# 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.

```rust
#[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:**

- **q (Quantum Context):** Manages epistemic superposition
  - `q = 0`: Collapsed Ground Truth / Classical Axiom (permanent, verified fact)
  - `q > 0`: Parallel epistemic contexts, pending GSR resolutions, branching "what-if" scenarios

- **v (Topological Class):** Defines geometric "physics rules" for manifold regions
  - `v = 0`: Euclidean (flat semantic proximity, standard distance)
  - `v = 1`: Cyclic / Toroidal (feedback loops, circadian rhythms, periodic states)
  - `v = 2`: Hyperbolic / Tree (hierarchies, family trees, taxonomies)
  - `v = 3+`: Sovereign Boundary Cliques / Community Classes

- **w (Manifold Index):** Domain Index for Multi-Head Bifurcation
  - `w = 0`: Biological/Medical
  - `w = 1`: Legal/Jurisdictional (UDHR, APP, My Health Record)
  - `w = 2`: Personal/Agency (cryptographic preferences, DIDs, consents)
  - `w = 3`: Environmental/Sensor
  - `w = 4`: Socioeconomic/Wellbeing (Maslow/QALY)

**Spacetime Dimensions:**

- **x, y, z (Semantic Topology):** 3D spatial coordinates of concepts
  - Related concepts are physically clustered
  - Distance between coordinates dictates semantic relevance
  - Supports bounding-volume queries, kNN, and ray-casting

- **t (Temporal State):** Explicit time or state-version dimension
  - Medical: Biomarker normal at `t=0`, critical at `t=1`
  - Legal: Claim valid at `t=2024`, superseded at `t=2026`
  - Enables verifiable ledger for historical state queries

**Spectral-Logical Payload:**

- **α (Amplitude):** Linear floating-point intensity, energy density, trust/consensus weight
- **μ (Modulation):** Encodes phase, frequency modulation, or bit-packed metadata for DIDs and cryptographic provenance
- **σ (Spectral Signature):** Represents chromatic, timbral, or multi-band spectral profile. In the **phenomenal portal**, σ is the shared truth index for both vision (U2) and hearing (U3) — see §1.3.

### 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`](q42-acoustic-plane-draft.md).

**α and μ in audio:**

- **α** — linear gain staging (preserves dynamic-range sovereignty; clipping only at DAC under device policy).
- **μ** — phase / provenance modulation; drives FM index with epistemic **q** in U3 parametric voices.

## 2. Hardware Capability Tiers

### 2.1 Tier Classification

**Tier 0: Strict Edge / Battery Reserve**
- Hardware: Mobile CPUs, Raspberry Pi, basecamps on night-time battery reserves
- Execution: SIMD kernels (ARM NEON / x86 AVX2), aggressive quantization
- Power: < 1W idle, < 5W active
- Memory: ≤48 MB peak working set

**Tier 1: Mainstream Native**
- Hardware: Standard laptops, mobile Neural Engines
- Execution: Hybrid CPU/NPU model, minor heap buffering permitted
- Power: < 10W idle, < 20W active
- Memory: ≤256 MB peak working set

**Tier 2: High-Performance Local / Solar Surplus**
- Hardware: Dedicated GPUs (NVIDIA A2000, Apple Silicon GPU clusters)
- Execution: GPU VRAM mapping, parallel Texture Mapping Units
- Power: < 10W idle, < 50W active
- Memory: ≤2 GB peak working set

**Tier 3: Ground-State Resolver / QPU Escrow**
- Hardware: Scarce QPUs, classical exhaustion first
- Execution: Asynchronous, Proof-of-Demand mesh aggregation, stateless escrow
- Power: Variable based on QPU availability
- Memory: Stateless operations only

### 2.2 Telemetry-Aware Dispatching

The HardwareTierDispatcher must dynamically route execution based on:
- Physical capability profiles (CPU cores, GPU memory, NPU availability)
- Real-time power telemetry (current power draw, battery percentage)
- Thermal state (CPU/GPU temperature, thermal throttling status)
- User preferences (performance vs. power conservation)

### 2.3 Execution Strategies

- **SIMDOnly:** Stack-allocated vector processing via ARM NEON / x86 AVX2
- **HybridCPUNPU:** Hybrid CPU/NPU execution with minor heap buffering
- **GPUVRAM:** Direct VRAM mapping with parallel Texture Mapping Units
- **QPUAsync:** Asynchronous quantum context resolution via mesh aggregation
- **Throttled:** Power/thermal-constrained execution mode

## 3. Zero-Heap Execution Constraints

### 3.1 Hot Path Requirements

- **No Heap Allocation:** Vec, HashMap, Box allocations prohibited in execution paths
- **Caller-Supplied Buffers:** All output buffers must be provided by the caller
- **Stack Allocation:** Use `[T; N]` arrays for local state
- **O(1) Operations:** Graph traversal replaced by geometric bounding-box queries

### 3.2 Buffer Management Pattern

```rust
// 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

- **42MB Sentinel:** Any single execution pass must stay within 42 MB of memory
- **Stack Allocation:** Local state must fit within stack limits (typically 8 MB)
- **No Dynamic Growth:** Buffer sizes must be known at compile time

## 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:
- GPU kernel: `crates/qualia-core-db/src/shaders/tensor_volume.wgsl` (`metric_distance`).
- CPU reference (GPU-independent ground truth): `tensor::volume_gpu::cpu_tensor_search_into`.
- Substrate CPU fallback: `Q42TensorView::tensor_search_into` (uses `full_distance`).

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:
- Map topological shape from one w to correlated coordinate in another w
- Example: "Mobility Impairment" (w=0) → "Disability Accommodation Rights" (w=1)
- Pure geometric matrix operations without complex Rust logic

## 5. Ground-State Resolver (GSR) Integration

### 5.1 QUBO Problem Format

```rust
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

```rust
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:

- **Quantum Context:** Extract from metadata or context field
- **Topological Class:** Extract from context or metadata
- **Manifold Index:** Extract from context field bits [0..55]
- **Semantic Coordinates:** Extract from object field or use hash-based embedding
- **Temporal State:** Extract from metadata Lamport clock
- **Spectral Payload:** Extract from metadata modality payload

### 6.2 Tensor Metadata

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

### 6.3 Query Operations

- **Tensor Search:** Find NQuins within geometric distance threshold
- **Temporal Query:** Query state at specific time t with tolerance
- **Manifold Query:** Search across multiple w domains with spatial constraints

## 7. Cryptographic Integration

### 7.1 Sanctuary Lane Cryptography

- **PBKDF2 Key Derivation:** 48-byte derivation [32 bytes cipher key | 16 bytes volume root tweak]
- **Implicit Nonce Derivation:** XOR-based nonce derivation using volume tweak and chunk index
- **AEAD Ciphers:** AES-256-GCM integration with zero-heap guarantees

### 7.2 Zero-Heap Cryptographic API

```rust
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

- `tensor-10d`: Enables 10D tensor coordinate system and all tensor operations
- `tensor-gpu`: Enables GPU acceleration (CUDA/Metal/Vulkan)
- `tensor-npu`: Enables NPU acceleration (Neural Engine)
- `sanctuary-crypto`: Enables sanctuary lane cryptography

### 8.2 Build Configuration

```bash
# 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

- **Single Query:** < 10ms on Tier 0, < 1ms on Tier 2
- **Batch Processing:** 1000 queries/sec on Tier 0, 100,000 queries/sec on Tier 2
- **Memory Footprint:** < 100MB active working set on Tier 0

### 9.2 Power Consumption

- **Tier 0 (Idle):** < 1W
- **Tier 0 (Active):** < 5W
- **Tier 2 (Idle):** < 10W
- **Tier 2 (Active):** < 50W

### 9.3 Storage Efficiency

- **Quantization Ratio:** 4:1 (INT8 vs FP32)
- **Compression:** LZ4 for container storage
- **Memory Mapping:** Zero-copy load for execution

## 10. Security & Sovereignty

### 10.1 Cryptographic Provenance

- **σ Channel:** Encodes cryptographic origin
- **Sanctuary Lane:** Verified encrypted storage
- **Mesh Verification:** Trust scores for unverified sources

### 10.2 Zero-Heap Security Benefits

- **No Heap Spraying:** Eliminates memory corruption attack surface
- **Predictable Memory:** Easier security auditing
- **Sandbox Safety:** Stack allocation limits attack scope

### 10.3 Sovereign Data Assets

- **Information Banking:** Pre-processed, mathematically dense
- **Local-First:** No cloud dependency for inference
- **Offline Capable:** Full functionality without network

## 11. Compliance & Standards

### 11.1 Data Sovereignty

- **GDPR Compliance:** Local-first architecture ensures data never leaves jurisdiction
- **HIPAA Compliance:** Sanctuary lane encryption for medical data
- **Accessibility:** Multi-cultural tokenisation layer for oral traditions

### 11.2 Interoperability

- **RDF Integration:** Seamless mapping from NQuin to Tensor10D
- **SPARQL Support:** Query tensor data via SPARQL extensions
- **Web Standards:** Compatible with Semantic Web technologies

## 12. Implementation Status

### 12.1 Completed Components

- ✅ Phase 1: Cryptographic infrastructure (PBKDF2, nonce derivation, AEAD)
- ✅ Phase 2: 10D tensor foundation (all dimensions implemented)
- ✅ Phase 2.7: GSR Integration (async QPU communication, classical fallback)
- ✅ Phase 2.8: Hardware-Tier Dispatching (telemetry-aware routing)
- ✅ Phase 2.9: Zero-Heap Guarantees (Vec allocations resolved)
- ✅ Phase 2.10: Q42 Volume Integration (NQuin to Tensor10D bridge)

### 12.2 Future Work

- ⏳ Pipeline implementation for ingestion phase
- ⏳ VM enhancement with tensor opcodes
- ⏳ Graph theory resolution via pre-computation
- ⏳ Performance optimization and benchmarking

## 13. References

- **Q42_PIPELINE_CONTAINER_SPEC.md:** Comprehensive architectural specification
- **CLAUDE.md:** AI agent orientation and architectural boundaries
- **AGENTS.md:** Multi-agent collaboration ecosystem coordination
- **ARCHITECTURE.md:** Qualia-DB architecture overview

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