Finite correction
With compatible edit atoms and complete intervals, a representation cell permits a common correction exactly when every required edit is permitted throughout the cell.
Read the criterion and assumptionsResearch overview · Formal systems
ETI foundations
What must a system remember to correct a decision when its evidence changes?
Epistemic Transition Integrity studies correction-sufficient state: the information needed to make a valid revision. Explore the mathematical scope and worked example below, or try the interactive illustration.
The question
Two records can support the same answer yet require different corrections after a source is withdrawn. If one record has an independent supporting source and the other does not, saving only the answer loses a distinction needed for revision.
ETI asks which distinctions a retained state must preserve. The formal models assume specified evidence and rules; they do not establish source trustworthiness or record accuracy.
Mathematical scope
Stochastic repair
Unrestricted additive repair loss gives interval-form optima. Preserving optimality for every positive cost vector requires the posterior-impact signature, under stated common-support assumptions.
Compare the expected-loss exampleSequential revision
Fixed-current-state encodings also require transition congruence: deterministic exogenous transitions, without additional history, a clock, or reference-state rereads.
Read about sequential maintenanceGrounded support
Fixed admitted positive-Horn rules distinguish alternative support from ungrounded cycles. This is not a general model of uncertain or conflicting natural-language evidence.
Explore alternative supportThe contribution is a correction-specific formulation and integration of established mathematical machinery.
Decision-theoretic illustration
Worked example
Two equally likely contexts share one uninformative signal. For one artifact, keeping an affected artifact active costs 1; reopening an unaffected artifact costs 3. The probability that the artifact is affected is ¼ in context L and ¾ in context H.
| Context | Impact probability q | Keep: q | Reopen: 3(1 − q) | Optima |
|---|---|---|---|---|
| L | ¼ | ¼ | 9/4 | Keep |
| H | ¾ | ¾ | ¾ | Keep or reopen |
Keeping is optimal in both contexts: average loss ½, equal to the full-information Bayes risk. A “reopen on ties” convention needs two representation codes without improving that risk. Preserving some optimum differs from reproducing a chosen policy; zero regret does not imply zero loss.
In this example, distinguishing the two contexts is unnecessary if the goal is simply to choose an optimal action. It becomes necessary if the system must follow the particular tie-breaking policy.
Evidence and open questions
Formal research
The underlying manuscript develops assumption-bound proofs, counterexamples, and reported finite reconstruction checks. Historical validation code is not fully recovered; the browser example is a separate explanatory implementation.
Inspect the public finite modelOpen empirical work
Study 14’s competitive retriever and full constructor/scheduler have not yet been frozen for evaluation. Construction accuracy, cost, and comparative performance remain to be tested.
Read the Study 14 designAbout this overview
The explanations and demonstrations linked here are publicly available. The full ETI manuscript is not currently published; this page is a research overview, not a PDF download.
Underlying manuscript record
Epistemic Transition Integrity: Foundations of Correction-Sufficient State and Sequential Revision. ETI-SYNTHESIS-2026-09-07.1, 7 September 2026. The worked example above corresponds to Example 5.3.
Original manuscript SHA-256: e87a88c4dedbd9d53978d4bb90dbfe5186aacc007950dc5a8d87a5b2a31e2578