SIMD execution
cargo build --features tensor-10d

# Enable GPU acceleration
cargo build --features tensor-10d,tensor-gpu

9. Performance Targets

9.1 Latency Requirements

9.2 Power Consumption

9.3 Storage Efficiency

10. Security & Sovereignty

10.1 Cryptographic Provenance

10.2 Zero-Heap Security Benefits

10.3 Sovereign Data Assets

11. Compliance & Standards

11.1 Data Sovereignty

11.2 Interoperability

12. Implementation Status

12.1 Completed Components

12.2 Future Work

13. References

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