Heat that leaves and will not return — scheduled by exact command states.
KEEP · scheduled thermal valve13.0 vs 0.87 cycle ratioword [2,5] → 2 · word [2,4] → 0
A surface that runs 390 K by day and 100 K by night has a thermal problem no
coating solves: whatever you do to shed the day's heat also sheds the night's, and whatever holds
the night's heat traps the day's. In the declared always-open control, the surface is a
net absorber over the cycle. The
fix has to be a valve — open one way, shut the other, on a schedule — with no one there to
retune it.
Selenoform Valve computes that schedule as an exact integer channel state: two protected channels
on the cooling branch and zero protected channels on the heating branch. The closed state still has
declared residual analog transmission of 1/15; zero is the protected-channel count, not a
claim of perfect insulation. A thermochromic VO2/Morin-class layer is a candidate physical
realization, not demonstrated hardware.
What this is, precisely: a hysteretic scheduled-state calculation against a declared thermal
readout. It is not a passive steady-state two-terminal blackbody diode — that object is
forbidden here by a reciprocity result the paper proves rather than dodges. The lunation figures
are design-model outputs; hardware qualification, contact losses, lifetime, and environmental
testing are outside the claim.
THE SURFACE A declared 390 K day /
100 K night lunar surface, with a two-channel OPEN cooling branch, a zero-protected-channel
CLOSED heating branch, residual closed-state transmission 1/15, a 6 K deadband, and a
candidate thermochromic VO2/Morin-class switching layer.
THE RESULT Exact walls first, then the scheduled
device:
The null is exact, and it is checked to 10−14. At net flux 0 or π the
circulation vanishes for every tested coupling, band, and geometry — worst residual
4.0×10−14 all the way through N = 106. A
nonzero null reading flags numerical error, assembly error, or unmodelled symmetry breaking and
must be resolved before the effect is accepted.
Linear in the site count, at a million sites. The ring is tridiagonal plus a rank-two
corner, so a banded solve with an exact rank-two correction returns the required blocks in
O(N) time and O(N) storage. At N = 106 the banded calculation takes
4.8 s; the dense complex Green matrix alone would be 14.9 TB before
factorization. Dense, sparse, spectral and banded agree to
1.55×10−13.
The command has no fractional channel state. Word [2,5] selects two protected
channels; word [2,4] selects zero. Around the declared 295 K setpoint, warming closes
at 298 K and cooling reopens at 292 K. The 6 K separation is the hysteresis ansatz;
the 2/0 channel count is the exact transport law.
Staging is graded by an integer. Co-phased stages compose multiplicatively; over
n = 2…8 the contrast follows tanh[(κn − c)/2] with
R2 = 0.99994, giving an integer sizing rule for a target leakage. The
exponent is the integer; κ is a measured rate, not an exact constant.
Net absorber becomes net radiator. Over one lunation with blocking contrast 15, the
integrated model gives Qout/Qin = 13.0 against 0.87 for the
same surface without the valve — the cycle crosses break-even and stays there.
The exact command state drives a numerical cycle model. Under the declared 390 K day
peak, 100 K night floor, fixed 295 K interior, 6 K deadband, and blocking contrast 15,
the always-open control ends at −85 MJ/m2 while the scheduled state ends at
+523 MJ/m2. These are modelled surface-flux integrals, not a coupled habitat
energy balance or a flight-qualified device. The rounded public receipt is
available here.
The measured walls and the scheduled device
Result
What was established
The number
Time-reversal null
net flux 0 or π gives zero circulation for every tested coupling, band and geometry, through N = 106
worst residual 4.0×10−14
Solver agreement
banded, dense-LU and sparse-SuperLU on the disordered case; dense, sparse, spectral and banded on the common range
3.82×10−17 · 1.55×10−13
Independent quadrature
adaptive quadrature run separately against the integrated-asymmetry statistic
5.2732×10−3, err 9.3×10−16
Linear ring solve
banded solve plus exact rank-two correction at one million sites, against the dense formulation's footprint
4.8 s vs 14.9 TB
Exact command state
word [2,5] on the open branch and word [2,4] on the closed branch; 6 K declared hysteresis around 295 K
2 or 0 protected channels
Staged contrast
co-phased stages compose multiplicatively over n = 2…8; integer sizing rule for a target leakage
R20.99994
Lunation
scheduled hysteretic valve on the declared 390 K / 100 K surface at blocking contrast 15
13.0 vs 0.87 always-open
Valve steel thread — a driven quarter-flux three-port ring on the standard
coherent-transport formulation, an integer-staged cascade, and a scheduled lunar-cycle valve. The
second, energy-integrated wall is conditional: it holds on the particle–hole-symmetric
family and fails when that symmetry is broken. The lunar case is a hysteretic word-state calculation,
not a passive steady-state two-terminal blackbody diode. Design-model outputs; hardware
qualification, contact losses, lifetime and environmental testing remain outside the claim.
Here a word is a two-entry integer substrate address [2,d], not software
text or a mechanical position. Its residue class selects the protected-channel count:
[2,5] gives exactly two and [2,4] gives exactly zero. The 6 K hysteresis is the
temperature rule that selects between those words. In this worked case a thermochromic
VO2/Morin-class phase change supplies the switch with no macroscopic moving parts.
The declared cycle models radiative blackbody exchange; convection is outside it. Zero protected
channels does not mean zero analog transmission: the closed state retains 1/15. The rounded public receipt is
available here.
How — the wall, the linear solve, the schedule
Establish the null before claiming the effect. Time reversal forces
zero circulation at net flux 0 or π. Measuring that null to 10−14 at a million
sites is what licenses the non-zero readings; generic quarter flux breaks the symmetry and reverses
the circulation when the flux sign reverses.
the exact wall · residual 4.0e−14
Exploit the ring's shape, not its size. Tridiagonal plus a rank-two
corner means a banded factorization and an exact rank-two correction return the needed blocks in
linear time and storage — an algorithmic scale demonstration, not a projected dense runtime.
O(N) time · O(N) storage
Size the cascade with an integer. Stage contrast composes
multiplicatively, so the leakage falls geometrically in the stage count and the required number of
stages is a ceiling, not a tuning exercise.
integer grading · stage exponent
Schedule the states against the cycle. Two channels open on the
cooling branch, zero protected channels on the heating branch with residual analog transmission
1/15, a 6 K deadband, and a candidate thermochromic switching layer — a hysteretic word-state
calculation integrated over one lunation.
Q_out/Q_in = 13.0 vs 0.87 always-open
![Two-state hysteresis chart. The open word [2,5] selects exactly two protected transport channels and the closed word [2,4] selects exactly zero. A six-kelvin deadband separates the warming transition at 298 kelvin from the cooling transition at 292 kelvin.](charts/valve_state.png)