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\title{Electromagnetism}
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\date{September 22, 2025 \\ Version control: new version only (do not overwrite prior files)}

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\maketitle

\noindent Constants: CODATA-2022 (NIST SP 961, May 2024); portal physics.nist.gov/constants; accessed Sep 22, 2025.

\section*{Scope}

This pillar covers electromagnetism as a consequence of loop-geometry and transport. We don't assume charge we derive its effects from geometry---no new dimensional scales beyond $S_0 = \hbar$ (set once at the electron anchor; later anchors only verify). In the simple limit we recover Maxwell's equations. Structure beyond that limit enters only through geometry (index gradients, closure/orientation budgets). We work in vacuum first (spectral lines and line-ratios), then in media (how $n(\lambda)$ scales and steers rays). Calibration is local to the pillar, with ratio-first checks if they beat calibration, and explicit falsifiers when data disagree.

\section*{Coverage map:}

Foundation --- $S_0 = \hbar$; operators ($E\kappa$, $T$, $S$, $C$)
\begin{itemize}
\item $\to$ Maxwell limit (vacuum)
\item $\to$ Propagation in gradients: $n(\lambda, r)$, curvature balance $1/a = \|{\nabla} \ln n\|$
\item $\to$ Spectroscopy (vacuum): H$\alpha$ 656.281 nm, H$\beta$ 486.133 nm, H$\gamma$ 434.047 nm; stable ratios
  \begin{itemize}
  \item $\to$ Wave optics: interference/diffraction (Fresnel/Fraunhofer); coherence hooks.
  \item $\to$ Polarization: Jones/Stokes transport, Brewster/Fresnel coefficients; Faraday as a medium add-on.
  \end{itemize}
\item $\to$ Media predictions: $n(\lambda)$ scaling; graded-index transport
\end{itemize}

\section*{What Is Charge in VMS?}

\textbf{Short version:} A ``charged'' thing here is a \textbf{rotating void-loop} that's constantly throwing off null-gravity waves (NGWs) \textbf{ripples}. Those ripples don't pile anything up---no net space-density change. Another loop only feels something if \textbf{it's also spinning} and its \textbf{facing lines up} with the ripple pattern. The effect is \textbf{purely orientation-gated}.

\textbf{Right spin, right facing} $\to$ you get a push; \textbf{wrong facing} $\to$ the pushes cancel over a cycle and you feel nothing net. \textbf{opposite facing} you get a pull

\subsection*{1) Core picture --- the surfer analogy (why this actually works)}

Think of the second loop as a \textbf{surfer} and the NGW pattern as \textbf{ocean swell}. The swell isn't a ``standing downhill''---it's a \textbf{traveling pattern}.

\begin{itemize}
\item If the surfer \textbf{angles the board} into the swell the right way, the \textbf{path bends} and you ``catch'' it.
\item If you're \textbf{misaligned}, the chops shove you back and forth but \textbf{average out}---no net drift.
\item If you're \textbf{faced the other way}, you get the \textbf{opposite path change}.
\end{itemize}

That's the charge interaction here: \textbf{path steering by alignment}. No alignment $\to$ no net change. Opposite alignment $\to$ opposite change. There's \textbf{no new stuff} in space doing the pushing; it's all in how a \textbf{spinning, oriented loop} rides the pattern.

\subsection*{2) Preferred plane from display-area expansion (why there's a ``facing'' at all)}

Display-area merge contraction (closed-form).

For fragments with volumes $\{V_i\}$ that merge into one body:
$$F_{\text{merge}} = A_{\text{after}} / A_{\text{before}} = \left(\sum_i V_i\right)^{2/3} / \left(\sum_i V_i^{2/3}\right) \leq 1.$$

Two equal fragments $V/2, V/2$:
$$F_{\text{merge}} = V^{2/3} / [2(V/2)^{2/3}] = 2^{-1/3} = 0.7937$$
(inverse of split factor $2^{1/3}$).

When a loop splits and merges space along its route, \textbf{splitting expands display-area} and \textbf{merging contracts it}. That rule naturally picks out the \textbf{preferred plane} for the loop's motion from the caustic---on that plane the expansion/merging bookkeeping balances best. ``Facing'' is judged against that plane. The \textbf{sign} we call ``positive'' or ``negative'' is just \textbf{which direction}, counterclockwise vs clockwise locked to that common plane.

[Diagram] Loop orientation $\to$ expansion arrows $\to$ the picked preferred plane.

\subsection*{3) Sign, size, and steps (how much ``charge,'' and why it comes in chunks)}

\begin{itemize}
\item \textbf{Sign:} which side of the preferred plane the loop's orientation locks to.
\item \textbf{Size:} how many \textbf{aligned turns per cycle} the loop contributes (an integer count when you coarse-grain over time).
\item \textbf{Steps (quantization):} you only change the count at \textbf{discrete orientation-flip} or \textbf{merge/split events}; it doesn't slide continuously when closure holds.
\end{itemize}

\subsection*{4) Continuity (nothing pops in from nowhere)}

Orientation doesn't just appear or vanish away from real tear/closure events. So the net ``effect you feel'' changes \textbf{continuously in time} as loops move and re-align. That's the common-sense ``nothing up my sleeve'' rule---what we'll later formalize as the usual conservation statement, but the point here is physical: \textbf{no surprise jumps} unless you actually cross a defect.

[Sketch] Orientation flow lines showing smooth passage vs. a defect surface where in/out is accounted.

\subsection*{5) From geometry to the usual EM laws (why engineers recognize the result)}

When you average these \textbf{orientation-gated path nudges} over time and over many loops---in \textbf{smooth, weak-curvature conditions}---the \textbf{effective path law} you recover is the same set engineers already use: the \textbf{standard Maxwell equations}. We'll show that ``Maxwell-limit'' in the math walk-through; here the message is simple: \textbf{EM is the alignment-driven path steering, and its coarse-grained bookkeeping matches Maxwell}.

\subsection*{6) How this is not gravity (why orientation matters here but not there)}

Gravity behaves like a \textbf{standing curvature gradient}---a downhill. Anything with inertia ``rolls'' the same way no matter how it's turned. \textbf{Electromagnetism here is different: there's no standing downhill}---just a traveling pattern---so the outcome \textbf{depends completely on how you're oriented}. Right facing $\to$ push. Wrong facing $\to$ it cancels. \textbf{Opposite facing} $\to$ pull.

\section*{Problem \& Promise}

Falsifier (pillar-level): sustained $\geq 3\sigma$ disagreement in stable line ratios or index-scaling ratios after instrument/systematic control; same rule for the neutral-rotor push/zero/pull and spin-flip sign tests.

\textbf{The problem with the usual story:} Classical EM is insanely predictive, but \textbf{it starts by assuming charge} and ``the rest of the furniture are already there.'' It doesn't tell you where that \emph{stuff} \textbf{comes from}. In VMS, we don't assume it --- we \textbf{build it from geometry}. ``Charged'' isn't a magic label; it's a \textbf{spinning void-loop throwing off NGW ripples}. There's \textbf{no standing downhill} like gravity. The only way another loop feels anything is if \textbf{it's also spinning} and its \textbf{facing lines up} with the pattern. Right spin, right facing $\to$ you get a push; wrong facing $\to$ the pushes cancel over a cycle and you feel nothing net; \textbf{opposite facing you get a pull}.

\subsection*{What we're promising:}

\begin{enumerate}
\item We recover the same \textbf{equations engineers already use} --- the Maxwell set --- when you average these orientation-gated nudges in smooth, weak-curvature conditions. No new dials, no hidden units. Just the limit you know, from a cleaner origin story.

\item We show \textbf{where controlled corrections could live} --- tied to torsion and shear --- and we put hard gates on how big those can be before we call it wrong.

\item We publish \textbf{quantitative, falsifiable tests}: what to measure, how to judge pass/fail, and where a ratio-first estimate is the right operational choice.
\end{enumerate}

\section*{In the real world --- why bother if Maxwell already nails a lot of it}

\textbf{First, the truth:} the everyday ``orientation stuff'' below is \textbf{already predicted by classical EM (Maxwell) / SM's QED}. That's not the point of VMS. The point is: we

\textbf{don't assume charge}; we build it from geometry, we explain why orientation gates the effect, we unify the intuition with gravity (no standing downhill here), and we predict \textbf{new orientation-gated behaviors} in regimes nobody is instrumenting yet. Maxwell is the right limit; VMS is the mechanism and the next set of tests.

\subsection*{What you already see (Maxwell explains it) --- in plain talk:}

\begin{itemize}
\item \textbf{Phones/links that ``wake up'' when you turn them.} Antennas are picky about facing. Line them up and it talks; turn $90°$ and it goes quiet (that's polarization-loss factor). \href{https://www.digikey.com}{DigiKey+1}

\item \textbf{RFID/NFC that only reads when the tag is ``just so.''} Parallel coils read; perpendicular is basically \textbf{zero} (vendor app notes say it exactly). \href{https://www.stmicroelectronics.com}{STMicroelectronics+1}

\item \textbf{Wireless charging that's great when it snaps, bad when it doesn't.} Qi2 adds \textbf{magnets to force the right plane} because alignment matters for speed/heat. \href{https://www.wired.com}{WIRED+1}

\item \textbf{Fiber links that ``get moody'' with heat/bends.} The glass has tiny preferred directions; when they drift you get \textbf{PMD} and smearing. Same facing story hiding in glass. \href{https://www.rp-photonics.com}{RP Photonics}

\item \textbf{Space radar that sees rows of crops---or misses them.} Flip HH/HV/VV and scenes pop or disappear based on orientation. Everyday polarimetry. \href{https://www.descansosoftware.com}{Descanso+1}

\item \textbf{Skies that rotate your facing.} The ionosphere rotates polarization (\textbf{Faraday rotation}); track it or your link fades. \href{https://www.agu.org}{AGU Publications+1}

\item \textbf{Glare that vanishes at one angle.} Brewster's angle + a quarter-turn on polarizers and the glare dies. Same rule: right vs wrong facing. \href{https://www.bu.edu/physics}{BU Physics}
\end{itemize}

\textbf{Why we bother:} because our model says the effect \textbf{isn't standing downhill}---it's \textbf{alignment-driven path steering from null-gravity-wave (NGW) patterns}. That origin leads to \textbf{new, simple tests} that standard EM doesn't hand you:
$$\text{Right spin, right facing} \to \text{push}; \text{ wrong facing} \to \text{it cancels}; \text{ opposite facing} \to \text{pull}.$$

\section*{New tests to run now (neutral, no hidden EM handles):}

Expected scale (order-of-magnitude, to refine in Calibration/Appendix):

For a neutral micro-rotor of radius $r \sim 10^{-6}$ m, moment $I \sim 10^{-24}$ kg$\cdot$m$^2$, spin at $\omega \sim 10^6$ s$^{-1}$ in UHV, the predicted orientation-gated force/torque is sub-pN / sub-zN$\cdot$m per cycle, rising with aligned surface speed and dropping sharply at null angles. Report both calibrated and ratio-based readouts (spin-flip lock-in recommended).

\begin{enumerate}
\item \textbf{Neutral, spinning loop} $\to$ \textbf{push/zero/pull} in high vacuum. Two neutral micro-rotors, isolated from EM coupling. Map three outcomes by facing alone: \textbf{push / cancel / pull}. The ``wrong-facing = zero'' is the tell.

\item \textbf{Spin-flip sign reversal with everything else fixed.} Keep geometry/materials constant; just flip the \textbf{spin} sense of the impacted loop. We predict \textbf{push$\leftrightarrow$pull}
flip; Maxwell has no stand-alone ``spin-sense'' lever in a neutral, non-current system.

\item \textbf{Sharp null-cones, not smooth roll-off.} Sweep relative orientation and publish the \textbf{angle map of zeros}. We expect \textbf{distinct nulls} at specific angles (not a gentle EM-style curve).

\item \textbf{Ratio-first spectroscopy with an orientation hook.} Where metrology is ultra-tight (e.g., hydrogen lines), publish the \textbf{Maxwell-limit numbers} and a small \textbf{orientation-tagged correction band}. Any \textbf{angle-tied split} beyond the calibrated band is a decisive falsification flag.

\item \textbf{``No standing downhill'' checks.} Build rigs that would react to a gravity-like stationary gradient. We predict \textbf{no effect} unless facing is right; gravity analogs wouldn't care about facing.
\end{enumerate}

There are public ``anecdotes'' of orientation-ish anomalies---but none cleanly match the \textbf{push/zero/pull triad}, and the best attempts either failed to \textbf{reproduce} or point to mundane systematics.

\section*{Here's the straight read:}
\section*{What people have claimed (and where it stands)}

\begin{itemize}
\item \textbf{Rotating superconductors (Podkletnov, 1990s):}
Claimed ``weight reduction'' above a spinning YBCO disc. NASA's own summary says MSFC tried to build a full replication but never finished; a \textbf{private replication (Hathaway---Cleveland---Bao, 2003)} saw no gravity-like force at sensitivities far beyond the original claim. So: \textbf{famous anecdote, no confirmed effect}. \href{https://ntrs.nasa.gov}{NASA Technical Reports Server+2ScienceDirect+2} (Background overview and pitfalls papers exist, but they reinforce how easy it is to fool yourself here.) \href{https://www.researchgate.net}{ResearchGate+1}

\item \textbf{Cryogenic rings \& gyros (Tajmar, 2006---2008):}
Reported anomalous fiber-optic gyroscope signals near spinning rings at low temperature, with odd ``parity'' dependence. Intriguing, widely discussed, \textbf{no consensus}; replications are sparse/inconclusive and the community remains skeptical. It's the closest ``spin/orientation anomaly'' with decent lab kit---but \textbf{not established}. \href{https://arxiv.org}{arXiv+1}

\item \textbf{Eclipse pendulums (Allais effect):}
Decades of mixed reports of pendulum/gravimeter blips during solar eclipses; multiple careful campaigns report \textbf{no unambiguous detection}. It's a classic ``lots of anecdotes, one signal once controls improve.'' \href{https://www.wikipedia.org}{Wikipedia}

\item \textbf{``Reactionless thrusters'' (EmDrive) as a cautionary tale:}
Early positive thrusts got attention; \textbf{high-accuracy tests} later traced them to \textbf{thermal/fixture artifacts} and set strong null bounds. Moral: tiny forces are slippery. \href{https://www.springerlink.com}{SpringerLink+1}

\item \textbf{State-of-the-art rotors/force sensors:}
Today's levitated nanomotors hit GHz spin and yocto/zepto-newton-scale torque sensitivity. That means \textbf{we have the hardware} to test push/zero/pull claim
cleanly---even though no one has publicly reported this specific triad in a neutral, no-EM-handle setup. \href{https://www.pubmed.gov}{PubMed}
\end{itemize}

\section*{Bottom line}

\begin{itemize}
\item There is anecdotal smoke (superconductors; cryogenic rings; eclipse tales), but \textbf{no robust test matches our prediction: neutral, spinning loop} $\to$ \textbf{orientation-gated push / true zero / pull}, with a spin-flip sign reversal. The strongest ``anecdotes'' either failed \textbf{reproducibility} or can be \textbf{explained away} with known systematics. \href{https://ntrs.nasa.gov}{NASA Technical Reports Server+2ScienceDirect+2}

\item That's exactly why these tests matter: with modern UHV, neutral rotors, and lock-in on \textbf{spin-flip}, they can give this a \textbf{decisive yes/no} instead of folklore.
\end{itemize}

Of the pillars, \textbf{Electromagnetism} has the \textit{fewest} non-standard, peer-reviewed experimental ``wins'' in the wild. In fact, EM is the most over-constrained arena in physics:

\begin{itemize}
\item \textbf{Coulomb's inverse-square law} has been hammered for a century; classic and modern tests push deviations to tiny levels. (E.g., Plimpton---Lawton verified the $1/r^2$ exponent to $\sim 1$ in $10^9$; Williams---Faller---Hill recast null results as a tight upper bound on photon mass.) \href{https://journals.aps.org}{Physical Review+1}

\item \textbf{The photon mass} is bounded to be essentially zero by a zoo of methods (space/plasma timing, planetary magnetospheres, etc.); the `s 2024 review summarizes extremely stringent limits.

\item \textbf{High-profile ``anomalies''} haven't survived hard replications: Podkletnov's spinning-superconductor ``gravity shielding'' returned \textbf{null} in serious follow-ups; EmDrive thrust claims were beaten down by precision balances (Tajmar et al., 2021---2022). \href{https://www.sciencedirect.com}{ScienceDirect+2ADS+2}

\item \textbf{The one recurring curiosity}---Tajmar's cryogenic ring/gyro signals---remains \textbf{unsettled and unconfirmed} by a broad community; it didn't turn into a standard effect. \href{https://www.semanticscholar.org}{Semantic Scholar}
\end{itemize}

\subsection*{So what's the point of this pillar?} Two things:

\begin{enumerate}
\item \textbf{Origin story + mechanism.} Maxwell is the right limit; we're not trying to out-predict radio engineers. We're replacing ``charge as a given'' with a concrete \textit{orientation-gated path-steering picture} (the surfer logic) that explains \textbf{why} alignment matters---then we use that to pose \textbf{new, clean tests}.

\item \textbf{New, decisive lab tests}---\textbf{enabled by today's hardware}. The kit now exists to check \textbf{push / zero / pull} triad in regimes \textbf{Maxwell doesn't motivate} (neutral objects, no applied fields, no currents): GHz-class \textbf{neutral rotors} and zepto-newton force/torque sensors in UHV are on the shelf. That makes a targeted \textbf{spin-flip lock-in} test realistic today. \href{https://www.sciencedirect.com}{ScienceDirect+1}
\end{enumerate}

\subsection*{Key Point:} EM's ``non-standard verification'' track record is sparse by design---the standard theory has passed innumerable tests and crushed most anomalies. That's exactly why this pillar matters: these predictions are \textbf{orthogonal to the usual EM playbook} and \textbf{falsifiable} with existing tools. Neutral means the positives and negatives sum to zero---no net monopole. Spin a neutral, non-magnetic rotor and align its circulation with the global caustic plane. The model predicts a tiny, orientation-gated mechanical response: right spin + right facing $\to$ push; wrong facing (null tilt) $\to$ true zero; opposite facing or spin-flip $\to$ pull. With $\varepsilon > 0$, the half-cycles aligned with $+n$ are weighted slightly more than the opposite half-cycles, so the cycle-average picks up a small odd term $\propto \varepsilon$ (push/zero/pull). This fingerprint isn't in standard EM and is falsifiable with existing tools; if absent, we publish a tight upper bound and move on. The real value comes later as we cross-link this channel with other pillars in the practical branches.

\subsection*{Cross-link value (right now, not someday)}

\textbf{The biggest value shows up when we cross-link this orientation-gated EM with the other pillars and aim it straight at active programs and standards.} That's how we turn the idea into knobs people already use---charge it, ship it, measure it, or cert it. \textbf{Five live ``branches'' to name-drop (and why they care):}

\begin{enumerate}
\item \textbf{Power \& devices (EM} $\times$ \textbf{mechanics):} auto-alignment became a standard. Qi2 wireless charging literally bakes in \textbf{magnetic alignment} so phones snap to the right \textbf{facing} for efficiency/speed. That's our rule in consumer hardware: right facing $\to$ it works; wrong facing $\to$ it stinks. Cross-link: predict when ``almost right'' wastes heat and how to shape the nulls. \href{https://www.wirelesspowerconsortium.com}{Wireless Power Consortium+1}

\item \textbf{Ultra-sensitive rigs (EM} $\times$ \textbf{precision mechanics):} neutral rotors are ready. Levitated nanoparticles now spin in vacuum at MHz---GHz and act as torque/force sensors. That's a turnkey platform to run our \textbf{push / zero / pull} test with spin-flip lock-in. Cross-link: spec the geometry from the mechanics pillar; we bring the orientation gates. \href{https://www.nature.com}{Nature+1}

\item \textbf{Backbone networks (EM} $\times$ \textbf{materials \& comms):} facing drifts are measurable. Long-haul fiber suffers \textbf{polarization-mode dispersion} when the glass's preferred axes wander with heat and stress. Standards and tutorials already define how to test/mitigate it; we add an \textbf{angle-map} way to forecast the nulls. \href{https://itu.int}{ITU+1}

\item \textbf{Earth imaging (EM} $\times$ \textbf{sensing):} polarimetry is mainstream and scaling up. Polarimetric SAR literally toggles HH/HV/VV to make features \textbf{appear or vanish by orientation}; NISAR just launched with multi-pol modes. Cross-link: publish ``invisibility'' predictions (where scenes drop out) and validate against NISAR passes. \href{https://science.nasa.gov}{NASA Science+1}

\item \textbf{Space weather (EM} $\times$ \textbf{environment):} the sky rotates your facing. \textbf{Faraday rotation} in the ionosphere twists polarization; ops teams already train on it and NASA just mapped gaps to upgrade models. Cross-link: a controller that keeps ``facing'' right in real time and kills fades. \href{https://nws.noaa.gov}{NWS Training Portal+1}
\end{enumerate}

\section*{Cross-Doc Rules \& Dependencies}

\begin{itemize}
\item No new dimensional scales beyond $S_0$ (loop-action constant).
\item Use `torsion constant' and `shear constant' terminology; numeric values live in Base/Calibration.
\item This pillar inherits locks from Base Calibration; no retune here.
\item Out-arrows keep traceability: Narrative $\to$ Math Walk-Through $\to$ Math Appendix $\to$ Calibration $\to$ Extensions.
\end{itemize}

\subsection*{Inputs $\to$ Outputs (Schematic)}

[diagram] Inputs: $\{S_0\}$, locks, torsion/shear constant names$\}$ $\to$ Outputs: $\{$Maxwell-limit recovery; EM source/field mapping; testable corrections$\}$.

\section*{Where This Pillar Sits in VMS}

Prereqs: void propagation, loop closure, and the main Math Appendix operator definitions. Electromagnetism provides the bridge from geometric descriptors (curvature-flux $\mathcal{K}$; oriented loop density $\Omega$) to observed fields (E,B), and hands forward quantitative targets to Calibration and Predictions for spectroscopy and field-law tests.

\section*{Non-Goals / No New Knobs}

We do not introduce new dimensional constants or retune base locks. We do not replace classical EM in its validated domain; we recover it as a limit and only propose tests where controlled deviations could appear within tolerances.

\section*{Maxwell-Limit Recovery Summary}

Define pillar-local potentials $\Phi[\mathbf{X}, \Omega]$, $A[\mathbf{X},\Omega]$, linear in the mapped geometric fields under coarse-graining: Set $\mathbf{E} := -\nabla\Phi - \partial\mathbf{A}/\partial t$ and $\mathbf{B} := \nabla \times \mathbf{A}$. Build source densities $(\rho)$ from orientation/topology so that continuity ($\partial\rho/\partial t + \nabla \cdot \mathbf{J} = 0$) holds away from defects. Under weak curvature and slow variation, $\mathbf{E}$ and $\mathbf{B}$ satisfy the Maxwell set with coefficients matched by calibration ($\varepsilon_0, \mu_0$).

\textbf{Out-of-Scope (this pillar):}
Nonlinear optics ($\chi^{(2)}/\chi^{(3)}$), strong-field QED (Schwinger), magnetized plasma microphysics, and device/material deep dives (these live in branches or the Thermodynamics pillar).

\subsection*{What's New vs. Classical}

\begin{itemize}
\item \textbf{Source genesis:} charge/current arise from orientation/topology of void loops (not postulated entities).
\item \textbf{Controlled corrections:} torsion/shear enter as bounded, testable departures from the Maxwell limit.
\item \textbf{Ratio-first operations:} when in-domain anchors are ultra-precise (e.g., hydrogen lines), prefer ratio-anchored estimates for operational use; retain cross-domain calibrated figures for audit.
\end{itemize}

\section*{Calibration capsule (targets \& ratios)}

The Calibration doc defines numeric gates (constants and spectroscopy). Example anchors include CODATA-2022 $\alpha$ and R$\infty$, and NIST ASD Balmer H$\alpha$/H$\beta$, with explicit air$\Rightarrow$vacuum handling. A worked example demonstrates predicting H$\beta$ from H$\alpha$ via the model line ratio $r=20/27$.

\section*{Documents in this Package}

$\to$ Electromagnetism Math Walkthrough
$\to$ Electromagnetism Math Appendix
$\to$ Electromagnetism Calibration
$\to$ Electromagnetism Extensions Predictions Tests

This doc zeros in on what's new to measure: \textbf{orientation-gated effects} with crisp falsification. It anchors numbers to CODATA-2022 and NIST ASD then uses real-world orientation lanes---\textbf{ionospheric Faraday rotation, SAR polarimetry (HH/HV/VV/VH), and fiber PMD}---to define acceptance gates. The non-standard piece is a neutral-rotor lab test for the \textbf{push / zero / pull} triad and \textbf{spin-flip sign}, with pre-registered $3\sigma$ calls and a ratio-first vs calibrated comparison to flag any divergence.

\section*{Air $\Leftrightarrow$ vacuum wavelengths (2-paragraph note)}

\subsection*{Why this matters \& how to do it right.}

When you compare line lists or model outputs to lab/astro data, say explicitly whether numbers are in \textbf{vacuum or standard air}. In vacuum the wavelength $\lambda_{\text{vac}}$ is tied to the wavenumber; in air the wavelength shortens by the refractive index $n$:

$$\lambda_{\text{air}} = \frac{\lambda_{\text{vac}}}{n} \quad \Rightarrow \quad \lambda_{\text{vac}} = n \lambda_{\text{air}}.$$

The NIST Atomic Spectra Database (ASD) converts with the \textbf{Peck---Reeder (1972)} ``standard air'' formula across 185---1700 nm (15 °C, 101 325 Pa, 0.033\% CO$_2$) and even calls out the boundary quirk near 200 nm (e.g., \textbf{200.0648 nm vacuum} $\to$ \textbf{200.00000 nm air}). If you need real conditions (not ``standard air''), use a \textbf{Ciddor-based index} (temperature, pressure, humidity, CO$_2$) or the \textbf{NIST Engineering Metrology Toolbox} calculator. Always state which model you used and the inputs. \href{https://emtoolbox.nist.gov}{emtoolbox.nist.gov+3NIST+3NIST+3}

\subsection*{Policy for this pillar.}

Unless required otherwise, convert \textbf{everything to vacuum} before fitting/plotting, or report \textbf{both with the model + inputs}. Record: (i) conversion model (Peck---Reeder vs Ciddor 1996), (ii) environmental inputs (T, P, RH, CO$_2$), (iii) tool/version (e.g., \textbf{NIST EMT} air-index calculator). Note that ASD warns \textbf{air-wavelength uncertainties don't include the air$\Leftrightarrow$vac conversion uncertainty}---log that separately. Be extra explicit if your bands straddle the $\sim$200 nm air/vac boundary used by ASD.

\section*{Constants registry (link + stamp)}

Use the \textbf{CODATA 2022} recommended values from NIST; stamp this in the doc header:
``Constants: CODATA-2022 (NIST SP 961, May 2024); portal: physics.nist.gov/constants (accessed Sep 22, 2025).''

Primary sources: the NIST constants portal and the \textbf{CODATA-2022 wall chart/wallet card}; background and citation summary in the 2025 RMP review. \href{https://physics.nist.gov/constants}{NIST+2NIST+2}

\section*{References (model)}

\begin{thebibliography}{99}

\bibitem{CODATA2022}
Mohr, P.J., Newell, D.B., Taylor, B.N., Tiesinga, E. (2023). CODATA Recommended Values of the Fundamental Physical Constants: 2022. \textit{Rev. Mod. Phys.} \textbf{95}, 035009.

\bibitem{NIST_ASD}
Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2023). NIST Atomic Spectra Database (ver. 5.11). National Institute of Standards and Technology.

\bibitem{Peck1972}
Peck, E.R., Reeder, K. (1972). Dispersion of Air. \textit{J. Opt. Soc. Am.} \textbf{62}, 958---962.

\bibitem{Ciddor1996}
Ciddor, P.E. (1996). Refractive index of air: new equations for the visible and near infrared. \textit{Appl. Opt.} \textbf{35}, 1566---1573.

\bibitem{Plimpton1936}
Plimpton, S.J., Lawton, W.E. (1936). A very accurate test of Coulomb's law of force between charges. \textit{Phys. Rev.} \textbf{50}, 1066---1071.

\bibitem{Williams1971}
Williams, E.R., Faller, J.E., Hill, H.A. (1971). New experimental test of Coulomb's law and a possible measurement of the photon rest mass. \textit{Phys. Rev. Lett.} \textbf{26}, 721---724.

\bibitem{Particle_Data_2024}
Particle Data Group (2024). Review of Particle Physics: limits on the photon mass and tests of electromagnetism.

\end{thebibliography}

\end{document}
