Keep the calibration with the details.
The one-step selector preserves the old code. Across two steps, inherited detail norms can change if the final complement receives fresh unit calibration. A retained hierarchy makes the same sequence consistent under regrouping.
Inspect the same retained detail state
Choose two opposite oriented descendant contributions whose coarse retractions cancel. Its first-level squared norm is2. The second subdivision has degree-dependent Gram factors1,2,6,24.
Adding a coarse unit vertex leaves its absolute stock1 under both metrics. The normalized coarse fraction changes because the full retained denominator changes. These are exact quadratic receipts, not measured probabilities or instability bounds.
Retain a hierarchy of calibrated components
Write the final chain as x=S20c+S21z1+z2: old coarse state, inherited first-level detail and newest detail. The decoding maps are R20, Q10R21 and Q21. They reconstruct every final chain exactly.
||x||²=cᵀG0c+||z1||²+||z2||²
This is the sequential calibrated norm. A regrouped construction must transport both detail pairings. Replacing them with ||S21z1+z2||² is a fresh final-coordinate convention and generally changes the result.
The induced composite detail form is positive on the complement but semidefinite on the ambient space. It kills the original coarse image. Keeping that distinction makes the metric completion exact.
Coarse observable pullback composes exactly: K20=R21ᵀ(R10ᵀD_U R10)R21. It does not select the full detail metric. The complete sequential receipt has15 coarse outcomes plus two retained detail outcomes.
Count the whole retained carrier
Levels0–2 have explicitly regenerated sparse maps. Later rows are exact strict-flag counts; their full matrices are not built. At level2, the2745 directions contain15 coarse,134 inherited detail and2596 new detail directions.
These are direct-sum chain coordinates, not qubits or tensor donor banks. A finite whole-chain budget limits this full tower. New coordinates, clocks, preparation, readout and outgoing-record/reset resources need their own implementation.
What remains a source question?
The transported hierarchy is consistent under regrouping the same retained sequence. It does not prove covariance across different subdivisions, retractions or detail calibrations. A source law must select the history and any detail excitations.
Refinement of a purely coarse state preserves its evolution and leaves detail amplitudes zero. Growth/clustering preferences and event times are not generated by that embedding. Physical/local observation, alternative-history comparison and independent human review remain open.