SilverTooth: Mathematician review (Step 2)

Reviewer role: PhD mathematician. I check derivations, notation, units and hidden assumptions, and I verify Step 1 rather than trust it. Physics verdicts belong mainly to the Physicist; where my verdict touches physics I say so.

Tags: [read] from a document (page images read where equations matter), [web] with URL, [memory] with confidence, [calc] my own computation (sympy/numpy, venv at .venv, script reproduced in the appendix).

Source note: the folder holds one 5-page paper (E. W. Silvertooth, "Experimental detection of the ether", received May 1986). No source gap in the text, but the paper gives no derivation for its measurement formula or for eq. (10). I therefore also read the Investigator's saved 1976 Applied Optics paper (research/files/Silvertooth-1976-AppliedOptics-15-1100-anomalous-redshifts.pdf), page images p.3-4 of the PDF = journal pp.1101-1102 [read], and Investigator notes on Marett and Forbes [read].

0. Corrections to Step 1

1. "v-bar" in eq. (10) is almost certainly an acceleration, as the Investigator suggested; I confirm it. The 1976 paper (journal p.1102, page image) prints the same extra factor as (1 ± L v̇_r / c^2), where "v̇_r" is the radial acceleration (a dot over v), and it defines it in the text ("the radial acceleration of the source", with v̇_r = d w^2 for a quasar at radius d in a galaxy rotating at angular speed w) [read: 1976 p.1102]. So the deep read's units alarm (L v-bar/c^2 is a time if v-bar is a velocity) dissolves for the 1976 form: L v̇/c^2 = cm * (cm/s^2) / (cm^2/s^2) is dimensionless [calc]. The 1986 retyping dropped the dot. This is an inference from the 1976 paper, not something the 1986 file says.
2. The deep read's reconstruction of the standing-wave shift is wrong. It says a slide move of one rest wavelength changes the two paths by (1+b) and (1-b) waves, the "difference is 2b waves", and the pattern "moves by half" that, giving delta = lambdab (b = v/c). The paper gives no such derivation (it only states the result, p.3-4). When the slide lengthens one beam path by Delta and shortens the other by Delta, the two phase changes add, they do not subtract; the pattern shift is then Delta exactly, with no first-order term. See claim 3 below. Step 1 should not be read as having confirmed the paper's delta = lambdab.
3. claims.md claim 2 says the wavelengths are lambda/(1 +/- v/c) "(first order in v/c)". Eq. (5) is not a first-order result. It is exact in b by construction, because eq. (3), the round-trip condition, is imposed exactly (an input, see claim 1). Only the Sagnac-derived difference, eq. (4), is first order in b, and eq. (4) is itself written as exactly (2L/lambda)(v/c).
4. Eq. (10) first term. The deep read flags that sqrt(1-b^2)/sqrt(1+b^2) differs from the standard Doppler factor and calls it a possible retyping error. The 1976 paper prints (1/gamma)(1 +/- v_r/c) (gamma = 1/sqrt(1-b^2)), which is a third form. Numbers [calc]: at b=0.5, standard relativistic recession factor sqrt((1-b)/(1+b)) = 0.577; 1976 form (1-b)/gamma = 0.433; 1986 first term = 0.775. At b=0.1 they are 0.905, 0.895, 0.990. All agree to first order in b only. So it is not just a typing slip in 1986; the author's Doppler formula was non-standard at second order already in 1976 (physical significance is for the Physicist).
5. Journal of the 1986 paper. facts.json leaves it unverified. Marett's page gives it as "1986 SST 10(1) 3-11" (Speculations in Science and Technology) [web: http://www.conspiracyoflight.com/Silvertooth/Silvertooth.html, via Investigator note; I did not open the page myself]. Treat as one secondary report, consistent with the earlier [memory, medium] guess.
6. Muller's number. Confirmed [web: https://www.scientificamerican.com/article/the-cosmic-background-radiation-and/ and https://ui.adsabs.harvard.edu/abs/1978SciAm.238e..64M/abstract]: Muller, Sci. Am. 238(5) 64-74 (1978), about 390 km/s, hotter toward Leo. Forbes gives the modern CMB dipole as 371 km/s (secondary, Investigator note). Upgrades the [memory, medium] item. The Sagnac note date (1913, not 1915) remains [memory, high], not rechecked.
7. Step 1 otherwise holds: eq. (5) follows from (3)+(4) [calc: both identities simplify to 0]; 378 km/s reproduces with c = 3e5 km/s (377.7 with 299,792) [calc]; the sign swap of labels 1/2 between eq. (5) and Fig. 2 is real, and the same swap appears in the 1989 EWW description per the Investigator.

1. Mathematics of the paper in plain terms (for the reader)

Notation: b = v/c; lambda = rest wavelength; nu = frequency; k = 2 pi/wavelength (wavenumber, radians per metre).

• Premise A1: for source and receiver moving together, nu is fixed, so if light speed along a leg is c_i then wavelength is lambda_i = c_i/nu.
• Premise A2 (eq. 3): the null of Michelson-Morley means the round-trip count L/lambda_1 + L/lambda_2 equals 2L/lambda exactly.
• Premise A3 (eq. 4): the Sagnac shift of a rotating loop is assigned to one straight segment and carried over to "pure translation", giving L/lambda_1 - L/lambda_2 = (2L/lambda) b.
• Solving: lambda_1,2 = lambda/(1 +/- b), c_1,2 = c/(1 +/- b) (eq. 5). Then round-trip count and time are 2L/lambda and 2L/c "independent of v" (eq. 6-7).

Worked check [calc]. Take b = 1.26e-3. Then 1/c_1 + 1/c_2 = (1+b)/c + (1-b)/c = 2/c exactly. A Galilean ether (speeds c-v, c+v) would give 2/(c(1-b^2)) = (2/c)(1 + 1.6e-6), the second-order Michelson effect. The paper's formulas simply remove that second-order term by choice of c_i. That is the whole content of "no Lorentz contraction needed".

2. Claim-by-claim review

Claim 1: Michelson-Morley cannot detect an ether because frequency is fixed and wavelength tracks speed; null needs neither isotropic c nor Lorentz contraction [read: pp.1-2]

a. Internal consistency. The algebra is valid. But the argument is circular as a rebuttal: "independent of v" in eq. (6)-(7) is the round-trip condition (3) coming back out (A2 in, A2 out). Also, "the count is unchanged" is not by itself what MM needs; MM measures the difference of round-trip times of two arms, nut. The author's c_i = c/(1 +/- b) make t = 2L/c for any arm orientation, which is a specific, non-Galilean choice. The equation form is exactly the known one-parameter family of one-way speeds c/(1 +/- xi) that keeps the two-way speed fixed (Reichenbach/Winnie/Mansouri-Sexl; Tangherlini/Selleri transformations in particular) [web: https://en.wikipedia.org/wiki/One-way_speed_of_light ; https://arxiv.org/pdf/0810.1728 ; both from search snippets only, not read in full]. So the "weak" statement (a round-trip experiment cannot reveal a direction-dependent one-way speed of that form) is the textbook conventionality point, and the paper cites Tyapkin (1973) in its own references, i.e. the point is not new. The "strong" statement, that this removes the need for Lorentz contraction as a physical effect and that "a real Lorentz contraction would yield a fringe shift" (p.2), is asserted with no calculation. Not addressed: Kennedy-Thorndike (round-trip time is 2L/c for any v, so trivially null, fine) and Ives-Stilwell (a frequency/time-dilation test the model would need to reproduce; not discussed). The justification for A1 is "a continuous increase or diminution of the number of waves... in conflict with thermodynamics" (p.1): an argument by assertion, not a derivation; it fixes nu but does not show the wavelength, rather than the clock or ruler, is what changes. b. Experiments: no experiment disagrees with the weak form (it is a coordinate/synchronisation freedom). Strong form versus Ives-Stilwell, Kennedy-Thorndike, Michelson-Morley-type modern tests belongs to the Physicist. c. Tested: no test is described for the principle itself. The 1976 paper reports an earlier two-laser experiment bearing on a related idea (see claim 3). d. If true: it would mean MM, KT and similar tests cannot distinguish a preferred frame from SR on one-way grounds; mainstream physics already says that for round-trip tests (Lorentz-ether theory and SR make the same predictions). What would have to change is only the interpretation* (preferred frame detectable by some other measurement), not the null results.

Verdict (split): weak form (round-trip experiments are blind to a one-way anisotropy of the form c/(1 +/- b); Silvertooth's form is one case of a known family): Established (as a mathematical/conventionality statement). Strong form (this undercuts the need for Lorentz contraction or isotropy as physical content): Not testable as stated, and circular as an argument (A2 in = A2 out).

Claim 2: Using Sagnac on a straight segment in "pure translation", one-way wavelengths are lambda/(1 +/- b) [read: p.2]

a. Internal consistency: the rotation algebra is correct: delta = 4 A w nu/c^2 with A = L r/2, w = v/r gives 2Lv nu/c^2 = (2L/lambda) b [read: Fig. 1, page image; calc agrees]. The failure is the step to translation (A3). - The Sagnac phase is a closed-loop quantity: (1/(c lambda)) * (closed line integral of v . ds), which equals 2 A w for rigid rotation. The 1976 paper itself says "Post has shown that the closed line integral (1/c lambda) loop-integral of v.ds = 0" for the translating case and that the full-loop shift is zero "for a Sagnac interferometer in pure translation" [read: 1976 p.1101]. So the author agrees the physical, measurable (closed-loop) shift vanishes in translation. - What survives is an open-segment integral from a to b. A segment's share of a closed-loop integral depends on where the loop's centre of rotation is placed, so it is not an intrinsic property of the segment. The paper picks the centre at corner o so the two long sides contribute zero; with another centre the segment ab would carry a different share. "Independent of r" (p.2) shows independence of one parameter in one special geometry, not gauge-independence. The limit r -> infinity with v fixed does not give a uniform velocity field (the sides of length r remain in a field that varies across them), so it does not reproduce "pure translation". - Hence eq. (4) is an assumption (A3), not a derived consequence of the Sagnac effect. - Independent route in 1976: using Lorentz transforms with nu' = nu/gamma, L' = L/gamma, the 1976 paper gets phase difference = +/- L v nu/c^2. Algebra check [calc by hand]: nu L/((c +/- v) gamma^2) - nu L/c = (nu L/c)[(1 -/+ b) - 1] = -/+ nu L v/c^2. Correct. But it rests on Hypothesis (2) (source frequency "Doppler-shifted into the ether", p.1102), i.e. on the same postulate, not an independent confirmation. b. Consistent with experiments? The first-order direction-dependent wavelength (not speed) is what the 1986 apparatus claims to measure; see claim 3. Sagnac effect for rotation is established; its extension to translation contradicts the established fact that uniform translation produces no Sagnac shift [memory, high; and the author's own cited Post 1967]. c. Tested: Sagnac rotation yes, widely. The translation extension: only through claim 3/4. d. If true: SR's relativity of simultaneity would need an absolute-frame component beyond convention; GPS Sagnac corrections are already applied for Earth rotation (rotation, not translation) [memory, high].

Verdict: Internally inconsistent as a derivation (A3 contradicts the author's own statement that the closed-loop shift is zero in translation and assigns a non-intrinsic segment share). The resulting formulas coincide with a convention-dependent description that SR already allows, so the numbers in eq. (5) are not wrong as a coordinate choice; the derivation from Sagnac is.

Claim 3: One-way wavelength measurable with a slide-mounted two-beam standing-wave interferometer, v/c = lambda/(2 Delta) [read: pp.3-4]

a. Internal consistency: the measurement principle does not follow from eq. (5). My check [calc, sympy]. Take the two opposed beams at detector D1 with wavenumbers k_1 = 2 pi/lambda_1, k_2 = 2 pi/lambda_2 from eq. (5). The slide lengthens one beam path by Delta and shortens the other by Delta. The relative phase of the two beams at a point x is phi_rel = k_1 (s_A + Delta + x) - k_2 (s_B - Delta + X - x). Then d(phi_rel)/d(Delta) = k_1 + k_2 = 4 pi/lambda and d(phi_rel)/dx = k_1 + k_2 = 4 pi/lambda, using k_1 + k_2 = 2 pi (1+b)/lambda + 2 pi (1-b)/lambda = 4 pi/lambda exactly. The standing-wave node spacing is lambda/2 (unchanged) and the node shifts by exactly Delta per slide travel Delta, independent of v. The reference interferometer D2 (round trip) accumulates phase (k_1 + k_2) per unit path as well, also 4 pi/lambda [calc]. So D1 and D2 stay in phase for every b. The paper's claimed shift delta = lambdab appears only if the two path phases subtract (difference 2b). In the geometry described (one path longer by Delta, the other shorter by the same Delta), they add. The first-order terms in b cancel because they enter as +b and -b in the sum k_1 + k_2. Caveat: the paper gives no derivation of delta = lambdab, only the sentence on p.3-4 ("will advance less than a wave... retard more than a wave... the standing wave pattern will have shifted... by a first-order amount"), and the apparatus is described in words and a figure whose inset is unclear; my reconstruction may differ from the author's intended geometry. Within the model of eqs. (1)-(5) and the apparatus as described, I find a null. - Consistency with the author's own 1976 null: in 1976 two opposed free-running laser beams were detected at two points 50 cm apart; the author expected 79 cycles for Delta v/c = 1e-4 [calc: 0.5 m / 0.63 um * 1e-4 = 79.4] and observed none, concluding "the relative phase between the oppositely directed beams at any pair of locations of detectors to be invariant with v" [read: 1976 p.1101]. By the k_1 + k_2 argument that null is what the model predicts. So the 1976 null and the 1986 positive result are mutually inconsistent within the author's own model, unless the 1986 apparatus differs in an essential way (the 1986 paper does not mention the 1976 experiment). - Internal notational defects (deep read, confirmed from page images): n and delta each carry two meanings; labels 1/2 swapped between eq. (5) and Fig. 2; the text layer "lambda2" for lambda/2 on p.3. - Working formula: n delta = lambda/2 with n = Delta/lambda and delta = lambda b gives Delta b = lambda/2, i.e. v/c = lambda/(2 Delta) [calc]. Dimensionally fine. b. Experiments: if the effect existed at 1.26e-3 fractional size, a one-way standing-wave anisotropy of that size is not seen in the other experiments the Investigator lists: JOSA 1972 "Isotropy of C" is recorded by FAQ authors as a null (not read; Investigator, via Roberts & Schleif FAQ) [web, as reported]. Marett's own single-laser standing-wave experiment gave a null (title only, not read; Investigator note). Navia et al. 2006 report a CMB-aligned anisotropy in laser diffraction, with a = -0.4106 +/- 0.0225 against -0.5 for SR [web: arXiv astro-ph/0608223, via Investigator; not read by me]; this is a different method and its relation to claim 3 is for the Physicist and Contrarian. c. Tested: by the author (1986, 1989 EWW: values "within +/-5%", several years, various configurations; S/N about 20,000:1 for the sensor, per Investigator) and by Marett (2012, see claim 4). No neutral controlled test. d. If true: a first-order observable of absolute motion would exist; SR's postulate that no local experiment distinguishes inertial frames would fail. This is the Physicist's ground.

Verdict: Internally inconsistent (on my reconstruction: the claimed first-order signal cancels in the sum k_1 + k_2, and the 1976 null in the same model agrees); flagged as dependent on the apparatus reconstruction because the paper omits the derivation. If someone derives delta = lambdab properly from a different geometry, the verdict would revert to Never properly tested*.

Claim 4: The experiment: E-W, Leo on horizon, Delta = 0.25 mm, v = 378 km/s; no effect N-S or with Leo 6 or 18 h from horizon; agrees with Muller [read: p.4]

a. Arithmetic: reproduces [calc]. v/c = 0.63e-6/(20.25e-3) = 1.26e-3; 1.26e-3 * 3e5 = 378.0 km/s (377.7 km/s with c = 299,792). n = Delta/lambda = 396.8 wavelengths. The quoted "378" equals the rounded inputs times 3e5; it is not an independent measurement of 3 significant figures. v is proportional to 1/Delta: an error of +/-0.01 mm in Delta changes v by +/-15 km/s; +/-0.025 mm, by +/-38 km/s [calc]. No reading uncertainty, run count, date, place or data are given [read: p.4]. The Investigator finds later statements by the author (1989) of values "within +/-5%" and, for others, Wesley "378 +/- 8 km/s" and Marinov "386 +/- 38 km/s" (Investigator, from wiki abstracts, not read by me). Geometry check [calc], Olga WA is about 48.6 N (the paper gives that as the author's address, not stated as the site). For the CMB dipole direction (declination about -7 deg [memory, medium]): the object is on the horizon at azimuth 100.6 deg from north (about 10 deg off due east), at hour angle 5.5 h, so the E-W component is cos(10 deg) = 0.98 of the full speed; 6 h later at transit its altitude is 90 - 55.6 = 34.4 deg and the horizontal component points due south with magnitude cos(34.4 deg) = 0.83 of the speed [calc]. The E-W component goes as cos(dec)sin(hour angle) : about +/-0.99 at HA = +/-6 h, 0 at transit and at nadir, with opposite signs east and west [calc]. So: - E-W vanishing at transit (6 h from horizon) fits [calc]. - N-S should show a signal near transit (0.83 of the amplitude, i.e. about 310 km/s equivalent) if the apparatus responds to the horizontal component along its axis. The paper's N-S test says only "outputs of the detectors remain in phase during an excursion of Delta" and gives no time of day or excursion length [read: p.4]. If N-S was run when Leo was low in the east or west the null is expected; if run near transit it would be a contradiction. The paper is silent. Marett makes the same point from Olga's latitude [web, via Investigator]. - The sign of the effect should reverse between the east and west horizon crossings; the phase-reversal (180 deg) criterion is blind to sign, so the data cannot confirm the direction vector, only |component|. A 12-hour pattern in |component| is what Marett saw (peaks about 5 h and 17 h sidereal) [web via Investigator]. This is consistent with a sign-blind readout but also with any 12-hour disturbance, e.g. a thermal cycle; Marett found the same 12-hour pattern in local solar time [web via Investigator]. - "Reasonable agreement" with Muller: 378 vs 390 +/- 60 km/s (Muller) [web, confirmed above] or vs 371 (modern dipole, Forbes). Agreement within quoted uncertainty is arithmetically true, but the Delta measurement has no stated error, and Earth's orbital speed (about 30 km/s) modulates the apparent dipole over the year; the paper does not discuss this. - Sensitivity to mechanical effects: reaching a 180 deg reversal at Delta = 0.25 mm is a fractional discrepancy of 1.26e-3 between the optical path scales of D1 and D2. A pure cosine error between the slide axis and the two beam directions gives 1 - cos(theta) = 1.26e-3, theta = 2.9 deg [calc]. (A fixed misalignment is removed in the zeroing procedure; only a change of alignment or index between the two interferometers over the run matters.) For scale, the refractivity of air at room conditions is n - 1 of about 2.7e-4 [memory, high], so the required fractional difference is about 4.7 times the whole refractivity of air; a differential index change is therefore unlikely to supply it, whereas a beam-pointing change is not excluded. This supports the plausibility of Marett's attribution only through the pointing route; it does not prove it. Sherwin (1989) and Phipps argue that a twist of order lambda/4 over the travel, or AC coupling, could mimic the phase reversal (Investigator, secondary; not read). b. Experiments: the observation itself is the experiment. Independent: Marett (2012, 18 months, SWD sensor from Julich per his page): reproduced a 12 h signal aligned to the sidereal directions with magnitude about the CMB velocity after normalisation; but non-zero offset when perpendicular, large day-to-day scatter, wrong sign relative to the prediction, 12 h pattern also in local time, correlation with room temperature and laser lock voltage; his conclusion "a very elaborate thermometer" [web via Investigator: http://www.conspiracyoflight.com/Silvertooth/Silvertooth.html ; I did not open the page]. Marinov (1987): "different arrangement", 386 +/- 38 km/s, declination -22 +/- 6 deg; Marinov is himself a claimant of absolute-motion detection, an interested party. Wesley (1987) 378 +/- 8 km/s, RA 11 +/- 2 h, source not checked [web, wiki abstracts via Investigator]. Aspden, Nanning, Wilczynski, Whitney-Marinov: not read. None of these is a blinded or neutral test; Marett's is the most informative: it supports the signal, not the interpretation. c. Tested: author's own runs (unreported); Marett 2012; Marinov 1987 (arrangement differs); Wesley's figures attribution unverified. No replication with the same method that supports the interpretation. Absence-of-evidence note (record goes quiet where it would be expected to continue): the stated RADC/DARPA sponsorship has no report trail found by the Investigator (DTIC direct search pending). I note the competing explanations the Investigator lists (informal support; unindexed or restricted reports; overstated sponsorship); a retrievable sponsor report with raw runs is what would decide whether a fuller data set exists. d. If true: an absolute rest frame close to the CMB frame would be measurable with a tabletop optical experiment; SR's principle that inertial frames are indistinguishable by local light experiments would be violated at first order in v/c; the many second-order tests would need to be reinterpreted.

Verdict: Never properly tested. The single reported value is arithmetically reproducible but unaccompanied by error bars, runs, dates or raw data; the one independent replication with logged controls found the signal and a non-ether (thermal/pointing) correlate. It was not dismissed without testing (Marett and others ran it), but no neutral, controlled test with the author's own apparatus exists. In light of claim 3 (the predicted signal cancels in the author's model), a genuine signal would not even mean what the paper says it means; that is why this claim and claim 3 should be read together.

Claim 5: Velocity-dependent wavelength count alters the Doppler frequency and explains the accelerating universe, quasar redshift anomalies and GPS errors via an extra L v-bar/c^2 term [read: p.4]

a. Internal consistency. - As printed in 1986, eq. (10) is incomplete: symbols v_obs, v_source, v-bar undefined; no derivation; if v-bar is a velocity the extra term has units of time and cannot be added to the dimensionless first term [read: deep read; calc agrees]. The 1976 paper supplies the intended meaning: acceleration v̇, term L v̇/c^2, dimensionless, derived by treating phase delta = L v nu/c^2, "if we allow v to vary uniformly with time, then there is a time rate of change of the phase, or a frequency shift" delta-dot = L v̇/(c lambda), added to the source frequency [read: 1976 p.1102]. So the corrected claim is derivable only through the unproven A3/Hypothesis (2) chain of claim 2. - Magnitude [calc]: for L = 1e27 cm (about 1e9 light years), c = 3e10 cm/s, the term reaches 1 for an acceleration of c^2/L = 9e-7 cm/s^2. For a source on a circular orbit of radius 3e22 cm (about 10 kpc) at 2e7 cm/s (200 km/s): v^2/d = 1.3e-8 cm/s^2, term = 0.015, which corresponds to an extra apparent redshift of order z = 0.015 (about 4,400 km/s). The 1976 paper proposes exactly this to explain redshift differences between quasars in the same galaxy. - The term is the bookkeeping of a retardation: a source with acceleration a changes velocity by aL/c while the light travels, so aL/(c*c) is the first-order Doppler shift between velocity "now" and velocity at emission. A Doppler formula that uses the velocity at the emission event has no such term. For a rotating source the assumption "v varies uniformly" over the light-travel time (L/c = 3.3e16 s, about 1e9 yr) is false: the orbital period at those numbers is 2 pi d/v = 9.4e15 s (about 3e8 yr), several times shorter than the travel time, so the acceleration direction rotates many times during the flight and the linear-in-L term cannot apply. This is an algebraic/kinematic point; whether any physical effect of the claimed type exists is for the Physicist. - The Doppler first term differs from the standard one at second order (Corrections item 4). - GPS and accelerating-universe statements: no numbers, no equation, no derivation [read: p.4]. The cited reference (Gunn and Tinsley, Nature 1975) predates the 1998 supernova result [memory, high]; the author's phrase "apparently accelerating universe" therefore refers to the 1975 claim, not the later discovery. The Investigator lists a later GPS paper (Galilean Electrodynamics 1990, "Position Error in Satellite Navigation Systems") that may contain the numerical working; abstract only, not read. b. Experiments: GPS operates with relativistic clock corrections and the Sagnac correction for Earth's rotation, which agree with the observed performance at the level the system reports [memory, high]; the claim of "significant errors in GPS" is stated without numbers in the paper. The Physicist should weigh this. c. Tested: no test reported in the paper. 1976 states an experiment "under way" at the University of Arizona OSC (a phase measurement between two oscillators 2 m apart, expected 59 cycles peak-to-peak [calc: 200 cm * 3e6 cm/s * 8.85e13 Hz / (3e10)^2 = 59] per the 1976 paper); the Investigator did not find its result and the OSC FY75 report is pending (absence of evidence to record: reported "under way", no outcome found). d. If true: cosmological redshift interpretation and the Doppler formula would require a new acceleration-dependent term; GPS error budgets would need an absolute-velocity term.

Verdict (split): eq. (10) as printed in 1986: Internally inconsistent (undefined symbols; units fail on the literal reading). The 1976 form with v̇: dimensionally consistent, but the mechanism rests on a retardation bookkeeping term and a uniform-acceleration assumption that fails for the author's own quasar example: Refuted by calculation for that example (the acceleration reverses direction within the light travel time, so the term is not Lv̇/c^2); the further assertions about GPS, quasars and the accelerating universe: Not testable as stated* (no numbers or derivation).

3. Summary table

4. Investigator findings kept in the record (whatever the verdict)

• 1976 Applied Optics 15(5) 1100: the earlier form of the argument, the extra Doppler term with v̇, Newcomb's 1881 letter quoted as the compensation principle (wavelength and velocity differ with direction, "when a ray returns on its own path the retardation in one direction is compensated by the acceleration in the other"), the two-laser null, and the Arizona experiment "under way" [read].
• 1989 EWW "Motion through the ether": values within +/-5% over several years, various configurations, S/N 20,000:1, maximum with detector axis at Leo (Investigator [web], not re-read). The author's statements are his own and unreproduced numbers.
• Marett 2012: signal reproduced as a 12 h sidereally aligned pattern of about CMB size, with offset, scatter, wrong sign, local-time pattern, and thermometer-like correlations; his conclusion is thermal/pointing. Kept both halves. Marett hoped the effect was real and is not an institutional critic (Investigator note).
• Marinov 1987 (interested party), Wesley 1987, Aspden, Nanning, Wilczynski: supporting or discussing; unverified, not read.
• Critiques: Sherwin 1989, Phipps (AC coupling, lambda/4 twist), Newburgh (RADC) and Gron 1977 on the 1976 paper; Winnie and Tyapkin (conventionality of the one-way speed) cited by Marett and Forbes against claims 1 and 3.
• Related: Navia et al. 2006 (CMB-aligned laser anisotropy, reported by authors); Whitney and Silvertooth 1992 (Physics Essays 5(1) 82): standing-wave nodal spacing departing from lambda/2 inside one Michelson arm. Math remark on that claim, from the abstract only: within the model c(theta) = c/(1 + b cos(theta)) with fixed nu, the node spacing of two opposed beams is exactly lambda/2 [calc, the same k_1 + k_2 identity]; a spacing departure at first order would need a different model than eqs. (1)-(5). I have not read the 1992 paper.
• Absence of evidence: RADC/DARPA sponsorship without a found report trail; Arizona OSC FY75 report; the sponsor-report record would decide between informal support, unindexed or restricted reports and overstated sponsorship.
• The 1986 Nature 322:590 letter and Koberlein's Forbes piece: popular commentary (one stakeless astrophysicist, relying on Marett).

5. What would settle the main points

1. Claim 3: a derivation of delta = lambda*b from the author's own geometry, or a run of the apparatus in which a known, deliberately imposed index or path change is added and the D1/D2 reading checked (calibration with the effect absent).
2. Claim 4: raw time series with dates, temperature and laser lock logging, an N-S run near transit, and a blinded or randomised orientation; the sponsor reports.
3. Claim 5: a numerical GPS error budget from the 1990 Galilean Electrodynamics paper, compared with published GPS residuals.

Appendix: calculation script (summary)

sympy/numpy checks run in /tmp/st/chk.py (not kept in the project): (i) eq. (3) and (4) identities with lambda_1,2 = lambda/(1 +/- b) reduce to 0; (ii) k_1 + k_2 = 4 pi/lambda, node period lambda/2, d(phi_rel)/d(Delta) = d(phi_rel)/dx = 4 pi/lambda, node shift per slide travel = Delta (magnitude 1) for all b; (iii) v/c = 1.26e-3, v = 378.0 km/s (3e5) or 377.7 km/s (299,792.458), n = 396.8, delta = 0.79 nm per rest wavelength; (iv) Delta uncertainty propagation; (v) Galilean 1/c_1 + 1/c_2 = 2/(c(1 - b^2)) vs 2/c; (vi) Doppler first-term comparison; (vii) L a/c^2 numbers; (viii) Leo geometry at latitude 48.6 N, dec -7 deg.