PhysWall inverts a closed, non-linear physical law at a single measurement point — and refuses when the inverse is not unique.
The gateway between what physics allows and what the numbers show — theory sets the boundary, the measurement says which side you are on.
Three columns: frequency GHz, S11 dB, phase degrees. Header row optional, # comments ignored. Q = |X|/R is computed per point; the worst Q binds the Bode-Fano bound.
D1–D7 answer whether a design can work. This answers why one did not. Each candidate cause is pushed forward through the same loss bound and compared against what you measured — the physics rules causes out, not a guess. When more than one survives, you get the measurement that separates them.
D1: target return loss in dB (e.g. −15) → max load Q · D3: target temperature in K (e.g. 300) → max length and max Df · D7: target wavelength in nm (e.g. 640) → disk radius. Two answers come back: the bound the physics permits, and the same solve with margin.
Select a domain above
⚠ Worked out in your browser. This tool is not an inversion of a physical law, so there is no server answer to sign — it is a status map of seven domains, and it says so rather than implying otherwise.
⚠ worked out in your browser
A question anyone running a line will recognise: "defect density doubled this week — what changed?"
Chip patterning at the smallest nodes is limited by counting statistics. The exposure delivers a finite number of photons per feature, and a feature either prints or it does not. Published work on one such process reports that a 0.4% change in exposure dose doubles the defect density. The relationship compounds:
dose drift 0.2% → defects ×1.4
0.4% → defects ×2.0
0.6% → defects ×2.8
1.0% → defects ×5.7
Nothing, on its own. A doubling is exactly what four-tenths of one percent of dose drift produces. The measurement cannot separate a process that changed from a dose that moved within a fraction of its own tolerance — and no amount of better defect counting will change that, because the ambiguity is in the relationship, not in the counting.
⚠ NO VERDICT — and the reason, stated: the dose at the same point in time is not in the measurement. Until it is, a doubling is consistent with both answers.
If defects rose six-fold, dose drift would have to be a full percent (1.0%) — an order of magnitude above the drift the first question ruled out. That one is a process change, and the same relationship that refused the first question answers the second.
⚠ Every figure above is from published literature, and none of this is our field. What the example shows is not an answer about chipmaking — it is what the four-way split does with a number that looks decisive and is not. The instrument, the formula, the sample, and which definition of "defect" was counted: three of those are familiar, and any of the four can produce a doubling.
Each one below carries its own note on what it rests on. They are worth reading, because the seven are not in the same position and the maturity label alone does not say how they differ:
D7 corrected by outside measurements
fitted to seven published anapoles, four of them measured.
Our band was 3.1x too wide at the top. It failed, and changed.
D3 ⚠ one of its two anchors is not a measurement
the constant sits between 0.195 from an Intel stackup guide and
0.146 from the CHIME radio telescope backplane. CHIME is a built
instrument with VLP copper, carrying a design expectation of 0.37 dB/inch. Intel's
figure comes from a formula with a 2 µm roughness assumed
into it and ±5% declared up front — so averaging
the two averages a model constant with a hardware measurement.
Splitting the frequency dependence closes 4 points of the 33%
gap and leaves 29. The roughness runs the wrong way: Intel
assumes smoother copper than CHIME used, so its figure should
be the lower one and it is the higher.
D1 cross-checked by a separate engine
the declaration engine, given the law and nothing about RF,
returned the same number this bound does.
D2 nothing in it to be wrong about
two CODATA constants and a temperature.
D6 measured six times — and one of them breaks it
a colloidal particle (2012), a feedback trap (2014),
nanomagnetic bits (2016), a single atom (2018), a
finite-time correction (2020) and DRAM cells (2025).
⚠ the bound is an inequality and this reads it
as an equality — see below.
D4 runs forwards only
D5 same — a different job, and not a lower grade.
⚠ And D1 and D4 are not independent of each other. D1 is Bode-Fano: how much bandwidth a match can hold at a given Q. D4 is a Q bound for electrically small resonators. The paper behind D4 says so itself — Q bounds limit the maximum operating bandwidth of devices including antennas, and that has been the subject of foundational work for decades.
They are the same relationship approached from two sides. Running both and getting agreement is not two confirmations, and anyone treating it that way is double-counting. That is stated here because the list of seven invites exactly that reading, and nothing else on the page corrects it.
⚠ And D6 has now failed a negative control — thirteen times over. A 2012 experiment published a table of thirteen measured operations at room temperature. Twelve of them erased nothing at all: they were logically reversible copies. Inverting their dissipation as though it were erasure gives anywhere from 0.014 to 15 bits.
operation dissipated D6 returns bits actually erased COPY 10.4 kT 15.0 bits 0 COPY 0.0094 kT 0.014 bits 0 ERASE WITH COPY 10.35 kT 14.9 bits 0 ERASE WITHOUT COPY 20.7 kT 29.9 bits 1
The last row is the one that did erase, and the answer is out by a factor of thirty. There is no reading of these numbers under which this inversion works.
The reason is structural rather than a tuning problem. Landauer says Q ≥ N·kT·ln2 — an inequality. Reading it backwards turns it into an equality, and an equality holds only when erasure actually happened and the process was quasi-static. Neither is true of a measurement handed to it cold, and nothing in the number itself says which.
Which is what a negative control is for, and this project had none for any bound until now. So D6 does not run backwards at all. Not as a temporary measure: an inequality has no unique inverse, and nothing in a dissipation figure says whether erasure happened. It answers whether a measurement is consistent with the bound, which is a different question and one it answers completely.
The same table carries the fix. Dissipation in it falls as one over the switching time, across two orders of magnitude of bit energy and within a few percent — which is exactly the finite-time correction to Landauer that was derived independently eight years later. The data confirming the correction was sitting in the paper that breaks the naive bound, published before anyone went looking for it.
bit energy 30 kT measured 1/τ predicts 64 µs 0.0917 (anchor) 256 µs 0.0273 0.0229 640 µs 0.00939 0.00917
D7 is the one that outside measurements have already reached. Seven published anapoles narrowed a band that had been too generous, and the number here is theirs as much as ours — which is the useful position for a bound to be in, and the one the others are still working towards.
⚠ The dielectric constant this page's map assumes is MAP_DK = 3.4, written in the code with those digits. It is a choice and not a property: Megtron 6 sits near 3.4 at 10 GHz and RO4350B near 3.48, while FR-4 is 4.2–4.7 and outside this map entirely. A page whose argument is that α1 differs by 33% between two boards of the same laminate cannot quietly fix Dk at one number, so the number is here where it can be checked.
Maturity: validated. five closed bounds, each cross-checked against its published source.
D1 — RF Matching
Current: Bode-Fano bound from published load impedance (R, X) and bandwidth.
Upgrade: actual VNA S-parameter sweep (Keysight/R&S, .s1p/.s2p files) — D1 transitions
from theoretical floor to measured result. The model stays identical; the input becomes real.
D2 — Thermal complexity (f*)
Current: temperature entered manually. Upgrade: thermocouple or RTD on-board readout
piped directly — f* updates in real time during thermal cycling.
D3 — PCB channel (T-critical)
Current: α₁ from a single published anchor (Intel, 0.85 dB/inch at 14 GHz);
Df from laminate datasheet nominal (0.002). Upgrade: VNA insertion-loss sweep (S₂₁ vs
frequency) gives both coefficients measured on the actual board. Published composite
Df for Megtron 6 runs 0.0063–0.0076 at 10 GHz against the 0.002 datasheet value —
a factor of three. On the 3-inch, 28 GHz, 3 dB configuration shown here that is not a shift of tens of Kelvin — it moves T_critical from 121 K, which liquid nitrogen reaches comfortably, to about 13 K, which it does not. The dielectric term rises to 2.26 dB and carries no temperature at all, leaving only 0.74 dB of the budget for the conductor loss that cooling does reduce. The change is not colder; it is a different cryogen.
D4 & D7 — Photonics (nanoparticle / anapole)
Current: r, λ, n_medium entered manually; Rayleigh validity check is geometric.
Upgrade: dark-field scattering spectra (confocal or integrating-sphere setup) gives
measured scattering cross-section — D7 r_min becomes the radius at which the measured
signal crosses the noise floor, not a shot-noise floor estimate.
D5 — NTK-BF Cascade
Current: stages 2–3 not implemented (VCSEL linewidth only). Upgrade: fiber OTDR trace
(stage 2) and integrating-sphere nanoparticle scattering spectrum (stage 3) would
complete the cascade — each domain feeds the next.
D6 — Landauer limit
Current: temperature entered manually. Upgrade: cryostat thermometry feed —
E_min updates continuously during cooldown, giving a live thermodynamic floor.
Physics sets where the frame ends. This dashboard decides that the frame gets checked, and what happens at its edge. Where physics has no opinion, we choose — and say so. Every threshold below is one kind or the other.
A threshold of the second kind wearing the costume of the first is a bug, not a decision. One is open: D7's anapole band gives ka ≈ 2.1–3.1 while the literature puts the anapole near ξ ≈ 0.5–0.7. It is flagged rather than silently adjusted — guessing which is right is the failure this gate exists to prevent.
The physical model does not change when better data arrives. Each domain computes the same constraint — Bode-Fano, Landauer, Hammerstad-Jensen — against whatever input it receives. The architecture is designed so that a calibrated measurement replaces a datasheet estimate without touching the physics. Verdicts get sharper; equations stay the same.
A checking tool, not professional advice. It tells you what a measurement does and does not support; what to do about that is your decision.