The word has a clock.
A supplied constant Hamiltonian delivers the finite programme at its terminal address. Positive rational metrics give a weighted-path Hodge representation. The clock, padding and complete return are part of the accounting.
Coherent histories through the window
At intermediate time the clock is a superposition of prefix addresses. Each address carries its complete work, state history and donor/receipt prefix. Selecting a prefix below inspects that branch; it does not model a measurement.
Clock probabilities by address
Geometry and resource accounting
Equal clock dimensions do not identify the cyclic step with this Hamiltonian. Identity padding changes the address count, spectrum and variance. It changes no terminal payload and supplies no extra donor.
The native comparison is now testable
Fix a native complex, chain basis, positive metric and complete retained environment. Supply a source-defined isometry E for the clock, work, memory and donor bank. Then compute the operator residual norm(HnativeE − EHprogramme); propagation discrepancy is bounded by |t| times that residual.
The full even clock with length at least four cannot embed exactly in a unit-metric single tetrahedron or identical copies: it has multiple positive frequencies, while that operator has only frequency 2. Other weighted or glued source classes need their own admission proof.
At κt=π the complete closed programme returns projectively, including its outgoing records. Protected export requires a separately supplied capture/isolation mechanism. Human review, physical calibration and native acquisition remain open.