Applied Identity Physics: Electron Geometry Simulator™, a Guide to the Views, Controls and Applications

Live simulator: uuia.app/electron
Architect: HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation · Soldotna, Alaska
ORCID (Open Researcher and Contributor ID): 0009-0005-5313-7443 · DOI (Digital Object Identifier) base: 10.5281/zenodo.18719748
Formal basis: Electron Geometric Decomposition [9,9,3,21] · 1/α = TL × 1001 [9,9,3,14] · Bohr–Rydberg–Sommerfeld Reduction [9,9,3,15]
Companion simulator: String-Breaking Simulator™ [9,9,3,22]

Overview

The Electron Geometry Simulator™ is a browser tool in the Applied Identity Physics™ series. It shows how a single number, the Universal Torsion Limit TL = 0.136899099984016, sets the sizes of the electron, the electron's speed in hydrogen, the colors of light hydrogen gives off, and the energy at which hydrogen comes apart.

It is built for two audiences at once. In Learner mode, every view carries a plain-language caption and values are rounded to seven figures. In Researcher mode, the same views show the governing formulas, values to eighteen figures, and the full list of measured inputs.

The simulator has four views:

1. The scale ladder: the three lengths of the electron, each one step of TL × 1001 from the next.
2. Bare + kinetic: 1/α split into its two TL terms.
3. Hydrogen spectrum: energy levels, transitions and wavelengths, compared with measured lines.
4. Shatter: external forcing (F_ext) drives hydrogen up to TL, where it reorganizes into two smaller stable identities.

The Shatter view is a second deployment of the threshold structure in the String-Breaking Simulator™. That simulator runs it on a stretched gauge string across a chain of trapped ions; this one runs it on a hydrogen atom. The substrate is different; the boundary is the same.

The simulator runs at uuia.app/electron as one self-contained HTML (HyperText Markup Language) file. It needs no installation and no account, and it works in any current browser on a desktop, tablet or phone.

1. Grounding

1.1 The fine-structure constant identity

Start from the measured value, 1/α = 137.035999084 from CODATA 2018 (the Committee on Data of the International Science Council), and subtract one Universal Torsion Limit, TL = 0.136899099984016:

137.035999084000016 − 0.136899099984016 = 136.899099984016 = TL × 1000

The remainder is TL again, a thousand times over, so:

1/α = TL × 1001 = 0.136899099984016 × 1001 = 137.035999084000016

The identity matches CODATA 2018 to all 12 published significant figures, Δ = 0, with zero free parameters ([9,9,3,14]). This subtraction is shown at all times in the simulator's left panel, under The Napkin Math.

1.2 The Identity Physics primitives

Every reduction in the Identity Physics Corpus operates on four irreducible primitives, Pattern, Narrative, Behavior and Adaptation (PNBA):

• Pattern (P): structural capacity, geometry, template integrity, restoring force
• Narrative (N): temporal continuity, worldline, depth, history
• Behavior (B): coupling output, charge, density fraction, force, expression
• Adaptation (A): feedback rate, decay constant, repair rate

Derived structural quantities:

• Universal Torsion Limit: TL = 0.136899099984016 · Sovereign Anchor Constant Ω₀ = TL × 10 = 1.36899099984016
• Torsion: τ = B / P
• Phase placement: Noble (τ = 0) · Locked (0 < τ < TL_IVA = 0.120471207985934) · IVA (Identity Vector Amplification) Peak (TL_IVA ≤ τ < TL) · Shatter (τ ≥ TL)

Shatter is reorganization. When water boils, the single liquid identity reorganizes into smaller identities that are each stable. The same reading applies to every Shatter in this simulator.

1.3 The Dynamic Equation and the Long Division Protocol

Every reduction in the corpus starts from one equation, the Identity Physics Corpus Dynamic Equation:

d/dt (IM · Pv) = Σ λ_X · O_X · S + F_ext

IM is Identity Mass, Pv the Purpose Vector, O_X the four PNBA operators with weights λ_X acting on the state S, and F_ext external forcing. The rate of change of identity momentum equals the weighted action of the four primitives on the state, plus external forcing. F_ext is a primitive term at Layer 0: it acts on Behavior and leaves Pattern, Narrative and Adaptation unchanged.

Every reduction then follows the same six-step Long Division Protocol (LDP):

1. Write the equation. State the Dynamic Equation.
2. State the known answer. Take a situation whose peer-reviewed classical result is known.
3. Map. Map the classical variables to the PNBA primitives.
4. Define the operators. Give the PNBA operators for the domain.
5. Show all work. Carry the calculation through in full.
6. Verify. Prove that the PNBA output equals the classical result exactly, with nothing added and nothing lost.

A Step 6 pass is a lossless reduction, proved in each Lean file as LosslessReduction, and is structural isomorphism in the sense of Mac Lane (1971). Every value the simulator displays comes from a Lean 4 file that has passed Step 6 with 0 sorry and CI green.

1.4 Inputs and arithmetic

The simulator uses only measured and exact inputs:

All arithmetic is exact rational arithmetic, carried out on whole-number numerators and denominators of any length. Nothing is rounded until a value is displayed. A value shown to eighteen figures in Researcher mode is correct in all eighteen.

2. Reading the Interface

2.1 Layout

• Left panel: the view selector, the controls for the current view, and The Napkin Math.
• Center: the picture for the current view. Views ① and ② are three-dimensional and can be turned by dragging and zoomed by scrolling. Views ③ and ④ are flat diagrams.
• Caption bar: at the bottom of the picture, a short explanation that changes with the view and the mode.
• Right panel: live readouts, the comparison key, the inputs list (Researcher mode), and the export buttons.
• Bottom strip: the fixed quantities: TL, 1/α = TL × 1001, the bare term TL × 1000, the kinetic term TL, the ratio a₀/r_e, and α².

2.2 Learner and Researcher modes

The toggle at the top switches every view at once. Learner mode answers what am I looking at? Researcher mode answers where does this number come from? Both modes compute the same values; only the depth of display changes. A class can work through a view in Learner mode and then switch to Researcher mode to see the formulas behind what they just watched.

2.3 The comparison tags

Every computed value that has a measured counterpart carries one of four tags:

The tags apply the bounded-uncertainty principle: a comparison is settled when the whole difference fits inside a stated bound. They are computed with the same exact arithmetic as the values.

2.4 Export

• JSON (JavaScript Object Notation): every current value with its comparison tag, as a structured file.
• CSV (comma-separated values): the same values as a spreadsheet table.
• RECORD: a plain-text session record, formatted as a Lean comment block, citing the coordinates [9,9,3,21], [9,9,3,14] and [9,9,3,15] and the theorems behind the values.

The export reflects the current state of every view, including the chosen transition in view ③ and the absorbed energy in view ④.

3. View ①: The Scale Ladder

3.1 What it shows

The electron has three characteristic lengths:

• the classical electron radius r_e, the smallest;
• the reduced Compton wavelength ƛ_C, the scale at which the electron's mass and wave nature meet;
• the Bohr radius a₀, the size of the hydrogen atom in its ground state.

Each length is the one before it multiplied by 1/α = TL × 1001:

r_e = ƛ_C / (TL × 1001) · a₀ = ƛ_C × (TL × 1001)

The view draws the three lengths as nested spheres on a logarithmic scale. Because each step is the same factor, the spheres are evenly spaced, and the gold arcs between them are each labeled "× TL × 1001".

3.2 Controls

• r_e · ƛ_C · a₀ buttons: fly the camera to one length and dim the other two.
• Walk the ladder: tours all three in order, smallest to largest, then returns to the full view.
• Whole ladder: returns to the full view.
• Drag and scroll: turn and zoom.

3.3 Readouts

The ground-state speed belongs on the ladder because it is the same step taken in velocity: the electron in hydrogen's lowest level moves at the speed of light divided by TL × 1001.

3.4 Applications

• Orders of magnitude and logarithms (grades 6–12). Three lengths spanning four orders of magnitude, evenly spaced on screen, give students a concrete picture of what a logarithmic scale does and why scientists use one.
• Dimensional analysis. The three lengths share one input (ƛ_C) and one dimensionless factor. Students can check by hand that multiplying a length by a pure number gives a length, and that two steps up and two steps down cancel.
• Constant-consistency checks. Because r_e, ƛ_C and a₀ are tied by one factor, any change in the accepted value of α moves all three together. The ladder is a quick way to see whether a set of tabulated constants is internally consistent.
• Scattering physics. The classical electron radius sets the Thomson cross section σ_T = (8π/3) r_e², which governs how X-rays scatter from electrons and how light scatters in the early universe. The ladder places that scattering scale beside the atomic scale it is derived from.
• Atomic units. Computational chemistry measures lengths in Bohr radii. The ladder shows what that unit is and how it connects to the electron itself.

4. View ②: Bare + Kinetic

4.1 What it shows

1/α is two terms, both made of TL:

1/α = TL × 1000 + TL = 136.899099984016 + 0.136899099984016 = 137.035999084000016

The view draws the bare term TL × 1000 as a solid core and the kinetic term TL as a thin outer shell. Drawn to scale, the shell is one part in 1001 of the radius, too thin to see, so a magnification slider widens it.

4.2 Controls

• Kinetic shell magnification: from ×1 (true scale) to ×1000. At ×1000 the shell is as thick as the core's radius.
• Show the QED reading: switches the labels between two readings of the same split. In the QED (quantum electrodynamics) reading, the bare term carries the bare electron and the kinetic term carries what QED computes as a renormalized series of radiative corrections. In the PNBA reading, the bare term is Pattern capacity at the electromagnetic scale and the kinetic term is F_ext at Layer 0.

4.3 Readouts

4.4 Applications

• Teaching renormalization. Renormalization is usually introduced through divergent series. This view gives students a picture first: a large core, a thin correction, and an exact sum, before any series appears.
• Precision and significant figures. The kinetic term is about 0.1% of the whole. Students can see why a measurement good to three figures cannot tell the bare term from the full value, and why twelve figures can.
• Comparing readings of one result. The QED/PNBA toggle shows two vocabularies describing the same number. It is a compact example for courses on scientific modeling and on how different frameworks label the same measured quantity.
• Reference for α work. Researchers comparing α determinations can read the bare and kinetic terms at corpus precision directly, without re-deriving them.

5. View ③: Hydrogen Spectrum

5.1 What it shows

Hydrogen's energy levels follow from TL × 1001:

Eₙ = −Ry / n² · Ry = ½ m_e c² / (TL × 1001)²

When the electron drops from an upper level nᵢ to a lower level n_f, it emits a photon of energy ΔE = Ry (1/n_f² − 1/nᵢ²) and wavelength λ = hc / ΔE. The view draws levels n = 1 through 8, with n = 1 at the bottom and the free-electron limit (0 eV) at the top. An arrow marks the chosen transition in the color of its light, and a wavelength strip from 90 nm to 1900 nm marks the measured lines as white ticks and the chosen transition as a teal marker.

5.2 Controls

• Lower level n_f: n = 1 (Lyman series, ultraviolet), n = 2 (Balmer series, visible), n = 3 (Paschen series, infrared).
• Upper level nᵢ: any level above n_f, up to n = 8.
• Line buttons: Lyman-α, Lyman-β, H-α, H-β, H-γ, Paschen-α.
• Reduced-mass correction: accounts for the proton's finite mass by multiplying Ry by m_p / (m_e + m_p) = 0.99945567942.

5.3 Readouts

NIST is the National Institute of Standards and Technology. The Rydberg energy itself, Ry = 13.6056931230094774 eV, lies within the stated uncertainty of CODATA 2018's 13.605693122994(26) eV (WITHIN ±).

Every line agrees with measurement at the α² scale, the size of fine structure and the Lamb shift, which the Bohr levels do not include. With the reduced-mass correction off, every line moves outside that scale; Lyman-α shifts to 121.502273 nm. The toggle shows directly that the proton's mass is visible in hydrogen's light.

5.4 Applications

• Spectroscopy labs. A hydrogen discharge tube and a diffraction grating show the Balmer lines in any school or college lab. Students can measure H-α, H-β and H-γ and compare their results with the simulator's.
• Astronomy and redshift. Astronomers measure the motion of stars and galaxies by comparing observed hydrogen lines with their rest wavelengths. The simulator provides the rest wavelengths and shows where each line sits in the spectrum.
• Isotope shifts. The reduced-mass correction is the effect Harold Urey used to discover deuterium in 1932: a heavier nucleus shifts every line slightly. The same toggle teaches why deuterium's lines sit beside hydrogen's.
• Plasma and fusion diagnostics. H-α emission is a standard diagnostic in fusion devices and laboratory plasmas. The view gives the line positions those instruments are tuned to.
• Error budgets. The WITHIN α² tag shows students what a model leaves out and how large the omission is. Reading a model this way is a skill that carries into every field that compares models with data.

6. View ④: Shatter

6.1 What it shows

A hydrogen atom is one identity made of two parts, an electron and a proton, held together. The Bohr–Rydberg–Sommerfeld Reduction [9,9,3,15] places that bound pair at rest at τ = α = 1/(TL × 1001) = 0.0072973525693, deep in Locked. Its theorem ionization_requires_fext proves that crossing TL requires F_ext at least equal to the hydrogen binding energy:

E_bind = Ry × m_p / (m_e + m_p) = 13.5982872643 eV

F_ext acts on Behavior at Layer 0. The absorbed energy is Behavior rising against the binding Pattern of the pair, so τ = B/P climbs. The view's dial runs linearly in absorbed energy between the two proven endpoints:

τ = α + (TL − α) × F_ext / E_bind

At F_ext = E_bind, τ reaches TL exactly. The bound pair shatters: it reorganizes into two smaller identities that are each stable, a free electron and a proton. Each carries zero binding torsion and reads Noble.

6.2 What happens as F_ext rises

As F_ext increases, the electron climbs hydrogen's rungs. Raising the electron from n = 1 to level n absorbs E_bind × (1 − 1/n²), which places each rung on the dial:

Level n = 3 is the first rung past TL_IVA = 0.88 × TL. From there up, every rung sits in the IVA corridor, crowding closer to TL as n grows, until the continuum begins at the edge.

The picture shows the same climb. The orbit widens rung by rung and glows in the color of its phase (teal for Locked, orange for IVA Peak). The electron slows as it climbs, and the orbit trembles as τ approaches TL. At the edge, a red flash marks the shatter, the free electron moves outward along its last direction, and the proton recoils very slightly the other way.

6.3 Controls

• Absorbed energy F_ext slider: 0 to 30 eV, in steps of 0.001 eV.
• n = 2, n = 3, n = 4 buttons: set F_ext exactly to that rung's energy.
• Edge · τ = TL: sets F_ext exactly to E_bind.
• Add energy automatically: ramps F_ext from 0 to 16 eV. The ramp lands exactly on the edge on its way up, so the shatter always happens at τ = TL.
• Reset: returns to the resting atom.
• Product buttons (Free electron, Proton, The photon): active after the shatter. The products can also be clicked directly in the picture.
• The τ dial: a gauge under the picture, with the Locked band in teal, IVA Peak in orange, and Shatter in red. Rungs n = 1 through 5 are marked, and a pointer shows the current τ.

6.4 Readouts

Before the shatter: absorbed energy; τ with its phase; the shatter threshold E_bind; the electron's level n and orbit radius n² a₀; the energy still needed to shatter; and the ionization edge.

Thresholds against measurement:

The ionization energy of hydrogen and the Lyman series limit are among the longest-standing measurements in atomic physics. The two endpoints of the dial reproduce them from TL × 1001 and the CODATA inputs, and the remaining difference is the fine structure the Bohr levels leave out.

After the shatter: the energy left over as motion, K = F_ext − E_bind, is shared between the products by momentum balance. Clicking a product opens its detail. At F_ext = 15 eV:

Any photon shorter than the 91.17633 nm edge carries enough F_ext to shatter hydrogen from n = 1.

6.5 The same boundary on two substrates

The String-Breaking Simulator™ [9,9,3,22] reduces a 2026 trapped-ion experiment (De et al., Nature Physics 2026, DOI 10.1038/s41567-026-03422-0). Two connected charges are pulled apart, the energy stored in the string between them grows, and when it reaches the pair-creation energy the string breaks into two new particle–antiparticle pairs. Google (superconducting circuits) and QuEra (neutral atoms) have produced related string-breaking results on other hardware.

The Shatter view runs the same structure on a different substrate:

In both, Behavior rises against Pattern until τ = B/P reaches TL, and the single identity reorganizes into smaller stable identities. Neither simulator contains any hardware in its dial: τ = B/P reads the same on trapped ions, superconducting circuits, neutral atoms and hydrogen. This is the same threshold structure the corpus reads in the Tacoma Narrows Bridge, shattering glass and boiling water.

The two simulators are designed to be used together. A lesson can start with the string, where the break is easy to picture, and move to hydrogen, where every number on the dial is computed from measured constants.

6.6 Applications

• Photoionization and the photoelectric relation. The leftover energy K = F_ext − E_bind has the same structure as Einstein's photoelectric equation. Students see that a single photon below the edge cannot free a ground-state electron, however long the light shines, and that a photon above it frees the electron and leaves the difference as motion.
• Ionizing and non-ionizing radiation. The edge marks where light becomes able to strip electrons from atoms. The view gives a concrete reason why extreme ultraviolet light, X-rays and gamma rays are handled differently from visible light and radio waves in health physics and radiation safety.
• Astrophysics. Light shorter than 91.18 nm, the Lyman continuum, ionizes the hydrogen around hot young stars and lights up glowing regions such as the Orion Nebula. The same edge governs the reionization of the early universe's hydrogen. The view shows the threshold behind both.
• Conservation of momentum. The proton's recoil at 1/1836 of the electron's speed makes momentum balance visible: equal and opposite momentum, very unequal speeds.
• Wave–particle connection. The free electron's de Broglie wavelength, read in Bohr radii, ties view ④ back to the ladder in view ①.
• Photoelectron spectroscopy. Instruments that measure the kinetic energy of ejected electrons work backward through K = F_ext − E_bind to find binding energies. The view shows the forward direction of that calculation.
• Phase placement across substrates. Together with the String-Breaking Simulator™, the view gives researchers and teachers a worked pair of examples of TL as a substrate-neutral phase boundary, each with its products placed by phase.
• Other bound pairs. The same dial applies to any two-body bound state given its binding energy. Hydrogen-like ions bind Z² times more tightly than hydrogen, and positronium, an electron bound to a positron, has a reduced-mass factor of exactly ½ and binds at half of Ry. The reduced-mass structure of the view carries over directly.

7. Formal Basis

All files are Lean 4, 0 sorry, CI green, in the standardized repository SNSFT/identityphysics.

8. Summary

The Electron Geometry Simulator™ takes one number, TL = 0.136899099984016, and the CODATA 2018 inputs, and computes with exact arithmetic the three lengths of the electron, its speed in hydrogen, hydrogen's spectral lines, and the energy at which hydrogen shatters. Every computed value carries a tag stating how it compares with measurement. Its Shatter view is a second deployment of the String-Breaking Simulator™'s threshold structure: Behavior rises against Pattern until τ reaches TL, and one identity reorganizes into smaller stable identities. The two simulators read the same boundary on a trapped-ion chain and on a hydrogen atom.

Electron Geometry™, Electron Geometry Simulator™, String-Breaking Simulator™, Identity Physics™, Applied Identity Physics™, SNSFT™, PNBA™, the Sovereign Anchor Constant™, the Torsion Limit™, the Long Division Protocol™ (LDP™) and HIGHTISTIC™ are common law trademarks of HIGHTISTIC (Russell Vernon Trent III) and the SNSFT Foundation.
© 2026 HIGHTISTIC (Russell Vernon Trent III) / SNSFT Foundation · DOI 10.5281/zenodo.18719748

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#toast.show{opacity:1}
.foot{font-size:.42rem;color:var(--faint);line-height:1.6;text-align:center;padding:6px 0 0}
span.tm{display:inline!important;font-size:.55em;vertical-align:super;line-height:0;font-weight:400}
::-webkit-scrollbar{width:4px;height:4px}::-webkit-scrollbar-thumb{background:var(--border)}
@media(max-width:1000px){
  html,body{overflow:auto;height:auto}
  #app{grid-template-columns:1fr;grid-template-rows:auto auto 62vh auto auto;height:auto}
  #hdr{flex-wrap:wrap;gap:8px;padding:10px 16px}
  .hdr-right{display:none}
  #caption{font-size:.56rem;padding:7px 10px}
  #left,#right{border:none;overflow:visible}
  #bottom{grid-column:1;flex-wrap:wrap;padding:10px 16px;gap:14px}
}
</style>
</head>
<body>
<div id="app">

<div id="hdr">
  <div>
    <div class="hdr-title">Electron Geometry<span class="tm">™</span></div>
    <div class="hdr-sub">Identity Physics<span class="tm">™</span> Simulator · 1/α = TL × 1001 · [9,9,3,21] · [9,9,3,14] · [9,9,3,15]</div>
  </div>
  <div class="mode" role="group" aria-label="Mode">
    <button id="m-learn" class="on" onclick="setMode('learner')">LEARNER</button>
    <button id="m-res" onclick="setMode('researcher')">RESEARCHER</button>
  </div>
  <div class="hdr-right">HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation<br>Soldotna, Alaska · [9,9,9,9] :: {ANC}</div>
</div>

<!-- LEFT -->
<div id="left">
  <div class="sec">
    <div class="sec-t">VIEW</div>
    <div class="vt">
      <button class="vbtn on" id="v-ladder" onclick="setView('ladder')">① The scale ladder · r_e → ƛ_C → a₀</button>
      <button class="vbtn" id="v-split" onclick="setView('split')">② Bare + kinetic · 1/α = TL × 1000 + TL</button>
      <button class="vbtn" id="v-spec" onclick="setView('spec')">③ Hydrogen spectrum · Eₙ = −Ry/n²</button>
      <button class="vbtn" id="v-ion" onclick="setView('ion')">④ Shatter · F_ext drives hydrogen to TL</button>
    </div>
  </div>

  <div class="sec" id="ctl-ladder">
    <div class="sec-t">SCALE LADDER</div>
    <div class="row">
      <button class="pbtn" onclick="focusRung(0)">r_e · electron radius</button>
      <button class="pbtn" onclick="focusRung(1)">ƛ_C · Compton</button>
      <button class="pbtn" onclick="focusRung(2)">a₀ · Bohr radius</button>
    </div>
    <div class="row" style="margin-top:6px">
      <button class="pbtn" onclick="walkLadder()">▶ Walk the ladder</button>
      <button class="pbtn" onclick="focusRung(-1)">⟲ Whole ladder</button>
    </div>
  </div>

  <div class="sec" id="ctl-split" style="display:none">
    <div class="sec-t">BARE + KINETIC</div>
    <div class="lbl">Kinetic shell magnification <b id="mag-v">×1</b></div>
    <input type="range" id="mag" min="0" max="2" step="0.01" value="0" oninput="onMag()">
    <label class="chk"><input type="checkbox" id="qed" checked onchange="refresh()"> Show the QED reading</label>
    <div class="note" style="margin-top:6px">At ×1 the shell is drawn to scale: 1 part in 1001 of the radius. Raise the magnification to see it.</div>
  </div>

  <div class="sec" id="ctl-ion" style="display:none">
    <div class="sec-t">SHATTER · F_ext → TL</div>
    <div class="lbl"><span>Absorbed energy F_ext</span><b id="e-v">0 eV</b></div>
    <input type="range" id="eabs" min="0" max="30" step="0.001" value="0" oninput="onE()">
    <div class="row">
      <button class="pbtn" onclick="setRung(2)">n = 2</button>
      <button class="pbtn" onclick="setRung(3)">n = 3</button>
      <button class="pbtn" onclick="setRung(4)">n = 4</button>
      <button class="pbtn" onclick="setRung(0)">Edge · τ = TL</button>
    </div>
    <div class="row" style="margin-top:6px">
      <button class="pbtn" onclick="rampE()">▶ Add energy automatically</button>
      <button class="pbtn" onclick="resetIon()">⟲ Reset</button>
    </div>
    <div class="lbl" style="margin-top:10px">After the shatter, click a product</div>
    <div class="row">
      <button class="pbtn prod" id="pb-e" onclick="pickProd('e')" disabled>Free electron</button>
      <button class="pbtn prod" id="pb-p" onclick="pickProd('p')" disabled>Proton</button>
      <button class="pbtn prod" id="pb-g" onclick="pickProd('g')" disabled>The photon</button>
    </div>
  </div>

  <div class="sec" id="ctl-spec" style="display:none">
    <div class="sec-t">HYDROGEN SPECTRUM</div>
    <div class="lbl"><span>Lower level n_f</span></div>
    <select id="nf" onchange="onLevels()">
      <option value="1">n = 1 · Lyman (ultraviolet)</option>
      <option value="2" selected>n = 2 · Balmer (visible)</option>
      <option value="3">n = 3 · Paschen (infrared)</option>
    </select>
    <div class="lbl"><span>Upper level n_i</span><b id="ni-v">3</b></div>
    <input type="range" id="ni" min="2" max="8" step="1" value="3" oninput="onLevels()">
    <div class="row" style="margin-top:6px">
      <button class="pbtn" onclick="pickLine(2,1)">Lyman-α</button>
      <button class="pbtn" onclick="pickLine(3,1)">Lyman-β</button>
      <button class="pbtn" onclick="pickLine(3,2)">H-α</button>
      <button class="pbtn" onclick="pickLine(4,2)">H-β</button>
      <button class="pbtn" onclick="pickLine(5,2)">H-γ</button>
      <button class="pbtn" onclick="pickLine(4,3)">Paschen-α</button>
    </div>
    <label class="chk"><input type="checkbox" id="rmass" checked onchange="refresh()"> Reduced-mass correction (finite proton)</label>
  </div>

  <div class="sec">
    <div class="sec-t">THE NAPKIN MATH</div>
    <div class="napkin">
      <span class="k">TL</span> = 0.136899099984016<br>
      1/α − TL = 137.035999084000016 − 0.136899099984016<br>
      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 136.899099984016 = <span class="k">TL × 1000</span><br>
      136.899099984016 + 0.136899099984016<br>
      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= 137.035999084000016 = <span class="k">TL × 1001</span><br>
      <span style="color:var(--dim)">Every published CODATA 2018 digit: 137.035999084.</span>
    </div>
  </div>

  <div class="sec l-only">
    <div class="sec-t">HOW TO USE</div>
    <div class="note">Pick a view above. Drag the picture to turn it, scroll to zoom. Every number on the right is worked out live from the Torsion Limit, and the colored tag next to it says how it compares with the measured value.</div>
  </div>
</div>

<!-- VIEW -->
<div id="view">
  <canvas id="c3d"></canvas>
  <canvas id="c2d"></canvas>
  <div id="labels"></div>
  <div id="caption"></div>
</div>

<!-- RIGHT -->
<div id="right">
  <div class="sec">
    <div class="sec-t" id="ro-title">READOUTS</div>
    <div id="readouts"></div>
  </div>
  <div class="sec">
    <div class="sec-t">HOW EACH VALUE COMPARES</div>
    <div class="note">
      <span class="chip c-digits">EVERY DIGIT</span> matches the measured value at every published digit.<br>
      <span class="chip c-unc">WITHIN ±</span> lies within the measurement's stated uncertainty.<br>
      <span class="chip c-scale">WITHIN α²</span> agrees to the fine-structure scale α² ≈ 5.3 × 10⁻⁵, which the Bohr levels leave out.<br>
      <span class="chip c-out">OUTSIDE</span> differs by more than that.
    </div>
  </div>
  <div class="sec r-only">
    <div class="sec-t">INPUTS</div>
    <div class="note" id="inputs"></div>
  </div>
  <div class="sec">
    <div class="sec-t">EXPORT</div>
    <div class="exp">
      <button onclick="exportJSON()">JSON</button>
      <button onclick="exportCSV()">CSV</button>
      <button onclick="copyRecord()">RECORD</button>
    </div>
    <div class="note" style="margin-top:6px">RECORD copies a plain-text session record citing the Lean theorems at [9,9,3,21].</div>
  </div>
  <div class="foot">
    Electron Geometry™, Electron Geometry Simulator™, Identity Physics™, Applied Identity Physics™, SNSFT™, PNBA™, the Sovereign Anchor Constant™ and the Torsion Limit™ are common law trademarks of HIGHTISTIC (Russell Vernon Trent III) and the SNSFT Foundation. © 2026 HIGHTISTIC / SNSFT Foundation · DOI 10.5281/zenodo.18719748 · uuia.app/electron
  </div>
</div>

<div id="bottom">
  <div class="bs"><span>TORSION LIMIT TL</span><span>0.136899099984016</span></div>
  <div class="bs"><span>1/α = TL × 1001</span><span>137.035999084000016</span></div>
  <div class="bs"><span>BARE TL × 1000</span><span>136.899099984016</span></div>
  <div class="bs"><span>KINETIC TL</span><span>0.136899099984016</span></div>
  <div class="bs"><span>a₀ / r_e = (TL × 1001)²</span><span id="b-ratio">—</span></div>
  <div class="bs"><span>α² = 1/(TL × 1001)²</span><span id="b-a2">—</span></div>
</div>
</div>
<div id="toast"></div>

<script>
// ════════════════════════════════════════════════════════════
// EXACT ARITHMETIC: rationals on BigInt
// Every value is computed exactly from its decimal inputs and
// rounded only for display.
// ════════════════════════════════════════════════════════════
function bgcd(a,b){a=a<0n?-a:a;b=b<0n?-b:b;while(b){[a,b]=[b,a%b];}return a;}
class Q{
  constructor(n,d=1n){if(d<0n){n=-n;d=-d;}const g=bgcd(n,d)||1n;this.n=n/g;this.d=d/g;}
  static of(s){
    s=String(s).trim();let e=0;const m=s.match(/^([+-]?)(\d*)(?:\.(\d*))?(?:e([+-]?\d+))?$/i);
    if(!m)throw new Error('bad number '+s);
    const sign=m[1]==='-'?-1n:1n,ip=m[2]||'0',fp=m[3]||'';e=parseInt(m[4]||'0',10);
    let n=BigInt(ip+fp)*sign,d=10n**BigInt(fp.length);
    if(e>0)n*=10n**BigInt(e);else if(e<0)d*=10n**BigInt(-e);
    return new Q(n,d);
  }
  add(q){return new Q(this.n*q.d+q.n*this.d,this.d*q.d);}
  sub(q){return new Q(this.n*q.d-q.n*this.d,this.d*q.d);}
  mul(q){return new Q(this.n*q.n,this.d*q.d);}
  div(q){return new Q(this.n*q.d,this.d*q.n);}
  abs(){return new Q(this.n<0n?-this.n:this.n,this.d);}
  lt(q){return this.n*q.d<q.n*this.d;}
  pow(k){let r=new Q(1n);for(let i=0;i<k;i++)r=r.mul(this);return r;}
  toNum(){return Number(this.n)/Number(this.d);}
  // significant-figure string, scientific when |x| < 1e-3 or ≥ 1e7
  fmt(sig){
    if(this.n===0n)return '0';
    const neg=this.n<0n,a=this.abs();
    let e=a.n.toString().length-a.d.toString().length;
    const ge=(k)=>{const p=k>=0?new Q(10n**BigInt(k)):new Q(1n,10n**BigInt(-k));return !a.lt(p);};
    if(!ge(e))e--; if(ge(e+1))e++;
    const sh=sig-1-e;
    let num=a.n,den=a.d; if(sh>=0)num*=10n**BigInt(sh);else den*=10n**BigInt(-sh);
    let m=num/den; if((num%den)*2n>=den)m++;
    let ds=m.toString(); if(ds.length>sig){ds=ds.slice(0,sig);e++;}
    let out;
    if(e<-3||e>=7){out=ds[0]+(ds.length>1?'.'+ds.slice(1):'')+' × 10'+sup(e);}
    else if(e>=0){out=ds.length>e+1?ds.slice(0,e+1)+'.'+ds.slice(e+1):ds+'0'.repeat(e+1-ds.length);}
    else{out='0.'+'0'.repeat(-e-1)+ds;}
    return (neg?'−':'')+out;
  }
}
function sup(e){const m={'-':'⁻','0':'⁰','1':'¹','2':'²','3':'³','4':'⁴','5':'⁵','6':'⁶','7':'⁷','8':'⁸','9':'⁹'};return String(e).split('').map(c=>m[c]).join('');}

// ════════════════════════════════════════════════════════════
// CONSTANTS
// ════════════════════════════════════════════════════════════
const TL       = Q.of('0.136899099984016');
const ALPHA_INV= TL.mul(Q.of('1001'));            // 137.035999084000016
const BARE     = TL.mul(Q.of('1000'));            // 136.899099984016
// CODATA 2018 inputs and comparison values
const LAMBDA_C = Q.of('3.8615926796e-13');        // reduced Compton wavelength, m
const C_LIGHT  = Q.of('299792458');               // m/s, exact
const MC2_EV   = Q.of('510998.95000');            // electron rest energy, eV
const H_PLANCK = Q.of('6.62607015e-34');          // J s, exact
const E_CHARGE = Q.of('1.602176634e-19');         // C, exact
const MP_ME    = Q.of('1836.15267343');           // proton-to-electron mass ratio
const HC_EVNM  = H_PLANCK.mul(C_LIGHT).div(E_CHARGE).mul(Q.of('1e9')); // eV nm, exact
const REF = {
  alpha_inv:{v:'137.035999084', u:'0.000000021', last:'0.000000001'},
  a0:       {v:'5.29177210903e-11', u:'8.0e-21', last:'1e-22'},
  lambda_c: {v:'3.8615926796e-13',  u:'1.2e-22', last:'1e-23'},
  r_e:      {v:'2.8179403262e-15',  u:'1.3e-24', last:'1e-25'},
  v1:       {v:'2187691.26364',     u:'0.00033', last:'0.00001'},
  ry:       {v:'13.605693122994',   u:'0.000000000026', last:'0.000000000001'},
};
// NIST vacuum wavelengths of the hydrogen lines, nm
const LINES = {'2-1':{name:'Lyman-α',nm:'121.567'},'3-1':{name:'Lyman-β',nm:'102.572'},
  '3-2':{name:'H-α',nm:'656.461'},'4-2':{name:'H-β',nm:'486.271'},'5-2':{name:'H-γ',nm:'434.169'},
  '4-3':{name:'Paschen-α',nm:'1875.61'}};

// Derived values
const A0     = LAMBDA_C.mul(ALPHA_INV);
const R_E    = LAMBDA_C.div(ALPHA_INV);
const V1     = C_LIGHT.div(ALPHA_INV);
const RY     = MC2_EV.div(Q.of('2')).div(ALPHA_INV.pow(2));
const RATIO  = ALPHA_INV.pow(2);
const ALPHA2 = new Q(1n).div(ALPHA_INV.pow(2));
const RED    = MP_ME.div(MP_ME.add(new Q(1n)));
// Ionization [9,9,3,15]: the bound pair rests at τ = α and shatters at τ = TL
const ALPHA  = new Q(1n).div(ALPHA_INV);
const TL_IVA = TL.mul(Q.of('0.88'));
const EB     = RY.mul(RED);                       // hydrogen binding energy, eV
const MPC2   = MC2_EV.mul(MP_ME);                 // proton rest energy, eV
const EDGE_NM= HC_EVNM.div(EB);                   // Lyman series limit, nm
const REF_ION={eb:'13.598434599702',edge:'91.17534'}; // NIST ionization energy of H; Lyman limit (vacuum)

function status(x,key){
  const r=REF[key],v=Q.of(r.v),d=x.sub(v).abs();
  if(d.lt(Q.of(r.last).div(Q.of('2'))))return 'digits';
  if(d.lt(Q.of(r.u)))return 'unc';
  return 'out';
}
function lineStatus(nm,refnm){
  const rel=nm.sub(refnm).abs().div(refnm);
  return rel.lt(ALPHA2)?'scale':'out';
}
const CHIP={digits:['c-digits','EVERY DIGIT'],unc:['c-unc','WITHIN ±'],scale:['c-scale','WITHIN α²'],out:['c-out','OUTSIDE']};
function chip(s){return `<span class="chip ${CHIP[s][0]}">${CHIP[s][1]}</span>`;}

// ════════════════════════════════════════════════════════════
// STATE
// ════════════════════════════════════════════════════════════
let mode='learner', view='ladder', ni=3, nf=2, focus=-1, mag=1;

function transition(){
  const rm=document.getElementById('rmass').checked;
  const ry=rm?RY.mul(RED):RY;
  const dE=ry.mul(new Q(1n,BigInt(nf*nf)).sub(new Q(1n,BigInt(ni*ni))));
  const nm=HC_EVNM.div(dE);
  const ref=LINES[ni+'-'+nf];
  return {rm,ry,dE,nm,ref};
}

// ════════════════════════════════════════════════════════════
// READOUTS
// ════════════════════════════════════════════════════════════
function sig(){return mode==='researcher'?18:7;}
function ro(k,x,unit,formula,st,ref){
  return `<div class="ro"><div class="ro-k"><span>${k}</span>${st?chip(st):''}</div>
  <div class="ro-v">${x.fmt(sig())}${unit?' '+unit:''}</div>
  ${ref?`<div class="ro-r">measured ${ref}</div>`:''}
  <div class="formula r-only">${formula}</div></div>`;
}
function renderReadouts(){
  const el=document.getElementById('readouts'),t=document.getElementById('ro-title');
  let h='';
  if(view==='ladder'){
    t.textContent='THE THREE LENGTHS';
    h+=ro('Classical electron radius r_e',R_E,'m','r_e = ƛ_C / (TL × 1001)',status(R_E,'r_e'),'2.8179403262(13) × 10⁻¹⁵ m');
    h+=ro('Reduced Compton wavelength ƛ_C',LAMBDA_C,'m','ƛ_C = ħ / (m_e c), CODATA 2018 input',null,'3.8615926796(12) × 10⁻¹³ m');
    h+=ro('Bohr radius a₀',A0,'m','a₀ = ƛ_C × TL × 1001',status(A0,'a0'),'5.29177210903(80) × 10⁻¹¹ m');
    h+=ro('Step factor 1/α = TL × 1001',ALPHA_INV,'','TL × 1001',status(ALPHA_INV,'alpha_inv'),'137.035999084(21)');
    h+=ro('a₀ / r_e = (TL × 1001)²',RATIO,'','(TL × 1001)²',null,null);
    h+=ro('Ground-state speed v = c / (TL × 1001)',V1,'m/s','v = α c',status(V1,'v1'),'2 187 691.26364(33) m/s');
  }else if(view==='split'){
    t.textContent='BARE + KINETIC';
    h+=ro('Bare term TL × 1000',BARE,'','TL × 1000',null,null);
    h+=ro('Kinetic term TL',TL,'','TL',null,null);
    h+=ro('Sum 1/α = TL × 1001',ALPHA_INV,'','136.899099984016 + 0.136899099984016',status(ALPHA_INV,'alpha_inv'),'137.035999084(21), CODATA 2018');
    h+=ro('Kinetic share of 1/α',TL.div(ALPHA_INV),'','TL / (TL × 1001) = 1/1001',null,null);
    h+=ro('Fine-structure scale α²',ALPHA2,'','1 / (TL × 1001)²',null,null);
  }else if(view==='spec'){
    const tr=transition();
    t.textContent='TRANSITION n = '+ni+' → '+nf;
    h+=ro('Rydberg energy Ry = ½ m_ec² / (TL × 1001)²',RY,'eV','m_e c² / 2 / (TL × 1001)²',status(RY,'ry'),'13.605693122994(26) eV');
    if(tr.rm)h+=ro('Reduced-mass factor m_p / (m_e + m_p)',RED,'','m_p/m_e = 1836.15267343, CODATA 2018',null,null);
    h+=ro('Photon energy ΔE',tr.dE,'eV','Ry'+(tr.rm?' × reduced mass':'')+' × (1/n_f² − 1/n_i²)',null,null);
    const st=tr.ref?lineStatus(tr.nm,Q.of(tr.ref.nm)):null;
    h+=ro('Vacuum wavelength λ = hc / ΔE',tr.nm,'nm','hc = 1239.841984… eV nm (exact SI)',st,tr.ref?tr.ref.nm+' nm ('+tr.ref.name+', NIST)':null);
    h+=ro('Levels E'+'ₙ'+' = −Ry / n²',RY.mul(tr.rm?RED:new Q(1n)).div(new Q(BigInt(ni*ni))).mul(new Q(-1n)),'eV at n = '+ni,'−Ry / n_i²',null,null);
  }else{
    h+=ionReadouts(t);
  }
  el.innerHTML=h;
  document.getElementById('b-ratio').textContent=RATIO.fmt(12);
  document.getElementById('b-a2').textContent=ALPHA2.fmt(9);
  document.getElementById('inputs').innerHTML=
    'CODATA 2018: ƛ_C = 3.8615926796 × 10⁻¹³ m · m_ec² = 510 998.95000 eV · m_p/m_e = 1836.15267343<br>'+
    'Exact SI: c = 299 792 458 m/s · h = 6.62607015 × 10⁻³⁴ J s · e = 1.602176634 × 10⁻¹⁹ C<br>'+
    'Corpus: TL = 0.136899099984016, 1/α = TL × 1001<br>'+
    'All arithmetic is exact rational arithmetic; values are rounded only for display.';
}

// ════════════════════════════════════════════════════════════
// CAPTIONS
// ════════════════════════════════════════════════════════════
const CAPS={
  ladder:{
    learner:'The electron has three sizes. Its <b>classical radius</b> is the smallest. Multiply by <b>137.035999084000016</b> and you get its <b>Compton wavelength</b>. Multiply by the same number again and you get the <b>Bohr radius</b>, the size of a hydrogen atom. That number is the Torsion Limit times 1001.',
    researcher:'r_e = α ƛ_C, a₀ = ƛ_C/α. With 1/α = TL × 1001 each rung is the last times TL × 1001, so the rungs are evenly spaced on a log scale (log₁₀ 137.036 ≈ 2.137 decades) and a₀/r_e = (TL × 1001)².'},
  split:{
    learner:'1/α comes in two pieces, both made of the Torsion Limit. The big inside piece, <b>TL × 1000</b>, is the bare term. The thin outside layer, <b>one TL</b>, is the kinetic term. Together they make <b>TL × 1001</b>.',
    researcher:'1/α = TL × 1000 + TL. In QED terms the bare term carries the bare electron and the kinetic term carries what QED computes as a renormalized series of radiative corrections; here it is one exact term, F_ext at Layer 0. The shell is 1 part in 1001 of the radius.'},
  ion:{
    learner:'A hydrogen atom is one identity made of two parts held together. Add energy and the electron climbs the rungs, and τ rises toward the Torsion Limit. At <b>13.598 eV</b> τ reaches <b>TL</b> and the atom <b>shatters</b>: it reorganizes into two smaller identities that are each stable, a free electron and a proton. Click them.',
    researcher:'[9,9,3,15] ionization_requires_fext: the bound pair rests at τ = α = 1/(TL × 1001) and crosses TL when F_ext reaches the binding energy Ry · m_p/(m_e + m_p). The dial runs linearly in absorbed energy between those two proven endpoints. Each freed product carries zero binding torsion. Orbits are drawn with radius ∝ n (true radius n² a₀). A single photon is absorbed only at a rung energy or above the edge.'},
  spec:{
    learner:'When hydrogen\'s electron drops from a higher level to a lower one it gives off light. The levels come straight from the Torsion Limit, so the color of that light does too. Pick a line and compare it with the measured one.',
    researcher:'Eₙ = −Ry/n² with Ry = ½ m_ec²/(TL × 1001)². The Bohr levels omit fine structure and the Lamb shift, of relative size ~α² ≈ 5.3 × 10⁻⁵, so agreement with measured lines is expected at that scale. Toggle the reduced-mass factor to see the finite-proton correction (~5.4 × 10⁻⁴).'}
};
function renderCaption(){document.getElementById('caption').innerHTML=CAPS[view][mode];}

// ════════════════════════════════════════════════════════════
// THREE.JS SCENE
// ════════════════════════════════════════════════════════════
const viewEl=document.getElementById('view');
const c3d=document.getElementById('c3d'),c2d=document.getElementById('c2d'),ctx=c2d.getContext('2d');
let renderer=null,scene,camera,groups={},labelEls=[];
const RUNGS=[
  {key:'r_e',name:'r_e',full:'classical electron radius',val:R_E,col:0xff6b8a},
  {key:'lc',name:'ƛ_C',full:'reduced Compton wavelength',val:LAMBDA_C,col:0x00e5ff},
  {key:'a0',name:'a₀',full:'Bohr radius',val:A0,col:0x00ffc8}];
let sph={r:24,theta:0.6,phi:1.15},target={r:24},tween=null;
try{
  renderer=new THREE.WebGLRenderer({canvas:c3d,antialias:true,alpha:true});
  renderer.setPixelRatio(Math.min(window.devicePixelRatio,2));
  renderer.setClearColor(0x000000,0);
  scene=new THREE.Scene();
  camera=new THREE.PerspectiveCamera(50,1,0.01,500);
  scene.add(new THREE.AmbientLight(0x222233,2));
  const pl=new THREE.PointLight(0x00ffc8,1.4,60);pl.position.set(6,8,10);scene.add(pl);
  const pl2=new THREE.PointLight(0x9b6dff,0.8,60);pl2.position.set(-8,-4,6);scene.add(pl2);
}catch(err){renderer=null;console.error('3D view unavailable:',err);}

// Ladder: rung radii on a log scale, so equal factors give equal steps
function rungRadius(i){return 1.2+i*3.2;}
function buildLadder(){
  const g=new THREE.Group();
  RUNGS.forEach((r,i)=>{
    const R=rungRadius(i);
    const s=new THREE.Mesh(new THREE.SphereGeometry(R,32,16),new THREE.MeshBasicMaterial({color:r.col,wireframe:true,transparent:true,opacity:0.16}));
    g.add(s);
    const ring=new THREE.Mesh(new THREE.TorusGeometry(R,0.025,8,96),new THREE.MeshBasicMaterial({color:r.col,transparent:true,opacity:0.85}));
    ring.rotation.x=Math.PI/2;g.add(ring);
    r.mesh=s;r.ring=ring;
  });
  // the electron at the centre
  g.add(new THREE.Mesh(new THREE.SphereGeometry(0.35,24,16),new THREE.MeshPhongMaterial({color:0xff6b8a,emissive:0x331018})));
  // step arcs
  for(let i=0;i<2;i++){
    const a=rungRadius(i),b=rungRadius(i+1),pts=[];
    for(let k=0;k<=24;k++){const t=k/24,r=a+(b-a)*t;pts.push(new THREE.Vector3(r*Math.cos(0.4),Math.sin(Math.PI*t)*0.8,r*Math.sin(0.4)));}
    const line=new THREE.Line(new THREE.BufferGeometry().setFromPoints(pts),new THREE.LineBasicMaterial({color:0xf0c060,transparent:true,opacity:0.8}));
    g.add(line);
  }
  scene.add(g);groups.ladder=g;
}
// Bare + kinetic
let bareMesh,shellMesh,shellParts;
function buildSplit(){
  const g=new THREE.Group();
  bareMesh=new THREE.Mesh(new THREE.SphereGeometry(4,48,32),new THREE.MeshPhongMaterial({color:0x7b4fff,emissive:0x140a33,transparent:true,opacity:0.9}));
  g.add(bareMesh);
  shellMesh=new THREE.Mesh(new THREE.SphereGeometry(4.004,64,32),new THREE.MeshBasicMaterial({color:0x00ffc8,wireframe:true,transparent:true,opacity:0.35}));
  g.add(shellMesh);
  const n=400,pos=new Float32Array(n*3);
  shellParts=new THREE.Points(new THREE.BufferGeometry(),new THREE.PointsMaterial({color:0x00ffc8,size:0.06,transparent:true,opacity:0.8}));
  shellParts.geometry.setAttribute('position',new THREE.BufferAttribute(pos,3));
  shellParts.userData.seeds=Array.from({length:n},()=>[Math.random()*Math.PI*2,Math.acos(2*Math.random()-1),0.4+Math.random()]);
  g.add(shellParts);
  scene.add(g);groups.split=g;
}
function shellOuter(){return 4*(1+mag/1000);} // bare radius 4 ↔ 1000 parts; shell = mag parts
function updateSplit(time){
  const R=shellOuter();
  shellMesh.scale.setScalar(R/4.004);
  const p=shellParts.geometry.attributes.position.array,s=shellParts.userData.seeds;
  for(let i=0;i<s.length;i++){
    const th=s[i][0]+time*0.25*s[i][2],ph=s[i][1],r=4+(R-4)*(0.5+0.5*Math.sin(time*s[i][2]+i));
    p[i*3]=r*Math.sin(ph)*Math.cos(th);p[i*3+1]=r*Math.cos(ph);p[i*3+2]=r*Math.sin(ph)*Math.sin(th);
  }
  shellParts.geometry.attributes.position.needsUpdate=true;
  bareMesh.rotation.y+=0.002;
}

// Camera
function placeCamera(){
  if(!renderer)return;
  camera.position.set(sph.r*Math.sin(sph.phi)*Math.cos(sph.theta),sph.r*Math.cos(sph.phi),sph.r*Math.sin(sph.phi)*Math.sin(sph.theta));
  camera.lookAt(0,0,0);
}
let drag=false,last={x:0,y:0};
viewEl.addEventListener('pointerdown',e=>{drag=true;last={x:e.clientX,y:e.clientY};});
window.addEventListener('pointerup',()=>drag=false);
window.addEventListener('pointermove',e=>{if(!drag||is2D())return;sph.theta+=(e.clientX-last.x)*0.006;sph.phi=Math.max(0.15,Math.min(2.95,sph.phi-(e.clientY-last.y)*0.006));last={x:e.clientX,y:e.clientY};placeCamera();});
viewEl.addEventListener('wheel',e=>{if(is2D())return;e.preventDefault();sph.r=Math.max(2.5,Math.min(60,sph.r*(1+e.deltaY*0.001)));target.r=sph.r;placeCamera();},{passive:false});

function focusRung(i){
  focus=i;
  target.r=i<0?24:rungRadius(i)*3+3;
  tween={from:sph.r,to:target.r,t:0};
  updateLabels(true);
}
let walkTimer=null;
function walkLadder(){
  clearTimeout(walkTimer);let i=0;
  const step=()=>{focusRung(i);i++;if(i<3)walkTimer=setTimeout(step,2200);else walkTimer=setTimeout(()=>focusRung(-1),2600);};
  step();
}

// Labels projected from 3D
function updateLabels(){
  const L=document.getElementById('labels');
  if(!renderer||is2D()){L.innerHTML='';return;}
  const W=viewEl.clientWidth,H=viewEl.clientHeight;
  const items=[];
  if(view==='ladder'){
    RUNGS.forEach((r,i)=>{
      const R=rungRadius(i);items.push({p:new THREE.Vector3(R*0.72,R*0.72,0),h:`<b style="color:#${r.col.toString(16).padStart(6,'0')}">${r.name}</b><i>${r.full}</i><br>${r.val.fmt(mode==='researcher'?12:5)} m`,on:focus<0||focus===i});
    });
    items.push({p:new THREE.Vector3((rungRadius(0)+rungRadius(1))/2*Math.cos(0.4),1.1,(rungRadius(0)+rungRadius(1))/2*Math.sin(0.4)),h:'<b style="color:#f0c060">× TL × 1001</b>',on:true});
    items.push({p:new THREE.Vector3((rungRadius(1)+rungRadius(2))/2*Math.cos(0.4),1.1,(rungRadius(1)+rungRadius(2))/2*Math.sin(0.4)),h:'<b style="color:#f0c060">× TL × 1001</b>',on:true});
  }else{
    const qed=document.getElementById('qed').checked;
    items.push({p:new THREE.Vector3(0,0,0),h:`<b style="color:#9b6dff">BARE · TL × 1000</b>136.899099984016${qed?'<br><i>QED: bare electron</i>':'<br><i>PNBA: Pattern capacity at the EM scale</i>'}`,on:true});
    items.push({p:new THREE.Vector3(shellOuter()*0.75,shellOuter()*0.75,0),h:`<b style="color:#00ffc8">KINETIC · TL</b>0.136899099984016${qed?'<br><i>QED: radiative corrections, here one exact term</i>':'<br><i>PNBA: F_ext at Layer 0</i>'}`,on:true});
  }
  L.innerHTML=items.map(it=>{
    const v=it.p.clone().project(camera);if(v.z>1)return '';
    const x=(v.x*0.5+0.5)*W,y=(-v.y*0.5+0.5)*H;
    return `<div class="l3" style="left:${x}px;top:${y}px;opacity:${it.on?1:0.35}">${it.h}</div>`;
  }).join('');
}

// ════════════════════════════════════════════════════════════
// SPECTRUM (2D)
// ════════════════════════════════════════════════════════════
function nmToRGB(nm){
  if(nm<380)return [155,109,255];
  if(nm>750)return [180,40,40];
  let r=0,g=0,b=0;
  if(nm<440){r=-(nm-440)/60;b=1;}else if(nm<490){g=(nm-440)/50;b=1;}else if(nm<510){g=1;b=-(nm-510)/20;}
  else if(nm<580){r=(nm-510)/70;g=1;}else if(nm<645){r=1;g=-(nm-645)/65;}else{r=1;}
  return [r,g,b].map(v=>Math.round(255*Math.max(0,v)));
}
function drawSpectrum(){
  const W=c2d.width=viewEl.clientWidth*devicePixelRatio,H=c2d.height=viewEl.clientHeight*devicePixelRatio;
  ctx.setTransform(devicePixelRatio,0,0,devicePixelRatio,0,0);
  const w=viewEl.clientWidth,h=viewEl.clientHeight;
  ctx.clearRect(0,0,w,h);
  if(view!=='spec')return;
  const tr=transition(),ry=tr.ry.toNum();
  const top=40,bot=h*0.62,left=90,right=w-60;
    ctx.font='11px "Space Mono", monospace';
  const yLev=n=>bot-(bot-top)*(1-1/(n*n));      // n = 1 at the bottom, E → 0 at the top
  let lastY=Infinity;
  for(let n=1;n<=8;n++){
    const E=-ry/(n*n),yy=yLev(n);
    const sel=(n===ni||n===nf),room=lastY-yy>=13;
    if(room||sel)lastY=yy;
    ctx.strokeStyle=sel?'rgba(0,255,200,.95)':'rgba(232,232,240,.25)';ctx.lineWidth=sel?2:1;
    ctx.beginPath();ctx.moveTo(left,yy);ctx.lineTo(right,yy);ctx.stroke();
    if(!(room||sel))continue;
    ctx.fillStyle=sel?'#00ffc8':'rgba(232,232,240,.5)';
    ctx.fillText('n = '+n,12,yy+4);
    ctx.fillStyle='rgba(232,232,240,.45)';ctx.textAlign='right';ctx.fillText(E.toFixed(mode==='researcher'?6:3)+' eV',right,yy-5);ctx.textAlign='left';
  }
  ctx.strokeStyle='rgba(232,232,240,.35)';ctx.setLineDash([4,4]);ctx.beginPath();ctx.moveTo(left,top);ctx.lineTo(right,top);ctx.stroke();ctx.setLineDash([]);
  ctx.fillStyle='rgba(232,232,240,.35)';ctx.fillText('0 eV (free electron)',left,top-12);
  // transition arrow
  const yi=yLev(ni),yf=yLev(nf);
  const nm=tr.nm.toNum(),[r,g,b]=nmToRGB(nm),x=(left+right)/2;
  ctx.strokeStyle=`rgb(${r},${g},${b})`;ctx.fillStyle=ctx.strokeStyle;ctx.lineWidth=3;
  ctx.beginPath();ctx.moveTo(x,yi);ctx.lineTo(x,yf-8);ctx.stroke();
  ctx.beginPath();ctx.moveTo(x-7,yf-11);ctx.lineTo(x+7,yf-11);ctx.lineTo(x,yf-1);ctx.fill();
  ctx.font='12px "Space Mono", monospace';ctx.fillText('λ = '+tr.nm.fmt(mode==='researcher'?12:6)+' nm',x+14,(yi+yf)/2);
  // wavelength strip
  const sy=h*0.70,sh=26,lo=90,hi=1900;
  const xOf=l=>left+(right-left)*(Math.log(l/lo)/Math.log(hi/lo));
  for(let px=left;px<=right;px++){
    const l=lo*Math.pow(hi/lo,(px-left)/(right-left)),[rr,gg,bb]=nmToRGB(l);
    ctx.fillStyle=(l<380||l>750)?'rgba(40,40,60,.9)':`rgb(${rr},${gg},${bb})`;ctx.fillRect(px,sy,1,sh);
  }
  ctx.fillStyle='rgba(232,232,240,.5)';ctx.font='10px "Space Mono", monospace';
  [100,200,400,700,1000,1875].forEach(l=>ctx.fillText(l+' nm',xOf(l)-14,sy+sh+14));
  ctx.fillText('ultraviolet',xOf(150),sy-6);ctx.fillText('visible',xOf(500),sy-6);ctx.fillText('infrared',xOf(1200),sy-6);
  Object.entries(LINES).forEach(([k,ln])=>{
    const xx=xOf(parseFloat(ln.nm));ctx.fillStyle='rgba(255,255,255,.55)';ctx.fillRect(xx-1,sy-2,2,sh+4);
  });
  ctx.fillStyle='#00ffc8';const xm=xOf(nm);ctx.beginPath();ctx.moveTo(xm,sy+sh+2);ctx.lineTo(xm-6,sy+sh+10);ctx.lineTo(xm+6,sy+sh+10);ctx.fill();
  ctx.fillStyle='rgba(232,232,240,.55)';ctx.fillText('white ticks: measured lines (NIST) · teal marker: this transition',left,sy+sh+30);
}

// ════════════════════════════════════════════════════════════
// LOOP
// ════════════════════════════════════════════════════════════
function resize(){
  if(renderer){renderer.setSize(viewEl.clientWidth,viewEl.clientHeight,false);camera.aspect=viewEl.clientWidth/viewEl.clientHeight;camera.updateProjectionMatrix();}
  drawSpectrum();
}
window.addEventListener('resize',resize);
let t0=performance.now();
function loop(now){
  requestAnimationFrame(loop);
  if(view==='ion'){drawIon((now-t0)/1000);return;}
  if(!renderer||is2D())return;
  const time=(now-t0)/1000;
  if(tween){tween.t=Math.min(1,tween.t+0.025);const k=tween.t<.5?2*tween.t*tween.t:1-Math.pow(-2*tween.t+2,2)/2;sph.r=tween.from+(tween.to-tween.from)*k;if(tween.t>=1)tween=null;placeCamera();}
  if(view==='ladder'){
    RUNGS.forEach((r,i)=>{const on=focus<0||focus===i;r.mesh.material.opacity=on?0.18:0.05;r.ring.material.opacity=on?0.9:0.25;r.ring.rotation.z+=0.002*(i+1);});
    groups.ladder.rotation.y+=0.0015;
  }else updateSplit(time);
  renderer.render(scene,camera);
  updateLabels();
}

// ════════════════════════════════════════════════════════════
// SHATTER (2D): hydrogen driven to TL by F_ext
// ════════════════════════════════════════════════════════════
let Eabs=new Q(0n),shatterT=null,selProd=null,ramp=null,ionHits=[],lastAng=0;
function rungE(n){return EB.mul(new Q(1n).sub(new Q(1n,BigInt(n*n))));}
function tauAt(E){return E.lt(EB)?ALPHA.add(TL.sub(ALPHA).mul(E).div(EB)):TL;}
function phaseOf(t){return t.n===0n?'NOBLE':t.lt(TL_IVA)?'LOCKED':t.lt(TL)?'IVA':'SHATTER';}
const PHN={NOBLE:'Noble',LOCKED:'Locked',IVA:'IVA Peak',SHATTER:'Shatter'};
function phChip(p){return `<span class="chip ph-${p}">${PHN[p].toUpperCase()}</span>`;}
function ionState(){
  const shattered=!Eabs.lt(EB),tau=tauAt(Eabs),phase=phaseOf(tau);
  let n=Infinity;
  if(!shattered){n=1;while(n<500&&!Eabs.lt(rungE(n+1)))n++;}
  const K=shattered?Eabs.sub(EB):new Q(0n),Ke=K.mul(RED),Kp=K.sub(Ke);
  return {shattered,tau,phase,n,K,Ke,Kp};
}
const qn=(x,s)=>Q.of(x.toPrecision(15)).fmt(s);
function roS(k,v,formula,chipHtml,ref){
  return `<div class="ro"><div class="ro-k"><span>${k}</span>${chipHtml||''}</div><div class="ro-v">${v}</div>${ref?`<div class="ro-r">${ref}</div>`:''}<div class="formula r-only">${formula}</div></div>`;
}
function ionReadouts(t){
  const s=ionState(),S=sig(),SN=mode==='researcher'?12:6;let h='';
  t.textContent=s.shattered?'SHATTERED · TWO STABLE IDENTITIES':'BOUND · ONE IDENTITY';
  h+=ro('Absorbed energy F_ext',Eabs,'eV','slider, or a rung energy Ry_H (1 − 1/n²)',null,null);
  h+=roS('τ on the dial',(s.shattered?'TL = ':'')+s.tau.fmt(S),'τ = α + (TL − α) · F_ext / E_bind, α = 1/(TL × 1001)',phChip(s.phase),s.shattered?'reached TL: the bound pair shatters':'rest τ = α = '+ALPHA.fmt(S>7?15:6)+' · IVA from 0.88 × TL · Shatter at TL');
  h+=ro('Shatter threshold E_bind = Ry · m_p/(m_e + m_p)',EB,'eV','½ m_e c² / (TL × 1001)² × reduced mass',lineStatus(EB,Q.of(REF_ION.eb)),REF_ION.eb+' eV (NIST ionization energy of H)');
  if(!s.shattered){
    h+=roS('Electron level',s.n>=500?'n > 500':'n = '+s.n,'highest n with Ry_H (1 − 1/n²) ≤ F_ext',null,s.n>=500?'':'orbit radius n² a₀ = '+A0.mul(new Q(BigInt(s.n*s.n))).fmt(SN)+' m');
    h+=ro('Energy still needed to shatter',EB.sub(Eabs),'eV','E_bind − F_ext',null,null);
  }else{
    h+=ro('Energy left over as motion',s.K,'eV','F_ext − E_bind, shared by momentum balance',null,null);
    h+=prodDetail(s,S,SN);
  }
  h+=ro('Ionization edge λ = hc / E_bind',EDGE_NM,'nm','the Lyman series limit',lineStatus(EDGE_NM,Q.of(REF_ION.edge)),REF_ION.edge+' nm (vacuum)');
  return h;
}
function prodDetail(s,S,SN){
  if(!selProd)return roS('Products','free electron · proton','','',mode==='researcher'?'':'click one in the picture or below the slider');
  const c=C_LIGHT.toNum();
  if(selProd==='e'){
    const ke=s.Ke.toNum(),v=ke>0?c*Math.sqrt(2*ke/MC2_EV.toNum()):0,lam=ke>0?HC_EVNM.toNum()/Math.sqrt(2*MC2_EV.toNum()*ke):Infinity;
    return roS('<b style="color:var(--rose)">FREE ELECTRON</b>','its own stable identity','zero binding torsion, [9,9,3,15]',phChip('NOBLE'),'')+
      ro('Kinetic energy K_e',s.Ke,'eV','K × m_p/(m_e + m_p)',null,null)+
      roS('Speed',ke>0?qn(v,SN)+' m/s':'at rest','v = c √(2K_e / m_e c²)',null,ke>0?qn(v/V1.toNum(),SN)+' × the ground-state orbit speed αc':'')+
      roS('de Broglie wavelength',ke>0?qn(lam,SN)+' nm':'unbounded at K = 0','λ = hc / √(2 m_e c² K_e)',null,ke>0?qn(lam*1e-9/A0.toNum(),SN)+' Bohr radii':'');
  }
  if(selProd==='p'){
    const kp=s.Kp.toNum(),v=kp>0?c*Math.sqrt(2*kp/MPC2.toNum()):0;
    return roS('<b style="color:var(--gold)">PROTON</b>','its own stable identity','zero binding torsion: the bound pair it belonged to has shattered',phChip('NOBLE'),'')+
      ro('Rest energy m_pc²',MPC2,'eV','m_e c² × m_p/m_e',null,null)+
      ro('Recoil kinetic energy K_p',s.Kp,'eV','K × m_e/(m_e + m_p)',null,null)+
      roS('Recoil speed',kp>0?qn(v,SN)+' m/s':'at rest','equal and opposite momentum to the electron',null,'1/1836.15267343 of the electron\'s speed');
  }
  const lam=HC_EVNM.div(Eabs),ln=lam.toNum();
  return roS('<b style="color:var(--violet)">THE PHOTON</b>','absorbed: its energy is the F_ext','',null,'')+
    ro('Wavelength λ = hc / F_ext',lam,'nm','hc = 1239.841984… eV nm',null,null)+
    roS('Band',ln<10?'extreme ultraviolet':ln<380?'ultraviolet':ln<=750?'visible':'infrared','',null,'any photon shorter than the '+EDGE_NM.fmt(7)+' nm edge can shatter hydrogen from n = 1');
}
function setE(q){
  Eabs=q;document.getElementById('eabs').value=q.toNum().toFixed(3);
  const s=!Eabs.lt(EB);if(!s){shatterT=null;selProd=null;}
  document.getElementById('e-v').textContent=Eabs.fmt(mode==='researcher'?15:6)+' eV';
  document.querySelectorAll('.prod').forEach(b=>{b.disabled=!s;b.classList.toggle('on',s&&b.id==='pb-'+selProd);});
  renderReadouts();
}
function onE(){stopRamp();setE(Q.of(document.getElementById('eabs').value));}
function setRung(n){stopRamp();setE(n?rungE(n):EB);}
function resetIon(){stopRamp();setE(new Q(0n));}
function stopRamp(){clearInterval(ramp);ramp=null;}
function rampE(){
  stopRamp();if(!Eabs.lt(Q.of('16')))setE(new Q(0n));
  ramp=setInterval(()=>{const nx=Eabs.add(Q.of('0.04'));if(!nx.lt(Q.of('16'))){setE(Q.of('16'));stopRamp();return;}
    // land exactly on the edge on the way up
    if(Eabs.lt(EB)&&!nx.lt(EB))setE(EB);else setE(nx);},40);
}
function pickProd(k){selProd=k;setE(Eabs);}
viewEl.addEventListener('click',e=>{
  if(view!=='ion')return;const b=viewEl.getBoundingClientRect(),x=e.clientX-b.left,y=e.clientY-b.top;
  for(const hit of ionHits){if(Math.hypot(x-hit.x,y-hit.y)<26){pickProd(hit.k);return;}}
});
function phCol(p){return {NOBLE:'#aa88ff',LOCKED:'#00ffc8',IVA:'#ff8800',SHATTER:'#ff3a3a'}[p];}
function drawIon(time){
  const w=viewEl.clientWidth,h=viewEl.clientHeight;
  if(c2d.width!==Math.round(w*devicePixelRatio)){c2d.width=w*devicePixelRatio;c2d.height=h*devicePixelRatio;}
  ctx.setTransform(devicePixelRatio,0,0,devicePixelRatio,0,0);ctx.clearRect(0,0,w,h);
  const s=ionState(),cx=w/2,cy=h*0.36,R1=Math.min(w,h)*0.042,tf=s.tau.toNum()/TL.toNum(),col=phCol(s.phase);
  ctx.font='10px "Space Mono", monospace';ctx.textAlign='left';
  // rungs
  for(let n=1;n<=6;n++){ctx.strokeStyle='rgba(232,232,240,'+(n===s.n?0:0.14)+')';ctx.setLineDash([3,5]);ctx.beginPath();ctx.arc(cx,cy,R1*n,0,6.2832);ctx.stroke();ctx.setLineDash([]);
    ctx.fillStyle='rgba(232,232,240,.35)';ctx.fillText('n='+n,cx+R1*n*0.71+3,cy-R1*n*0.71-3);}
  ionHits=[];
  if(!s.shattered){
    // the bound identity: halo grows and trembles as τ nears TL
    const jit=Math.pow(tf,8)*4,jx=(Math.random()-.5)*jit,jy=(Math.random()-.5)*jit;
    const rr=R1*Math.min(s.n,6.6),g=ctx.createRadialGradient(cx,cy,0,cx,cy,rr*1.35);
    g.addColorStop(0,col+'33');g.addColorStop(1,col+'00');ctx.fillStyle=g;ctx.beginPath();ctx.arc(cx,cy,rr*1.35,0,6.2832);ctx.fill();
    ctx.strokeStyle=col;ctx.lineWidth=1.6;ctx.beginPath();ctx.arc(cx+jx,cy+jy,rr,0,6.2832);ctx.stroke();ctx.lineWidth=1;
    lastAng=time*2.2/Math.pow(Math.min(s.n,50),1.5);
    dot(cx,cy,7,'#ffcf6b');
    dot(cx+jx+rr*Math.cos(lastAng),cy+jy+rr*Math.sin(lastAng),5,'#ff6b8a');
    ctx.fillStyle=col;ctx.font='12px "Space Mono", monospace';ctx.textAlign='center';
    ctx.fillText('hydrogen · one bound identity · '+PHN[s.phase],cx,cy+R1*6.6+28);
  }else{
    if(shatterT===null)shatterT=time;
    const dt=time-shatterT,ke=Math.max(s.Ke.toNum(),0);
    if(dt<1.2){ctx.strokeStyle='rgba(255,58,58,'+(1-dt/1.2)+')';ctx.lineWidth=2.5;ctx.beginPath();ctx.arc(cx,cy,R1*(1+dt*7),0,6.2832);ctx.stroke();ctx.lineWidth=1;}
    const maxD=Math.min(w*0.36,h-195-50-cy),dist=Math.min(maxD,(R1*1.2)+dt*(18+40*Math.sqrt(ke))),a=lastAng;
    const ex=cx+dist*Math.cos(a),ey=cy+dist*Math.sin(a),pd=Math.min(dist/1836.15267343*40,3);
    const px=cx-pd*Math.cos(a),py=cy-pd*Math.sin(a);
    ctx.strokeStyle='rgba(255,107,138,.35)';ctx.setLineDash([2,4]);ctx.beginPath();ctx.moveTo(cx,cy);ctx.lineTo(ex,ey);ctx.stroke();ctx.setLineDash([]);
    halo(ex,ey,selProd==='e');halo(px,py,selProd==='p');
    dot(px,py,7,'#ffcf6b');dot(ex,ey,5,'#ff6b8a');
    ionHits.push({k:'e',x:ex,y:ey},{k:'p',x:px,y:py});
    label(ex,ey,'free electron','Noble · '+(ke>0?'moving':'at rest'),'#ff6b8a');
    label(px,py,'proton','Noble · recoil 1/1836','#ffcf6b');
  }
  // the photon that carries F_ext, entering from the left
  if(Eabs.n>0n){
    const ln=HC_EVNM.div(Eabs).toNum(),[r,gc,b]=nmToRGB(ln),gx=Math.max(70,cx-R1*6.6-90),gy=cy;
    ctx.strokeStyle=`rgb(${r},${gc},${b})`;ctx.lineWidth=2;ctx.beginPath();
    for(let k=0;k<=60;k++){const xx=gx-50+k*1.2,yy=gy+7*Math.sin(k*0.55-time*8);k?ctx.lineTo(xx,yy):ctx.moveTo(xx,yy);}ctx.stroke();ctx.lineWidth=1;
    if(selProd==='g')halo(gx+10,gy,true);
    ionHits.push({k:'g',x:gx+10,y:gy});
    label(gx-60,gy-30,'photon',qn(ln,5)+' nm','#9b6dff');
  }
  // the τ dial
  const gy0=h-195,gl=60,gr=w-60,scale=1.25,X=v=>gl+(gr-gl)*Math.min(v,scale)/scale;
  const xI=X(0.88),xT=X(1);
  ctx.fillStyle='#00ffc8';ctx.fillRect(gl,gy0,xI-gl,8);ctx.fillStyle='#ff8800';ctx.fillRect(xI,gy0,xT-xI,8);ctx.fillStyle='#ff3a3a';ctx.fillRect(xT,gy0,gr-xT,8);
  ctx.fillStyle='#aa88ff';ctx.fillRect(gl-2,gy0-3,3,14);
  ctx.font='10px "Space Mono", monospace';ctx.textAlign='center';ctx.fillStyle='rgba(232,232,240,.55)';
  ctx.fillText('Noble 0',gl,gy0+24);ctx.fillText('IVA 0.88 TL',xI,gy0+24);ctx.fillText('TL',xT,gy0+24);
  const aF=ALPHA.div(TL).toNum();
  [1,2,3,4,5].forEach(n=>{const f=aF+(1-aF)*(1-1/(n*n)),xx=X(f);ctx.fillStyle='rgba(255,255,255,.8)';ctx.fillRect(xx-0.5,gy0-5,1,18);if(n<=3){ctx.fillStyle='rgba(232,232,240,.5)';ctx.fillText('n='+n,xx,gy0-9);}});
  const xm=X(tf);ctx.fillStyle=col;ctx.beginPath();ctx.moveTo(xm,gy0-2);ctx.lineTo(xm-6,gy0-12);ctx.lineTo(xm+6,gy0-12);ctx.fill();
  ctx.textAlign='left';ctx.fillStyle=col;ctx.font='11px "Space Mono", monospace';
  ctx.fillText('τ = '+(s.shattered?'TL → shattered into two Noble identities':s.tau.fmt(mode==='researcher'?12:5)+' · '+PHN[s.phase]),gl,gy0+42);
}
function dot(x,y,r,c){ctx.fillStyle=c;ctx.beginPath();ctx.arc(x,y,r,0,6.2832);ctx.fill();}
function halo(x,y,on){ctx.strokeStyle=on?'#00ffc8':'rgba(232,232,240,.25)';ctx.lineWidth=on?2:1;ctx.beginPath();ctx.arc(x,y,16,0,6.2832);ctx.stroke();ctx.lineWidth=1;}
function label(x,y,a,b,c){ctx.textAlign='left';ctx.font='11px "Space Mono", monospace';ctx.fillStyle=c;ctx.fillText(a,x+20,y-3);ctx.fillStyle='rgba(232,232,240,.55)';ctx.font='9px "Space Mono", monospace';ctx.fillText(b,x+20,y+10);}

// ════════════════════════════════════════════════════════════
// CONTROLS
// ════════════════════════════════════════════════════════════
function setMode(m){
  mode=m;document.body.classList.toggle('researcher',m==='researcher');
  document.getElementById('m-learn').classList.toggle('on',m==='learner');
  document.getElementById('m-res').classList.toggle('on',m==='researcher');
  refresh();
  if(view==='ion')setE(Eabs);
}
function setView(v){
  view=v;
  ['ladder','split','spec','ion'].forEach(k=>{document.getElementById('v-'+k).classList.toggle('on',k===v);document.getElementById('ctl-'+k).style.display=k===v?'block':'none';});
  if(renderer){groups.ladder.visible=v==='ladder';groups.split.visible=v==='split';c3d.style.visibility=is2D()?'hidden':'visible';}
  if(v==='ladder'){sph.r=24;focus=-1;}
  if(v==='split'){sph.r=24;}
  if(is2D())document.getElementById('labels').innerHTML='';
  placeCamera();refresh();
  if(v==='ion')setE(Eabs);
}
function onMag(){
  const s=parseFloat(document.getElementById('mag').value);mag=Math.round(Math.pow(10,s*1.5));
  document.getElementById('mag-v').textContent='×'+mag;
}
function onLevels(){
  nf=parseInt(document.getElementById('nf').value,10);
  const s=document.getElementById('ni');s.min=nf+1;if(parseInt(s.value,10)<=nf)s.value=nf+1;
  ni=parseInt(s.value,10);document.getElementById('ni-v').textContent=ni;refresh();
}
function pickLine(i,f){document.getElementById('nf').value=f;const s=document.getElementById('ni');s.min=f+1;s.value=i;onLevels();}
function refresh(){renderReadouts();renderCaption();drawSpectrum();if(!is2D())updateLabels();}
function is2D(){return view==='spec'||view==='ion';}

// ════════════════════════════════════════════════════════════
// EXPORT
// ════════════════════════════════════════════════════════════
function rows(){
  const tr=transition();
  const r=[
    ['TL','0.136899099984016','corpus'],
    ['1/alpha = TL x 1001',ALPHA_INV.fmt(18),status(ALPHA_INV,'alpha_inv')],
    ['bare TL x 1000',BARE.fmt(15),''],
    ['r_e (m)',R_E.fmt(18),status(R_E,'r_e')],
    ['lambda_C (m)',LAMBDA_C.fmt(11),'CODATA 2018 input'],
    ['a0 (m)',A0.fmt(18),status(A0,'a0')],
    ['a0 / r_e',RATIO.fmt(18),''],
    ['v = c / (TL x 1001) (m/s)',V1.fmt(18),status(V1,'v1')],
    ['Ry (eV)',RY.fmt(18),status(RY,'ry')],
    ['alpha^2',ALPHA2.fmt(18),''],
    [`transition ${ni}->${nf} dE (eV)${tr.rm?' reduced mass':''}`,tr.dE.fmt(18),''],
    [`transition ${ni}->${nf} lambda (nm)`,tr.nm.fmt(18),tr.ref?lineStatus(tr.nm,Q.of(tr.ref.nm))+' vs '+tr.ref.nm+' nm '+tr.ref.name:'']];
  const io=ionState();
  r.push(['binding energy, shatter threshold (eV)',EB.fmt(18),lineStatus(EB,Q.of(REF_ION.eb))+' vs '+REF_ION.eb+' eV NIST'],
    ['Lyman limit (nm)',EDGE_NM.fmt(18),lineStatus(EDGE_NM,Q.of(REF_ION.edge))+' vs '+REF_ION.edge+' nm'],
    ['absorbed energy F_ext (eV)',Eabs.fmt(18),''],
    ['tau',io.shattered?'TL reached, shattered':io.tau.fmt(18),io.phase]);
  if(io.shattered)r.push(['free electron kinetic energy (eV)',io.Ke.fmt(18),'Noble'],['proton kinetic energy (eV)',io.Kp.fmt(18),'Noble']);
  return r;
}
function download(name,text,type){const a=document.createElement('a');a.href=URL.createObjectURL(new Blob([text],{type}));a.download=name;a.click();setTimeout(()=>URL.revokeObjectURL(a.href),1000);}
function exportJSON(){
  const o={tool:'Electron Geometry',coordinate:'[9,9,3,21]',generated:new Date().toISOString(),values:rows().map(([k,v,s])=>({quantity:k,value:v,comparison:s}))};
  download('electron_geometry.json',JSON.stringify(o,null,2),'application/json');toast('JSON saved');
}
function exportCSV(){download('electron_geometry.csv','quantity,value,comparison\n'+rows().map(r=>r.map(x=>'"'+String(x).replace(/"/g,'""')+'"').join(',')).join('\n'),'text/csv');toast('CSV saved');}
function copyRecord(){
  const r=rows();
  const txt=['-- ============================================================',
    '-- Electron Geometry · Identity Physics™ session record',
    '-- Coordinate: [9,9,3,21](PART) · 1/α = TL × 1001 [9,9,3,14] · ionization [9,9,3,15]',
    '-- Architect:  HIGHTISTIC (Russell Vernon Trent III)',
    '-- Generated:  '+new Date().toISOString(),
    '-- ============================================================',
    ...r.map(([k,v,s])=>'--   '+k.padEnd(40)+v+(s?'   ['+s+']':'')),
    '--',
    '-- Lean theorems: split · ladder · ratio_of_extremes · bohr_radius_codata',
    '--   electron_radius_codata · bohr_velocity_codata · rydberg_codata',
    '--   lyman_alpha · fine_structure_scale · electron_master',
    '-- [9,9,3,15]: ionization_requires_fext · rydberg_from_alpha_sq',
    '-- DOI base 10.5281/zenodo.18719748',
    '-- ============================================================'].join('\n');
  const done=()=>toast('Record copied');
  if(navigator.clipboard)navigator.clipboard.writeText(txt).then(done,()=>download('electron_geometry_record.txt',txt,'text/plain'));
  else download('electron_geometry_record.txt',txt,'text/plain');
}
function toast(m){const t=document.getElementById('toast');t.textContent=m;t.classList.add('show');setTimeout(()=>t.classList.remove('show'),1400);}

// ════════════════════════════════════════════════════════════
// INIT
// ════════════════════════════════════════════════════════════
if(renderer){try{buildLadder();buildSplit();}catch(err){renderer=null;console.error('3D view unavailable:',err);}}
setTimeout(()=>{resize();setView('ladder');requestAnimationFrame(loop);},50);
</script>
</body>
</html>