t81-tensor-ops

name	t81_tensor_ops
description	Perform deterministic tensor operations with ternary precision and policy enforcement
metadata	{"openclaw":{"os":["darwin","linux"],"requires":{"bins":["t81"]}}}

T81 Tensor Operations Skill

This skill performs deterministic tensor operations using T81's ternary arithmetic with guaranteed bit-identical results and policy enforcement.

Usage

When the user needs to perform mathematical tensor operations with deterministic guarantees, use this skill for ternary-precision computations.

Commands

Basic tensor operations:

tensor-math <operation> <tensor_a> <tensor_b> [--output <output_file>] [--precision ternary|binary]

Tensor reshaping:

tensor-reshape <tensor_file> <new_shape> [--output <output_file>]

Tensor validation:

tensor-validate <tensor_file> [--check-integrity] [--check-determinism]

Tensor conversion:

tensor-convert <tensor_file> [--to-format t81w|safetensors|gguf] [--output <output_file>]

Tensor statistics:

tensor-stats <tensor_file> [--detailed] [--histogram] [--output <stats_file>]

Batch operations:

tensor-batch <operation> <tensor_dir> [--recursive] [--output-dir <dir>]

Examples

# Add two tensors with ternary precision
tensor-math add tensor_a.t81w tensor_b.t81w --output result.t81w --precision ternary

# Reshape tensor to new dimensions
tensor-reshape model.t81w "[1,256,256,3]" --output reshaped.t81w

# Validate tensor integrity and determinism
tensor-validate weights.t81w --check-integrity --check-determinism

# Convert tensor format
tensor-convert model.gguf --to-format t81w --output model.t81w

# Get detailed tensor statistics
tensor-stats layer_weights.t81w --detailed --histogram --output stats.json

# Batch process all tensors in directory
tensor-batch normalize ./tensors/ --recursive --output-dir ./normalized/

Supported Operations

Arithmetic Operations:

• add - Element-wise tensor addition
• subtract - Element-wise tensor subtraction
• multiply - Element-wise tensor multiplication
• divide - Element-wise tensor division
• dot - Dot product / matrix multiplication
• cross - Cross product (for 3D tensors)

Unary Operations:

• abs - Absolute value
• neg - Negation
• sqrt - Square root
• exp - Exponential
• log - Natural logarithm
• normalize - L2 normalization

Comparison Operations:

• equal - Element-wise equality
• greater - Element-wise greater than
• less - Element-wise less than
• max - Element-wise maximum
• min - Element-wise minimum

Aggregation Operations:

• sum - Sum of all elements
• mean - Mean of all elements
• max - Global maximum
• min - Global minimum
• std - Standard deviation

Precision Modes

Ternary Precision:

• Balanced ternary representation (-1, 0, +1)
• Zero floating-point drift
• Bit-identical results across platforms
• Optimal for verifiable inference

Binary Precision:

• Standard binary floating-point
• Compatible with external formats
• Faster for non-critical computations
• May have minor precision differences

Output Format

Operation Result:

{
  "status": "success",
  "operation": "add",
  "tensor_a": "tensor_a.t81w",
  "tensor_b": "tensor_b.t81w",
  "output": "result.t81w",
  "timestamp": "2026-04-04T15:30:00Z",
  "precision": "ternary",
  "properties": {
    "shape": "[256,256]",
    "dtype": "ternary_float",
    "size_bytes": 262144,
    "determinism_hash": "CanonHash81..."
  },
  "validation": {
    "integrity": "passed",
    "determinism": "verified",
    "policy_compliance": "approved"
  }
}

Tensor Statistics:

{
  "tensor_file": "weights.t81w",
  "timestamp": "2026-04-04T15:30:00Z",
  "shape": "[512,512]",
  "dtype": "ternary_float",
  "statistics": {
    "min": -1.0,
    "max": 1.0,
    "mean": 0.0,
    "std": 0.577,
    "zeros": 134217728,
    "positives": 67108864,
    "negatives": 67108864
  },
  "histogram": {
    "-1.0": 67108864,
    "0.0": 134217728,
    "1.0": 67108864
  },
  "provenance": {
    "tensor_hash": "CanonHash81...",
    "creation_time": "2026-04-04T14:15:00Z",
    "last_modified": "2026-04-04T15:30:00Z"
  }
}

Determinism Guarantees

• Bit-identical results: Same operation produces identical outputs
• Platform independence: Results consistent across different systems
• Temporal stability: Results don't change over time
• Policy consistency: Operations respect governance constraints

File Formats

Input Formats:

• .t81w - T81 native ternary tensor format
• .safetensors - Hugging Face safe tensors
• .gguf - GGUF format (limited support)
• .npy - NumPy arrays

Output Formats:

• .t81w - Native T81 format (recommended)
• .json - Metadata and statistics
• .csv - Tabular data for 1D tensors

Error Handling

• Shape mismatches: Detailed dimension compatibility errors
• Type errors: Precision and format validation
• Memory errors: Resource limit handling
• Policy violations: Operation restriction enforcement

Performance Characteristics

Ternary Advantages:

• Multiplication-free dot products
• Constant-time negation
• Zero floating-point drift
• Energy-efficient computation

Optimization Features:

• SIMD vectorization where available
• Memory-mapped operations for large tensors
• Parallel processing for batch operations
• Cache-friendly memory layouts

Security Notes

• All operations subject to Axion policy validation
• Tensor integrity verification before operations
• Complete audit trail for tensor modifications
• Deterministic results prevent manipulation

Integration

This skill wraps T81's tensor operation engine:

t81 tensor <operation> <tensor_a> <tensor_b> --output <output> --precision ternary --json