MD66 established continuity as a lineage relation linking admissible trajectories under a differentiated identity coordinate across discontinuous spacetime.
MD67 addresses a different question.
The problem is no longer continuity. The problem is restoration.
A system may preserve continuity while repeatedly departing from its intended trajectory. The relevant inquiry therefore becomes: What allows reliable return after displacement?
This thesis proposes that coherence is not the absence of error, deviation, uncertainty, or perturbation. Coherence is the structural capacity for reliable restoration toward an identity coordinate following displacement.
A navigation-domain baseline is introduced to distinguish three operational regions: Coherent, Restoration, and Incoherent.
The central hypothesis is that restoration depends not only upon distance from a destination but upon accessibility of the governing coordinate itself.
The paper defines a provisional coherence object C(θ, I*) where interpretation θ remains coupled to an identity coordinate I* through bounded restoration dynamics. Boundary conditions are specified. Falsification pathways are specified. Empirical verification remains open.
A wrong turn is not incoherence.
A delay is not incoherence.
A setback is not incoherence.
Systems frequently depart from their intended trajectory while retaining the ability to recover.
The relevant distinction is therefore not between success and failure.
The relevant distinction is between recoverable displacement and loss of reliable return.
The object of inquiry becomes restoration.
Consider a traveler moving toward a destination.
When the destination remains visible and familiar, corrective action remains direct. Errors may occur. Recovery remains straightforward because the destination coordinate remains accessible.
When the destination is obscured, externally mediated, or uncertain, corrective action becomes increasingly interpretive.
The traveler no longer asks: "How do I return?"
The traveler asks: "Am I moving toward the correct destination?"
Recovery cost rises. Oscillation appears. Decision overhead expands. Destination uncertainty becomes part of the problem itself.
This distinction motivates the formal study of coherence.
Coherent Region: The governing coordinate remains accessible. Restoration remains bounded. Return is reliable. Temporary deviations do not threaten system integrity.
Restoration Region: Displacement has occurred. Correction requires effort. The destination remains reachable. Recovery remains structurally possible.
Incoherent Region: The governing coordinate becomes inaccessible. Oscillation dominates correction. Restoration cost diverges. Reliable return is lost.
A wrong turn is not incoherence. Loss of destination accessibility is incoherence.
Let I* denote the identity coordinate. Let θ denote interpretation.
Define C(θ, I*) as the structural capacity of interpretation to restore alignment with the governing coordinate following perturbation.
Coherence is therefore not measured by perfect alignment.
Coherence is measured by restoration capability.
A coherent system may experience error. An incoherent system loses reliable return.
The deepest claim of the framework concerns restoration dynamics.
A coherent system is not defined by perpetual effort.
A coherent system eventually enters a restoration regime in which correction becomes progressively self-sustaining.
This provisional region is designated K_auto — the Sabbath Basin.
Within this basin: restoration cost decreases, recovery velocity increases, oscillation decreases, destination accessibility increases.
The basin does not eliminate perturbation. The basin preserves return.
The defining characteristic of the Sabbath Basin is not stillness. It is reliable restoration.
H1 — Restoration Compression: Repeated successful restoration decreases future restoration cost. Formally: dT_restore / dn < 0, where T_restore is restoration time and n is successful restoration cycle count.
H2 — Destination Accessibility: Restoration dynamics cannot necessarily be reduced to skill accumulation, resource accumulation, or confidence accumulation. An additional variable may be required: V_goal, representing destination accessibility.
H3 — Restoration Memory: If restoration cost decreases while skill, resources, and confidence remain controlled, then restoration dynamics possess memory-like properties requiring additional explanation. This proposed mechanism remains hypothetical. No claim of verification is made.
The framework is intended to be challengeable.
MD67 fails if repeated restoration cycles demonstrate no measurable reduction in future restoration cost once competing variables are controlled.
The framework further fails if destination accessibility provides no explanatory value beyond existing variables.
Either result requires revision.
MD66 addressed continuity. MD67 addresses coherence.
MD66 asks: What survives discontinuity? MD67 asks: What returns after discontinuity?
Continuity concerns persistence. Coherence concerns restoration.
The two frameworks are complementary but distinct.
Status: CONSTRUCT
Domain: Navigation Baseline
Boundary Conditions: Defined
Falsification Path: Defined
Empirical Verification: Open
Research Program: Active
Coherence is not the absence of error.
Coherence is the capacity for reliable return.
A system remains coherent not because it never departs from its trajectory, but because the governing coordinate remains accessible after perturbation.
The central claim of MD67 is therefore simple: A coherent system preserves reliable return.
The geometry of coherence is the geometry of restoration.