xkernel

Invariant Deterministic Kernel (k = 1, Boolean Closure)

xkernel is a minimal, invariant execution kernel.

It defines:

• a single admissible action quantum (k = 1),
• deterministic replay semantics,
• boolean closure against a target state,
• canonical execution hashing,
• and tamper-evident receipts.

xkernel is NOT a runtime engine, simulator, or pattern system. It has NO kernel object, NO mutable configuration, and NO hidden state.

The kernel is the law. Executions and receipts are the artifacts.

What xkernel guarantees

• Determinism Replaying the same execution always yields the same final state.

• Admissibility Any step with action != 1 is invalid.

• Closure Closure is a boolean: an execution either closes to a target state or it does not.

• Canonical identity Executions and receipts have stable, content-addressed identifiers:

  • xk:sha256:... for executions
  • xr:sha256:... for receipts

• Tamper evidence Any mutation of execution or receipt content changes its hash and fails verification.

What xkernel does NOT do

• No engine orchestration
• No filaments, fibers, or bundles
• No pattern detection or lenses
• No identity, signing, or trust semantics
• No backward compatibility with v1

Those concerns belong in downstream systems.

Installation

pip install -e .

Command-line interface

xkernel ships with a strict reference CLI.

xkernel --help

Available commands:

• validate Validate execution admissibility and replay
• hash Compute execution content address (xk:sha256:...)
• receipt Emit receipt JSON for an execution (optional target closure)
• verify Verify receipt integrity against an execution
• receipt-hash Compute receipt content address (xr:sha256:...)

Example:

xkernel validate exec.json
xkernel hash exec.json
xkernel receipt exec.json --target target.json > receipt.json
xkernel verify receipt.json exec.json

Core model (conceptual)

StateVector  : immutable integer coordinate vector
Step         : delta + action (must equal k = 1)
Execution    : init + ordered steps + final
Closure      : boolean equality to a target under replay
Receipt      : canonical record of execution + closure

There is no kernel instance. Correctness is enforced structurally.

Testing

pytest

All tests assert invariants, determinism, hashing stability, and tamper detection.

Versioning

v2.0.0 introduces invariant semantics and removes all v1 engine concepts. There is no backward compatibility.

License

MIT - see LICENSE.