Fault-Tolerant Observer Overlaps

Finite observer domains can form stable records while disagreeing locally, suffering false triggers, or receiving correlated disturbances. This paper develops a thermodynamic account of how overlapping domains can preserve a shared record sector without a central corrector. The mechanism is not a digital error-correcting code: no bit string, encoding map, parity-check circuit, decoding algorithm, or external controller is assumed. Instead, physical overlap supplies consistency pressure, independent evidence supplies correction direction, and detailed-balance dynamics supplies the irreversible cost of reconciliation. Pairwise overlap mismatch is represented by the minimum relative-entropy cost of reconciling two restrictions with a common state, equal to twice the classical or quantum Jensen-Shannon divergence. Near agreement this cost is governed by the Bogoliubov-Kubo-Mori metric. A stability bound relates horizontal overlap strain to record-channel information loss when retention is close to a BKM-orthogonal projection. For memoryful records, the same geometry lifts to finite process histories through conditional expectation of the path score. Classical and quantum conditional-response models identify the stored correction burden as relative-entropy free energy, with its decay governed by independently computed entropy production. In reciprocal networks, overlap alone enforces consensus rather than truth; fault tolerance appears only when evidence channels are sufficiently diverse. An exact graph-theoretic bound shows that local false-island protection is controlled by weighted boundary expansion, while the global sector is controlled by total evidence. Finite temperature and record barriers produce a bounded operating window between under-protection and excessive rigidity. Version 1.1 incorporates downstream validation from a companion finite-regulator study. A connected overlap atlas can collectively reconstruct Jacobson’s equilibrium equation of state even though each individual observer is rank deficient. This does not turn graph protection into a derivation of gravity: record-sector protection and null-direction tensor reconstruction are distinct roles of overlap, and neither internal consistency nor overlap consensus authenticates source truth without independent provenance.