Shared Clocks and Historical Targets

An appendix to MIND and predictive acquisition

Reports can disagree when read as descriptions of one instant and still fit a single changing history. This appendix to The MIND and Acquirable Predictive Models separates those questions, then asks what surviving archives can tell us after the current body has reset.

It is a compact synthesis and worked application, not a standalone new research theory. Finite-state reachability, temporal constraints, variable elimination and adaptive test selection are established methods. The appendix retains their attribution and makes no historical-priority claim.

Reports from one module share one clock

MIND’s static parity obstruction concerns a common time slice. With acquisition times declared, reports must instead fit a trajectory obeying the dynamics. A compatible trajectory is an admissible explanation, not evidence that a particular history occurred or that clock error caused the discrepancy.

All reports from a module use one constant clock offset. Giving every record its own offset can create false explanations: a two-bit example has no valid shared-offset trajectory but 18 relaxed offset/trajectory pairs. A complete-state distance criterion gives an elementary exact test under its stated hypotheses.

The elimination construction keeps body slices and each clock for its full required lifetime. Its bounds remain exponential in body width and the number of simultaneously retained clocks. Small clock uncertainty alone does not imply general scalability.

A historical target costs less than a full reconstruction

In the declared eight-history example, the current body eventually becomes 0000. Two passive archives retain old flags, and a trusted clock-context port determines which flag is the target. The archives and reference already exist; creating them is a common sunk cost.

Each serialized query costs seven wire bits and eight rounds. Asking the clock-context port and then the relevant archive attains the exact adaptive worst-case optimum of 14 bits and 16 rounds. A fixed identifying selection needs all three informative ports, for 21 bits and 24 rounds. A fixed order with answer-dependent stopping still has worst-case depth three.

The advantage is adaptive versus fixed query selection. Centralized and distributed controllers with the same ports, input ownership and communication rights attain the same optimum. The result is not a universal network or information bound.

Missing access is not necessarily erased information

Clock and current-body observations alone cannot recover a flag they never distinguish. If a remote archive survives, however, it belongs to the complete physical state. An inaccessible archive is an access restriction, not proof that all information was erased.

This distinction illustrates the existing erasure result in Diagnosing While Repairing. Its destructive repair-order separation remains a different result. The matched architecture comparison also complements Reflective Self-Models, where external-observer communication is idealized as free.

Read and reproduce

Read the complete appendix online, download the unchanged five-page PDF, or download the approved source and verification package.

The reader preserves the complete source prose, 107 mathematical expressions and ten references. Its two-row target definition is complete, named operators use proper MathML tokens, and source TeX is attached to every expression. The original Markdown, LaTeX, PDF and ZIP are unchanged.

Fresh runs of three original checkers and the separately implemented iteration-3 checker reproduce the preserved output bytes exactly. These include all eight declared histories, all sixteen port selections, 4,096 version-space/selection comparisons and 1,020 version-space/depth comparisons. Finite enumeration corroborates the examples; it does not replace the analytical arguments.

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The original package retains its earlier not-uploaded release wording; site publication is recorded separately. The PDF is untagged and specialist screen-reader testing remains outstanding. No additional reuse license is granted by this release. B-Theory here means the Being/Becoming programme, not the philosophical B-theory of time.