# Route R1, light as the field with a transparent lattice: the three first checks

2 November 2026, isla session, about 07:12 EST, for Doug Westmoreland (project lead: direction and review). Pre-registered in papers/Lock_R1_checks.md (committed as 89f2f90 at 07:09:36 EST; the script ran at 07:10). Script: sim/light/r1_checks.py, output r1_checks_out.txt (numpy/scipy, SI, CODATA 2018). The checks are those of Improvement_directions_2026-11-02.md §4, route R1. Labels: [A] Aspden's own, [D] derived, [M] our modelling choice, [P] proposed, [S] standard physics. Independently checked: sim/light/r1_check_fable/REPORT.md (a Fable agent with no part in the work; finished 07:40 EST; folded in at 07:55 EST, each correction marked with its finding number; see §6).

## 1. What R1 says, and what these checks ask

R1 keeps the quon lattice, the graviton balance and the muon sea, and makes light the electromagnetic field, propagating as Maxwell's field at c, with the lattice transparent to it: the lattice sets the constants but does not enact the wave. Three cheap checks were proposed: (a) does Aspden's chain of units (POC 7.1–7.29) survive if the quons do not respond to the field of light; (b) if the orbit is not perfectly rigid, how rigid must it be, from the GRB and cavity bounds; (c) does a transparent lattice pass the Lamb-shift test of static screening at the scale r.

## 2. Check (a): the chain does not use a response to an external field [D]

The chain as Part 1 §3 reconstructs it (its reproduction holds to 0.6 ppm), with the physics each piece uses. Classes: (i) the quon's own field or inertia; (ii) the continuum's field on the displaced lattice (the lattice's self-field, Part 1A §4); (iii) quon–quon Coulomb energy; (iv) a response of the quons to an external field, of matter or of light; (v) a quantum rule.

| Piece | What it says | Uses | External field? |
|---|---|---|---|
| I1a | the frames orbit at the Compton frequency, ħΩ = mₑc² (POC 6.14) | (v) | no |
| I1b | the frames move at c relative to each other (6.6, 6.13) | postulate | no |
| I2 | quon charge e; one opposite charge per cell, σ = e/d³ (7.7) | definition | no |
| I3 | the quon's inertia is half its Thomson energy over c² (7.4) | (i) | no |
| I4 | the lattice's electrostatic energy, with the orbital displacement and a finite-size term, is zero (7.18) | (iii), (ii) | no |
| I5 | the photon unit is a 3 × 3 × 3 cube; its angular momentum at Ω/4 is ħ; it radiates at four times its spin rate (7.19–7.24) | (v) applied to the lattice's own excitation; the radiation rule makes the unit a source or absorber of light | **not a response: an emitter** |
| I6 | N is odd, rounded down from the zero-energy value (7.26) | (v) | no |
| I7 | the aether's energy density equals that inside the quon's charge sphere (7.3) | (i) | no |
| step 1 | r = ħ/2mₑc, Ω = mₑc²/ħ | I1 | no |
| step 2 | r/d = (3/4)(8/1843)^(1/6) | I4 + I6 | no |
| step 3 | m₀Ω²r = (4πσe)(2r), m₀c² = 32πσer² (7.5–7.6) | (ii): the continuum's field on the displaced lattice; the k = 0 plasma mode, U32 | no |
| step 4 | b = d³/96πr² | step 3 + I3 | no |
| step 5 | N = (b/a)³ with the electron's Thomson radius; m₀/mₑ = (4/9)(r/d)² (7.25) | (i), [S] | no |
| step 6 | 36m₀d² = 4hr/cπ, so ħc/e² = 144π(r/d) (7.24) | I5: the unit's angular momentum ħ at Ω/4 | no |
| step 7 | E₀ = (1/2π)e²d³/b⁴ = 412.67 mₑc² (7.29) | (i), I7 | no |

**Result.** No input and no step uses a linear response of the quons to an external field. The restoring force in step 3 is the lattice's own field on its own displacement (U32 and U23: "the only restoring force on the uniform motion is the continuum's"), not a response to light. The chain survives a lattice that does not polarize in the field of light. **Check (a) passes.**

**Two things the audit adds.**
1. R1's rule as written ("the quons neither make nor feel the field of light and of ordinary matter") is too strong for I5. The photon unit is a lattice excitation that carries ħ and, by Aspden's rule, radiates when its rate is off Ω/4; the quantum of emission and absorption is made of quons. So the rule must be narrowed to: **the lattice has no linear response to the propagating field (no polarization, no dispersion, no drag), while its units still exchange quanta with it, and only where matter emits or absorbs.** Any exchange along the path in free space would be absorption, hence a linear response, and Kramers–Kronig would give dispersion with it (check F7). Step 6 needs only the unit's angular momentum, so the narrowing costs the chain nothing.
2. The cost it does carry: a charge that feels the continuum's field (step 3) and its neighbours' (I4) but not an external field of the same kind is not a Maxwellian charge. Superposition of fields has no room for it. R1 is a two-sector electrodynamics: the aether's charge couples to the aether's own fields and to matter only through the quantized units. That is Aspden's 1987b rule (the aether's charge "belongs to the electromagnetic reference frame and makes no field") turned into a law [P]. The rule has to sort by the motion as well as by the source: a unit set turning radiates into matter's field (I5), while a collective displacement must not (check F8). The chain also uses the measured e and the Coulomb constant e²/4πε₀ for the aether's own fields (steps 3 and 5, I3, I7; Part 1A §3 line 7), so the two sectors must share the same e²/ε₀, or the α the chain predicts is not the α matter measures: an added assumption [P] (check F10). And R1 drops POC ch. 6's identification of the vacuum displacement current with the quon displacement, the response reading of ε₀ that U11 withdrew and that (b) and (c) below exclude. The checks below say how exact the separation must be.

## 3. Check (b): how rigid the orbit must be [D, S]

Two ways the transparency can be imperfect, both locked.

**(b1) Stiff orbit, full coupling [M].** Each quon feels the full force eE of the light's field and is held by a force constant K = m₀ω_K², measured against the continuum's own K₀ = m₀ω_p² (Aspden's 4πσe; ħω_p = 361.331 keV for the quons alone, Part 1A W4). K₀ is a yardstick only: for transverse motion the continuum provides no restoring force (Part 1A §4.4), so K is the whole transverse stiffness; and the continuum is held still here, whereas if both frames respond (Part 1A §5) the oscillator strength doubles and ħω_K rises by 2^(1/4) = 1.19 (check F10). The lattice is then a Lorentz oscillator, χ(ω) = ω_p²/(ω_K² − ω²), with group index n_g = n + ω dn/dω. The high-energy photon is the slower one, the sign GRB 090510's main limit constrains (check F11 confirmed both the sign and the numbers with an exact 60-digit group index).

| Bound | Source, read at source | Value | ħω_K | K/K₀ | χ_s = ω_p²/ω_K² |
|---|---|---|---|---|---|
| GRB 090510, limit (a), the most conservative | Abdo et al. 2009, Nature 462, 331, Table 2 | \|Δv_g/c\| < 2 × 10⁻¹⁸ between 0.1 MeV and 28 GeV | **> 2.96 TeV** (3.3 TeV with the (1+z)² weighting a quadratic dispersion needs along the path, check F3; the bound scales as the fourth root) | **> 6.7 × 10¹³** | **< 1.5 × 10⁻¹⁴** |
| GRB 090510, limit (e), either sign | same, Table 2 | < 2.2 × 10⁻²⁰ | > 9.1 TeV | > 6.4 × 10¹⁴ | < 1.6 × 10⁻¹⁵ |
| cavity, Nagel et al. 2015 (Nat. Commun. 6, 8174; abstract at arXiv 1412.6954) | Δν/ν = 9.2 ± 10.7 × 10⁻¹⁹ (95% CI) | round-trip anisotropy χ_s(v/c)²/2 < 2 × 10⁻¹⁸ [D: relativistic ray-velocity composition, which R1 assumes for matter; the first-order Fresnel term cancels in the round trip] | > 0.28 GeV (v = 465 m/s, Aspden's Earth-carried non-rotating frame); > 0.22 TeV (v = 370 km/s, the CMB frame) | | < 1.7 × 10⁻⁶; < 2.6 × 10⁻¹² |

The GRB dispersion sets the floor: the orbit must be held against the field of light with a stiffness at least 7 × 10¹³ times the continuum's own, equivalent to an internal mode of the quon at 3 TeV or above. Its resonance would make a stop band only 0.02 eV wide at 3 TeV: unobservable. The cavity bound is weaker than the GRB floor by eight orders in χ_s if the lattice is Earth-carried (v = 465 m/s) and by two orders if it is at rest in the CMB frame (v = 370 km/s). (The first version of this page used χ_s²(v/c)² for the anisotropy and quoted 12 MeV and 0.34 GeV; the check, F1, derived the first-order form from the exact round-trip times, (n² − 1)(v/c)²/2, and confirmed it numerically; the cavity numbers moved by three and six orders, the floor did not.) A lattice meeting the floor contributes less than 1.5 × 10⁻¹⁴ of ε₀ through its response.

**(b2) Weak coupling [M].** Each quon feels gE and makes g times its field, with the lattice's own dynamics as Part 1A found them (a plasma): ε = 1 − g²ω_p²/ω², i.e. a photon mass għω_p. The low-energy photon is the slower one, so the high-energy photon arrives first, the sign Abdo et al.'s limits (a)–(d) do not constrain (they hold for a positive delay only); their limits (e) and (f) do (check F2; the first version used limit (a) and quoted g < 5.5 × 10⁻¹⁰).

| Bound | Value | g | Lattice's share of ε₀ by its response (g²) |
|---|---|---|---|
| GRB 090510, limit (f), a negative delay, \|Δt\| < 19 ms for 0.694 GeV against 0.1 MeV, with the (1+z)⁻² path weighting an inverse-square dispersion needs | 1.1 × 10⁻¹⁹ | **< 1.3 × 10⁻¹⁰** | < 2 × 10⁻²⁰ |
| GRB 090510, limit (e), either sign, \|Δt\| < 10 ms | 5.7 × 10⁻²⁰ | < 0.9 × 10⁻¹⁰ | < 10⁻²⁰ |
| photon mass m_γ < 10⁻¹⁸ eV (PDG 2024, Ryutov 2007, from the magnetohydrodynamics of the solar wind; read at source by the check, F4) | | **< 2.8 × 10⁻²⁴** | < 10⁻⁴⁷ (with the laboratory Coulomb-law limit of Williams, Faller and Hill 1971, 10⁻¹⁴ eV: g < 2.8 × 10⁻²⁰, g² < 10⁻³⁹) |

**Result.** The lattice's response to light must be below 1.5 × 10⁻¹⁴ of ε₀ (stiff orbit, GRB) or below 10⁻³⁹ to 10⁻⁴⁷ (weak coupling, photon-mass limits). **"The lattice is the vacuum's permittivity" cannot be a statement about its response.** If the lattice sets α, it does so through its geometry (r/d) and the unit's ħ, not by polarizing; c is an input to the chain (I1b), and R1 removes Aspden's reason for equating the orbital relative speed with it (check F9). That is the content of R1, now with a number on it.

## 4. Check (c): the Lamb shift and static screening at the scale r [D, S]

**Model [M].** The lattice screens a static charge by a fraction δ beyond the scale r and not inside it, so the proton's potential energy on the electron is −e²/r′ for r′ > r (the value that defines the measured e) and −(1 + δ)e²/r′ for r′ < r. The 2S level shifts by the contact term |ΔE| = δe²r²/(4a₀³) = δ × 21.90 GHz (|ψ_2S(0)|² = 1/8πa₀³; a step profile). A smooth profile at the same scale changes the coefficient by 1/3 (a linear ramp) to 2 (an exponential); a crossover at the cell size d = 3.3r instead of r, which a lattice of spacing d might rather have, would tighten the bound by up to (d/r)² = 11; the step at r is the conservative choice. The bound takes r_p from muonic hydrogen, since r_p² enters the 2S level through the same contact term (check F12).

**Checks of the formula's normalization.** The leading Uehling term for 2S, −(4/15)(α⁵/8π)mₑc² = −27.13 MHz (−27.08 MHz with the reduced-mass factor, which is exactly the tabulated value in Eides, Grotch and Shelyuto 2001; check F6), is QED's own screening at the scale ħ/mₑc = 2r; read through the contact formula it is δ_QED = 1.2 × 10⁻³ = (8/15)(α/π) exactly, four-fifths of the Uehling coefficient 2α/3π, as it should be (a pure number at this scale, not a logarithm; the first version said "times a logarithm", check F6). The proton's finite-size shift of 2S, (2π/3)e²|ψ(0)|²r_p² with r_p = 0.8409 fm, comes out at 138 kHz (138.4 kHz with 0.84087 fm). So the constants and the wavefunction at the origin are right.

**Bound [S; sources read by the check, F5].** The 2S₁/₂–2P₁/₂ Lamb shift of hydrogen is measured by Bezginov et al. 2019 (Science 365, 1007) as 1057.8298(32) MHz and computed by Yerokhin, Pachucki and Patkóš 2019 (Ann. Phys. 531, 1800324, Table VIII) as 1057.83412(26) MHz with the muonic-hydrogen proton radius: a residual of 4.3 ± 3.2 kHz. The older values are Lundeen and Pipkin 1981, 1057.845(9) MHz, and Hagley and Pipkin 1994, 1057.842(12) MHz; the 1057.8514(19) MHz of Sokolov and Yakovlev 1982 is disputed and not used by CODATA (the first version of this page attributed the ±1.9 kHz to Hagley and Pipkin: wrong, F5). With a 10 kHz residual (about the 95% bound of 10.7 kHz), **δ < 4.6 × 10⁻⁷**; with 2.7 kHz (10⁻⁴ of the Uehling term, the figure Improvement_directions used), δ < 1.2 × 10⁻⁷.

**Sources (Doug asked at 07:20 EST that these be checked at source; the independent check did so at 07:15–07:35 EST).**

| Input | Value used | Status |
|---|---|---|
| hydrogen 2S₁/₂–2P₁/₂ Lamb shift, measured | 1057.8298(32) MHz (Bezginov 2019); 1057.845(9) (Lundeen–Pipkin 1981); 1057.842(12) (Hagley–Pipkin 1994) | read in Eides et al. 2001 Table XX and Biraben's 2008 review (arXiv 0809.2985); Bezginov's primary interval 909 871.7(3.2) kHz read, its centroid taken from a secondary source; the original 1994 PRL not reachable |
| theory–experiment residual | 4.3 ± 3.2 kHz; 10 kHz used | Yerokhin, Pachucki, Patkóš 2019 Table VIII, read |
| Uehling part of the 2S level, and the leading formula | −27 084.48 kHz; −(4/15)α(Zα)⁴mₑc²(m_r/m)³/(πn³) | Eides, Grotch, Shelyuto 2001 (arXiv hep-ph/0002158) eqs. 31–32, 45 and the 2S table, read |
| proton charge radius | 0.84087(39) fm (muonic) | as used by Yerokhin 2019, read; CODATA 2018's own 0.8414(19) fm not re-read |
| proton finite-size shift of 2S | 138.4 kHz | computed from the Eides formula |
| photon-mass limit | < 10⁻¹⁸ eV | PDG 2024 listing and pdgLive, read: Ryutov 2007, solar-wind magnetohydrodynamics, the only entry PDG uses for the limit |

**Result.** A stiff-orbit lattice allowed by (b) has χ_s < 1.5 × 10⁻¹⁴, thirty million times below the Lamb bound: **check (c) is met, with seven orders to spare.** The reading in which the lattice's response is the whole permittivity (δ of order 1) is excluded by two million, unless its screening were scale-free down to below the proton's size, which a lattice of spacing d = 6.4 × 10⁻¹³ m cannot be. So (c) does not falsify R1; it closes the response reading of ε₀ a second time, independently of light.

## 5. Against the lock, and the reading

| Expected | Found | |
|---|---|---|
| (a) no step uses a response to an external field; I5 is the quantum of emission and absorption; the rule must be narrowed; the two-sector cost | as expected | met |
| (b) ħω_K about 3 TeV, K/K₀ about 10¹⁴; cavity weaker; χ_s < 10⁻¹³; g < 10⁻⁹ (GRB), 10⁻²³ (photon mass) | 2.96 TeV, 6.7 × 10¹³; cavity 2 to 8 orders weaker (after check F1); 1.5 × 10⁻¹⁴; 1.3 × 10⁻¹⁰ (after check F2) and 2.8 × 10⁻²⁴ | met |
| (c) δ < 5 × 10⁻⁷; met with seven orders; δ ~ 1 excluded by > 10⁶ | 4.6 × 10⁻⁷; 3 × 10⁷; 2 × 10⁶ | met |

One correction after the run, disclosed in the lock: the script's scale check of the proton's finite-size shift first used the step-screening formula with δ = 1 (415 kHz), which is a different model; it now uses the standard (2π/3)e²|ψ(0)|²r_p² (138 kHz). No result depends on it. After the independent check, two corrections of numbers (the cavity formula, F1; the sign of the plasma bound, F2) and several of wording and attribution were folded in; no conclusion changed (§6).

**Reading.**
1. **R1 passes its consistency audit (a), and (b) and (c) give the numbers its imperfect versions must live with.** Aspden's chain of units needs nothing from the lattice's response to an external field, so a transparent lattice keeps α, mₚ/mₑ, the hadron numbers, G and E₀ exactly as they stand. None of the three checks could have falsified R1 in its exact form, since they only bound how small a residual response must be; the tests that can are listed under 3 (check F13).
2. **What R1 now has to mean.** The lattice's response to light must be below 1.5 × 10⁻¹⁴ of ε₀ (stiff orbit, GRB) or below 10⁻³⁹ to 10⁻⁴⁷ (weak coupling, photon-mass limits); its static screening at the scale r is bounded directly at 5 × 10⁻⁷ by the Lamb shift, and by inference at 10⁻¹⁴ in the stiff-orbit model (check F14). So the lattice sets α, if it does, through its geometry and the unit's ħ and not by polarizing; c is an input to its chain. The quon's charge must couple to the aether's own fields and not to matter's, except through the quantized units, and the rule must sort by the kind of motion as well. That is a two-sector electrodynamics, Aspden's 1987b rule made exact. Nothing in the chain forbids it; nothing in the chain explains it. It replaces Aspden's own account of light (the 1969 dispersion formula, the resonance picture, the Earth-carried frame), and it needs Lorentz's kinematics for the lattice's rest frame to stay hidden, which Aspden refused.
3. **What would test it next.** (i) The rule itself: does Aspden's 1987b text, or his treatment of the aether charge in a moving frame, give a form for the two-sector coupling that can be written as equations (the question Part 1B §11 left open). (ii) The photon unit as the quantum: does a 27-quon cube that takes up ħ and E = hν from the field at the emitter or absorber, and radiates by Aspden's rule, make any prediction about emission or absorption that standard QED does not (a second-order effect in the unit's size, 3d = 1.9 × 10⁻¹² m, against the Lamb shift or g − 2). (iii) The hidden rest frame: with the lattice transparent, cavities, the CMB dipole and the Earth's rotation see nothing; a residual response χ_s would show as a round-trip anisotropy χ_s(v/c)²/2, which Nagel et al. 2015 already bound at 2.6 × 10⁻¹² (CMB frame) and 1.7 × 10⁻⁶ (Earth-carried frame) (check F15). (iv) Muonic hydrogen probes the scale r directly (check F16): its Bohr radius is 1.47 r; a step screening δ inside r shifts its 2S–2P interval by δ × 228 eV, and the agreement of the electronic and muonic proton radii to about 0.01 fm gives δ < 2.5 × 10⁻⁷, a first estimate independent of the step-profile assumption; a careful version would be a cheap paper, with its own lock. (v) Free-space transparency: if the units could exchange quanta anywhere along a light path, the lattice would absorb, and the transparency of the universe at every wavelength bounds that; the exchange-at-matter condition of §2 is a testable statement, not a definition (check F16).

## 6. Independent check

sim/light/r1_check_fable/REPORT.md, finished 07:40 EST (the harness blocked the checker from saving the file, so the main session saved its report verbatim at 07:46); folded in at 07:55 EST. Own code throughout, with the group velocities in 60-digit arithmetic; seven inputs read at source (Abdo 2009, Nagel 2015, PDG 2024, Eides 2001, Yerokhin 2019, Bezginov 2019, Biraben 2008).

- **Verdict:** the audit (a), the GRB floor of (b1), the weak-coupling and photon-mass arithmetic of (b2) and the whole of (c) reproduce; the lock's chronology is proven (committed 07:09:36, script born 07:10:24); the two disclosed script corrections change no result.
- **Corrections folded in:** F1 (Major, numbers only): the cavity anisotropy is χ_s(v/c)²/2, first order in χ_s, so the cavity rows moved by three and six orders; the GRB floor still rules, by eight orders (Earth-carried lattice) or two (CMB frame). F2 (Major by the rule, no conclusion changes): the plasma makes the high-energy photon arrive first, which Abdo's limit (a) does not constrain; limits (e) and (f) give g < 0.9–1.3 × 10⁻¹⁰, tighter than the 5.5 × 10⁻¹⁰ first quoted. F3: the (1+z)² path weighting gives 3.3 TeV. F4: the PDG photon-mass limit verified and its basis stated. F5: three Lamb-shift attributions corrected with sources; the 10 kHz residual is fair (4.3 ± 3.2 kHz today). F6: δ_QED is (8/15)(α/π) exactly, not "a logarithm". F7, F8, F9, F10: the narrowing of R1's rule (exchange only at matter), the motion-sorting it needs, c as an input, the shared e²/ε₀ and the dropped displacement-current reading. F12: profile and scale dependence of the Lamb bound. F13, F14, F15: three overstatements in the reading rewritten. F16: muonic hydrogen and free-space transparency added as tests.
- **Still unverified at source:** the original Hagley and Pipkin 1994 abstract; Bezginov's Lamb-shift centroid (its primary interval was read); CODATA 2018's r_p and Lamb-shift tabulation; the body of the Nagel paper; Aspden's 1987b text.