Rey.BEng 15th September 2026
Title:
A Practical Route — With the Clock Still Continuous
Chen, Serna & Sokolov, and the Rest Time Unit Their Framework Still Needs
The Future Begins
Chen, Serna & Sokolov (arXiv:2609.13098) write that frozen natural orbitals, with basis-set and thermodynamic-limit extrapolations, “provide a practical route to high-accuracy correlated calculations in periodic systems.”
Yes. They do.
Ground-state FNO, state-specific FNO, and state-averaged FNO cut the virtual space from a perturbative density matrix, put MP2, ADC and EOM-CC on periodic (k)-meshes in PySCF, and recover canonical correlation energies, equations of state, gaps and quasiparticle bands at a fraction of the cost. That is real engineering. Ace has no quarrel with the route as a route.
The limitation is the clock they keep.
What remains monostable
After the orbitals are frozen, the crystal is sent to the thermodynamic limit. That limit is an infinite, evenly ticking observational continuum. Time in the electronic Hamiltonian is either absent or a continuous parameter. The freeze is a lock on basis, not a lock on duration.
High accuracy in that frame is high accuracy of the continuous second. At macro scale — bulk modulus, room-temperature gap as a number on a datasheet — that clock is often justified. The laboratory does not resolve the tick. The limitation will continue wherever the physics is the tick: state-to-state conversion, pump–probe, defect jump, two-density solvent, any process whose rate is a counted residual rather than a density of states on an infinite cell.
Until Continuous Second is either replaced by a Rest Time unit, or explicitly justified as a macro-scale average, the framework is a practical route inside the can.
0^i2 (k.g.s^2) = r^2 m
State A — open virtuals / SS-FNO per target state
E = 2c / h
State B — frozen virtuals / ground FNO
E = hbar / c
Tick form of the energy package they already use as a constant:
E = ^m (c^2)
(m) counted. The completed 2 is not the object.
How to strengthen their framework
Four additions, none of which break PySCF.
1. Justify the clock.
State when TDL-plus-continuous-(t) is the intended observational member (static ground surface, interpolated band structure, equation of state). State when it is not (real-time EOM, core-hole lifetime, polaron hop, surface reaction). One paragraph in the methods. The route stays practical; the limit becomes visible.
2. Promote SS-FNO from a basis trick to a duration label.
SS-FNO is already “this state, not the eternal ground.” Attach a duration unit to that freeze: one Real second of occupancy, or one counted excitation. SA-FNO remains the simultaneous reading (metre.second). Ground FNO remains State B. Same three objects they built; named as Family of Time instead of only as compression grades.
3. Do not let TDL erase the freeze.
Extrapolate the frozen residual, not only the canonical complete-basis number. Report the FNO occupancy as a surviving \(\sigma_R\)-like term: the wall’s share of the virtual cut that does not vanish at infinite cell. If the error is flat in \(N_k\), that flatness is the lock. Publish it.
4. Second-order test they can run.
Pick one periodic system with a measured state lifetime or a two-density solvent shift. Compute SS-FNO gaps with and without a discrete time step in the subsequent propagation (or a two-state occupation constraint). If Continuous Second is justified, the two numbers agree at macro scale. If they split, the Rest Time unit is required and their own SS-FNO is the place it enters.
None of this asks them to abandon coupled cluster. It asks them not to sell the thermodynamic limit as a completed 2.
What we are not claiming
We are not claiming FNO is Rest Time. We are not claiming a QZ gap is a Lewe disc. We are claiming their practical route is already a lock-and-count machine wearing a continuous-second coat, and that the coat should be sized.
Practical, yes. Complete, not until the clock is chosen.
Linked: Minkowski in the can; four-colour (n) vs \(n^2\); two-state water; NS bistable route.
The observer shares r^2. The machine is the frozen cell that still ticks.
Pirate Canon Sealed.
The Future Begins.
Catalogue
Discipline: Quantum chemistry / periodic correlated methods
Field: Frozen natural orbitals, CC/ADC, (k)-point crystals
Observation: Chen, Serna & Sokolov, arXiv:2609.13098
Canon reading: Freeze = lock. SS-FNO = state-tick. TDL = continuous observational second retained.
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