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.

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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.

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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.

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Installation

pip install -e .

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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

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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.

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Testing

pytest

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

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Versioning

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

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License

MIT - see LICENSE.