Thesis
Reproducibility is not about determinism, tooling, or repeatable execution.
It is the condition under which correctness remains derivable from invariant space across time.
A system is reproducible when the relationship between its enforced constraints and its outcomes can be re-established under comparable conditions.
When this relationship holds, correctness can be demonstrated, questioned, and revised.
When it does not, correctness can only be inferred from results.
Without reproducibility, a system may function.
But it cannot justify itself.
1. Re-Deriving Invariant Space
Reproducibility is the ability to re-derive outcomes from enforced constraints.
It is not merely the ability to re-run code or replay inputs. Those are techniques. Reproducibility is structural.
A reproducible system preserves:
- The declared invariant space.
- The translation surfaces through which that space is enforced.
- The conditions under which constraints produced outcomes.
When behavior is questioned, the system can return to the invariant space that governed it and show why the outcome occurred.
If the effective invariant space cannot be reconstructed from declared inputs, then invariant space exists in fact but not in representation.
At that point, the system may execute — but it is no longer knowable.
2. When Success Masks Drift
Non-reproducible systems rarely fail loudly.
More often, they succeed.
Outputs remain plausible.
Metrics trend upward.
Incidents are rare.
But when invariant space cannot be reconstructed, correctness is inferred from outcomes rather than derived from constraint.
The question shifts from:
“Under what constraints did this occur?”
to:
“Did it work?”
As long as the second remains affirmative, the first is treated as optional.
Over time, execution paths become unrecoverable. Intermediate state is lost. The chain linking constraint to outcome dissolves.
The system’s history collapses into results without rationale.
When behavior is questioned later, there is no stable invariant space to return to — only precedent.
By the time explanation is demanded, the causal chain has already vanished.
Nothing has failed.
But the system can no longer answer for itself.
3. Substitution Without Failure
When reproducibility erodes, systems do not immediately become incorrect.
They substitute signals for structure.
Stability stands in for validity.
Consistency stands in for explanation.
Historical success stands in for constraint alignment.
These signals often correlate with correctness. That is what makes them dangerous.
Confidence migrates from enforced invariant space to observed coherence.
The system appears mature. Variability decreases. Outputs stabilize.
But correctness is no longer demonstrable.
It is assumed.
The effective invariant space continues to govern behavior — but it can no longer be reconstructed from declared constraints.
Authority migrates from structure to precedent.
4. Reproducibility and Epistemic Authority
Reproducibility is the temporal preservation mechanism for epistemic authority.
Epistemic authority exists when correctness is asserted by enforced invariants rather than inferred from outcomes.
Time erodes representation.
Dependencies evolve. Environments shift. Context drifts.
If invariant space cannot be reconstructed under these shifts, epistemic authority degrades into historical memory.
Correctness becomes anecdotal.
Reproducibility prevents that degradation.
It ensures that invariant space remains recoverable — not merely present in fact, but encoded in representation.
Conclusion: The Boundary
Reproducibility is not a quality attribute.
It is the condition that preserves knowability across time.
When reproducibility erodes, systems do not immediately become wrong.
They become unverifiable.
Outputs remain plausible.
Behavior remains coherent.
Confidence persists.
But the path from constraint to outcome has dissolved.
Once invariant space exists only in fact and not in representation, correctness can no longer be derived from structure.
Beyond this boundary, systems do not merely risk error.
They risk losing the ability to know whether they are correct.