TCFC-01 — Witnessed Continuation under Finite Capacity: Temporal Witness, Re-description, and the Transmission of Trace

This paper introduces Witnessed Continuation under Finite Capacity as the first record in the Trace–Continuation under Finite Capacity (TCFC) series of the Synkyria Project. Previous Synkyrian work established that accountable finite-horizon viability requires admissibility–execution coupling and boundary-legible witness. This paper isolates a further structural role of witness: not only as a condition of accountability for boundary conduct, but as a condition for the continuation of finite forms across time and scale. The paper introduces the notion of an admissibility-relevant trace: a component of a finite-capacity system’s history that may affect future viability while remaining externally non-legible. It proves an unwitnessed-trace indistinguishability result: if such a trace is not made witness-legible in the exported record, no external verifier can distinguish admissible continuation from continuation carrying hidden admissibility-relevant load. It follows that any trace affecting future admissibility must either be witnessed, safely discharged, or persist as unreviewable burden. The result is extended to scale transition. When a finite form can no longer continue under its current description, accountable continuation requires witness-consistent re-description: the form may change scale, but its boundary-relevant trace must remain legible. The paper characterizes witness-consistent re-description by a factorization condition and extends the same pattern to temporal witness decay, introducing review-safe coarsening as the condition under which witness compression remains accountable. The paper also develops the relation between witness and operational time. It proves that two configurations may coincide in clock time and present state while differing operationally because prior admissibility-relevant traces remain active. A disciplined human-scale translation is included, where lineage, name, memory, grief, and inherited burden are treated not as psychological diagnoses or biological mechanisms, but as phenomenological surfaces of the same finite-capacity grammar. The central thesis is that witness is the operational-temporal structure through which finite forms continue without pretending to remain identical. Witness does not make the finite immortal. It lets the finite end without becoming an unreviewable burden for what comes next. Series: Trace–Continuation under Finite Capacity (TCFC)Series code: TCFC-01