1. Introduction
Inference over time requires stable reference.
Any system that attempts to infer, predict, or generalize from historical state assumes that the state it observes has not been altered by the process of inference itself.
When this assumption is violated, learning collapses.
This paper formalizes the limits of inference in systems that lack canonical state.
2. Inference Requires Fixed Substrate
Inference operates on state.
For inference to be meaningful, the state being consumed must satisfy the following conditions:
- It must be append-only
- It must preserve temporal ordering
- It must preserve provenance
- It must not be rewritten by interpretation
If state is mutable, inference cannot distinguish:
- Observation from revision
- Error from correction
- Cause from effect
Inference over mutable state is undefined.
3. Learning Under Rewrite
When state is rewritten, learning becomes self-referential.
Later interpretations overwrite earlier assertions. Subsequent inference consumes the rewritten state rather than the original observation. The system no longer learns from reality, but from its own prior outputs.
This produces convergence without grounding.
The system may become internally consistent while diverging from the conditions that generated the data.
4. Temporal Collapse
Inference over time depends on the distinction between:
- When an event occurred
- When knowledge of that event was asserted
If this distinction is lost, temporal reasoning collapses.
Late-arriving knowledge becomes indistinguishable from revision. Correction becomes indistinguishable from fabrication. Models trained on such state cannot represent causality.
They learn sequences, not time.
5. Authority and Admissibility
Inference systems do not determine what is admissible as truth.
Admissibility is determined by valid assertion under authority. Inference may propose conclusions, but it does not confer authority on those conclusions.
When inference outputs are treated as admissible state without explicit authority, authority migrates silently to the inference mechanism itself.
This collapse is structural, not accidental.
6. Derived Outputs Remain Derived
All outputs of inference are derived.
They may be useful.
They may be correct.
They may influence future action.
They do not become canonical state unless asserted under authority as new assertions, with preserved provenance and time.
Feedback that bypasses this boundary rewrites history.
7. Disagreement as Constraint
Preserved contradiction constrains inference.
When disagreement and uncertainty are retained in canonical state, inference systems must contend with ambiguity. Calibration remains possible. Overconfidence is bounded.
When contradiction is removed by rewrite or normalization, inference converges prematurely.
The absence of disagreement is not evidence of correctness. It is evidence of suppression.
8. Placement of Inference
Inference must remain downstream of canonical state.
If inference is placed upstream, it modifies the substrate it consumes. Feedback loops form. Error compounds invisibly.
Downstream placement ensures that inference may fail without corrupting state.
Failure remains local. Recovery remains possible.
9. Invariants
The following invariants govern inference:
- Inference consumes canonical state
- Canonical state is not modified by inference
- Inference outputs are derived
- Authority is not conferred by inference
- Temporal ordering is preserved
- Preserved contradiction constrains inference
- Inference must remain downstream of canonical state
Violating any invariant renders inference unreliable.
10. Discussion
Inference does not fail because it is insufficiently powerful.
It fails when it is applied to state that cannot support it.
Canonical state does not improve inference.
It makes inference possible.
Systems that attempt learning without stable substrate will converge, but not on reality.