Flat-Earth: Physicist review (Step 2)

Reviewer: PhD physicist. Inputs read: claims.md, facts.json (catalogue), all 40 deep reads, the Investigator's sites.md "Leads for review", research/ notes, and research/files/ (Lady Blount's 1905 "Collapse of the Globular Theory" read directly). Source tags: [read] from a project document, [web] from a URL, [memory] recalled with confidence, [calc] my own arithmetic (numpy in the project venv, script not kept). Reader level: undergraduate; symbols are defined where first used.

Source gap: none for the claims themselves. The main primary works are readable, but Rowbotham 1865/1881, the Zetetic Review 1893-97 and the NASA reports were deep-read only in part (see claims.md coverage note). Where a conclusion rests on [memory] alone I say so.

Web checks (budget 6, 4 used). (1) Trefethen et al., Nature 207, 1084-1085 (1965), "The Bath-Tub Vortex in the Southern Hemisphere" exists; a secondary letter reports consistently clockwise draining in Sydney; I did not read the paper itself [web: https://link.springer.com/article/10.1038/2071084a0]. (2) Santiago-Sydney non-stop flights take about 13.5 to 15 hours [web: https://www.flightsfrom.com/SCL-SYD; https://airdatanews.com/latam-will-resume-direct-flights-between-santiago-de-chile-and-sydney-in-october]. (3) Ring lasers: G (Wettzell) is a 4 m x 4 m square, 16 m perimeter, He-Ne [web: https://www.geophysik.uni-muenchen.de/~igel/PDF/schreiberetal_springer_2006.pdf]; the 348 Hz figure and the C-II frequency could not be confirmed on the web, so they remain [memory, medium] and I use them only as consistency checks, not as evidence. (4) The Wikipedia page for Airy's water telescope returned 404; Airy's 1871 result is therefore [memory, high] (Proc. Roy. Soc. 20, 35) and is flagged where used.

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0. The physics in two pages (so the verdicts can be read)

Level versus straight. A still water surface is an equipotential of gravity (a surface of constant gravitational potential energy per unit mass). On a sphere of radius R that surface is itself curved. A straight line of sight between two points a distance L apart, both at height h above the water, passes below the water surface in the middle by the sagitta (the bulge of an arc over its chord)

s = L^2 / (8R).

With R = 3958.8 mi and L = 6 mi, s = 6.00 ft [calc]. This is the origin of Rowbotham's "8 inches times miles squared" rule: the drop of the surface below a tangent line at distance d is d^2/(2R) = 8.0 in per mi^2 [calc]. Rowbotham's arithmetic with it is almost always right [read: 1865 deep read; 1881 deep read]. Flat water predicts s = 0.

Refraction. Air density usually falls with height, so a nearly horizontal light ray bends downward, following a circle of radius R/k (k is the refraction coefficient; k = 0 is a straight ray; k = 1 is a ray that curves exactly as fast as the earth). The effective apparent bulge is s(1 - k). The textbook average is k near 0.13 [read: Hirt 2010, citing Gauss]. Close to the ground it varies enormously: Hirt et al. measured -4 to +16 at 1.8 m over grass on sunny days, with strongly positive values (+12 to +16) near and after sunset when the ground cools and an inversion forms; older cited work gives +1 to +18 about 5 m above water [read: Hirt 2010 deep read, section 3 and 6]. So refraction is not a hand-waving excuse: it is a measured, large, variable effect, largest exactly where the zetetic observations were made (low sight lines over water, calm still air).

Consequence for every "I could still see it" report. For each report I compute the k that a globe needs to make it happen (Section 2). If that k lies within measured values, the report is consistent with a globe but does not prove one either; it shows the design was refraction-sensitive. The decisive designs are those that are insensitive (high sight lines, equal heights, many repeats) or that measure k directly (reciprocal vertical angles, Hirt's method).

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1. Corrections to Step 1

1. claims.md claim 1, "Wallace 1870 and Oldham 1900-01 (middle mark about 6 ft above the sight line)". Only Oldham states "about six feet" [read: Oldham deep read]. Wallace gives no measured offset: he predicted 5 ft 8 in, "reduced a little by refraction to perhaps about five feet", and reports the result as "very nearly of the amount calculated", from signed sketches [read: Wallace 1905 deep read, sections 4 and 6]. Fix the wording: Wallace = qualitative agreement shown in sketches signed by both sides' referees; Oldham = about 6 ft.
2. Bedford Level wiki deep read, "the wiki's 'eleven feet' is not derived ... 16.7 ft". The error is in the deep read. Rowbotham's 11 ft 8 in is the hidden height of the top of a 5 ft flag: 5^2 x 8 in = 16 ft 8 in of drop minus 5 ft = 11 ft 8 in [read: Rowbotham 1881 deep read, Exp. 1]. The wiki's "eleven feet" is that figure rounded. My own check agrees: 16.7 ft drop, 11.7 ft hidden [calc].
3. Michelson-Gale-Pearson wiki deep read, "set sizes 12 x 20 + 23 = 263 versus 269". The Table I set sizes are eleven sets of 20, one of 26 and one of 23: 220 + 26 + 23 = 269 [calc, from the table in the Michelson-Gale deep read]. The 263 arithmetic is wrong (claims.md already has the OCR "2O" = 26 correction; I confirm the total).
4. TFES/Correa "mean +0.26 fringe". The paper's mean is 0.230 +/- 0.005 and my unweighted mean of the 13 set means is 0.2295 [calc]. +0.26 is not in the paper. Correa's "range -0.04 to +0.55" refers to single readings, which the paper's Fig. 3 shows (consistent with a scatter of about +/-0.1); that is not a contradiction, because the 269 readings are averaged.
5. claims.md claim 3, "sunset by Rowbotham's perspective law". Stated as a flat-earth explanation, it fails by calculation (Section 2, claim 3). The claims text is accurate as a description of what Rowbotham claimed; the problem is the physics, not the transcription.
6. Investigator's lead: Clifton as "a witness on the inventor's side ... not an interested party in the zetetic movement". Clifton wrote for J. H. Dallmeyer Ltd, which sold the Photo-Telescopic camera; that is a commercial stake in a favourable photographic result, though not in the flat-earth cause. His own letter, which I read, also says conditions were "very unfavourable", with "an aqueous shimmering vapour" floating on the canal, and that the sheet was seen "though not sharply defined" [read: research/files/tfeslib-Flat_or_Spherical_-_08...pdf, p.3]. Lady Blount's pamphlet adds that the experiment was done "in misty and ... dissatisfactory weather" (OCR garbled) and says the bottom "should have been certainly over 20 feet below the line of vision" [read: same, p.2-3]. My computation gives 12.1 ft hidden without refraction (Section 2, claim 1), not 20 ft; 20+ ft is what you get by ignoring the observer's own horizon distance. The Investigator's description should carry these points beside the quotation.
7. Koreshan survey (Investigator and deep read). Not an error, but an addition: the survey's own prose figures (8 in, 32 in, 6 ft) are the calculated values, not the tabled measurements (8.02, 30.62, 75 in) [read: Koreshan deep read, 5b]. I use the tabled figures.

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2. The claims

Claim 1. Water is level and the earth shows no curvature

a. Mathematics. The arithmetic is internally consistent: the 8 in x n^2 rule is correct for the geometric drop from a tangent plane, and Rowbotham's hidden-height sums reproduce [calc] (Nab light-ship 14 ft; Ryde funnel 40 in; Bedford flag 11 ft 8 in), with three slips of his own in the lighthouse table (Whitby 102 for 112, Lower Farn 67 for 21.7, the Grimsby refraction step) [read: 1865 deep read, 7]. The logic has three recurring faults: - It treats "level" as "straight". Rowbotham himself notes the distinction ("equidistant from a centre means ... level"), then argues that a curved level surface would still make a straight datum line look convex [read: 1881 deep read, refraction section]. The globe model predicts that the middle mark of an equal-height trio stands 6 ft above the sight line; the measurement tests that. - It treats stated visibility ranges and a reporter's phrase as observations. Findlay's lighthouse ranges are computed ranges that include 10 ft eye height and refraction (Calf of Man 23 vs 22.8 nmi computed; Cromer 23 vs 22.5; Eddystone 13 vs 13.3) [calc, from the 1865 deep read table]. Dubay repeats these numbers (items 81-86) [read: Dubay deep read]. - It applies a refraction allowance to the wrong quantity (1/12 "of the altitude of the object" rather than of the curvature drop) [read: 1881 deep read]. Dubay's own list also mixes two geometries (drop from a tangent: items 9, 13; mid-chord sag: items 10, 11) and cannot reproduce items 67, 72, 92 from the printed premises [read: Dubay deep read, 3a, 3b].

b. Consistency with experiment. Three groups of observations.

Equal-height, high sight line (the discriminating design). Wallace, 1870: Welney parapet 13 ft 3 in above water; mark on Old Bedford Bridge and mark on a pole at the 3-mile point at the same height. The middle disc stood above the sight line, and Hampden's own referee drew and signed the sketches [read: Wallace 1905 deep read, 3-5]. Oldham, 1900-01, same stretch, same design: the middle mark stood "about six feet above the line of sight" [read: Oldham deep read]. The geometric value is 6.00 ft, the value with k = 0.13 is 5.22 ft [calc]. Angles at the eyepiece: the middle mark sits 78 arcseconds below the horizontal through the telescope and the far mark 156, equal steps of angle, which is what a parabola gives and not what a straight line gives. Carpenter's reading "equal steps means a straight line" confuses the two (collinear points would hide behind each other) [read: Wallace deep read, section 6; [calc] agrees].

Low sight line, single-ended designs (Rowbotham 1838, 1870; Clifton 1904). Required k for a globe to permit what was reported (6 mi unless stated) [calc]: | Observation | Geometric hidden height | Hidden at k = 0.13 | k needed to see it | |---|---|---|---| | Rowbotham 1838: eye 8 in, flag top 5 ft | 16.7 ft | 14.1 ft | 0.61 | | Rowbotham 5 Apr 1870: eye 18 in, board bottom 6.5 ft | 13.5 ft | 11.2 ft | 0.41 | | Clifton 1904: eye 2 ft, sheet bottom at water, 15 ft sheet [read: Schadewald, research note] | 12.1 ft | 10.0 ft | 0.92 (waterline); with k = 0.13 top 5 ft of the sheet shows | | Nab light-ship 1864: eye 2 ft 8 in, bulwark top 10 ft, 8 mi | 14 ft below horizon | 9.9 ft | 0.46 [read: 1865 deep read] | These k values lie inside Hirt's measured range near the ground (up to +16 over grass; more over water in cited work) [read]. They are not typical (0.13) but they are the calm, still, sunny-afternoon conditions every account describes ("air exceedingly still and clear", "smooth as a molten mirror"; Clifton's "aqueous shimmering vapour") [read]. Rowbotham's own two-sided report is informative: the same objects were visible on calm days and invisible on rough days [read: Sinking Ship deep read, 2b-2c], which is what variable refraction does and what his waves hypothesis (qualitative, no wave heights) does not quantify. His barometer/thermometer test of "the same medium" compared air at the two ends at one height, not the vertical gradient along the path, which is what bends light [read: 1881 deep read; Hirt]. His surveyors' levelled theodolites showed the sea horizon below the cross-hair, as a globe predicts (dip 6.2 arcminutes for a 34 ft eye [calc]); he blamed the lens, but his own quoted instrument tolerance (0.001 ft in 10 chains, 0.3 arcsecond [calc]) is about 1,200 times smaller than the 372-arcsecond dip, so his quoted figure refutes his dismissal.

Koreshan "concave earth" survey, 1897. The tabled drops are 8.02 in at 1 mi, 30.62 in at 2 mi, 75 in at 3 mi, 128 in at 4 1/8 mi, against the calculated 8, 32, 72, 136 [read: Koreshan deep read, 5b]. This is the opposite sign to the globe's prediction (rise above the starting height) and to the flat model (no change). I cannot call it a measurement of curvature, because a tiny constant error per step produces the same quadratic: with 12 ft sections and 440 steps per mile, a systematic tilt of only 5.7 x 10^-7 rad (0.12 arcsecond, 0.7 micrometre on a 4 ft arm) per section gives 8 in at one mile [calc]. The authors' stated tolerance is 0.001 in in 4 ft, 4.3 arcseconds per step, which alone, if systematic, would produce a line of curvature radius about 109 mi, thirty-six times the earth's curvature [calc]. The "System of Reversals" cancels a constant right-angle error in principle but not gravity-induced sag of the arms, thermal gradients or settling of the standards on sand; the return check agreed only to about 0.25 in over 0.375 mi (not the ".0001 in" of the shorter 456 ft trial) [read: Koreshan deep read, 5d]. The last 1.6 miles were not mechanical but a telescope sight with refraction assumed small [read: same, 4d, 6], which is where I have just shown refraction is largest. The survey is by the colony whose doctrine it was to prove, with mostly colony witnesses [read]; I report that as the party's account and weigh the numbers on their merits. It also contradicts the flat-earth movement itself: flat and concave cannot both be true.

Modern replications. Hirt et al. (2010) is not a test of earth shape, and its method uses a known R [read], but it shows the k range. Skiba's 2016 Chicago photo from 3 ft at 42.6-46 mi shows the top of the city with the lower part missing, which he accepts [read: Skiba deep read, section 1]; the globe with k = 0.17 hides about 900-1,060 ft of the 1,450 ft tower [calc/read], so what he saw is what a globe predicts. The press (ABC57 meteorologist, later relabelling the 2015 Michigan photo as "looming", an atmospheric-refraction effect) and the Notre Dame optics expert (Rennie) explain the 2015 photo (observer at about 200 ft, 53 mi) by temperature-inversion refraction [read]. Rich's "5,200 ft inversion" argument mistakes the geometry (2,400 ft is 60^2 x 8 in, the drop below a tangent, not the hidden height for an observer above the water; and the sum 2,400 + 4,800 is not 5,200) [read: Skiba deep read, 6].

c. Tested? By whom? Replicated? Many times, mostly by the proponents or sympathisers: Rowbotham 1838-1870; Wallace 1870 (the only one with agreed prior predictions and referees from both sides); Carpenter 1870s (cited, not held); Naylor, August 1894 (held: Earth Review PDF pp.216-217, printed about 1896; corrected per arbiter section 4 item 15); Oldham 1900-01 (published as an abstract only: no heights, no refraction, no time of day, no photographs reproduced [read]); Blount/Clifton 1904; Koreshan 1897; Skiba 2016-17. Not replicated in a controlled way with measured refraction. The 2017 Skiba balloon test: the team narrator reports "a very slight curve" but says lens distortion and cloud make the horizon "hard to tell"; no result was published in the material found [read: research note, YouTube 15 Nov 2017]. Wallace's 1870 test was also followed by Carpenter's counter-reading and 15 years of litigation, which tells us about the people, not the optics; the courts decided a wager-law point only (Hampden v. Walsh, 1 QBD 189) [read: sites.md]. The folder's TFES statement that a court found Wallace "cheated" is unsupported by the primary record the Investigator located (see Corrections in claims.md).

d. What would have to change in mainstream physics? For the strong form (no curvature over any scale), everything in geodesy, navigation, astronomy and gravitation. For the weak form (low sight lines sometimes show more than geometry allows), nothing: it is standard refraction (looming, superior mirage) and is quantitatively inside measured ranges.

Verdicts (claim 1, split). - Strong form: water is level in the sense of a plane; earth not a globe of about 25,000 mi circumference: Tested, not supported. The only experiments with a refraction-robust design (Wallace 1870, Oldham 1900-01, equal heights, 13 ft above the water, signed by opponents) gave the globe's curvature to within the precision stated. - Weak form: distant low objects over calm water are sometimes visible beyond the geometric horizon: Established as an observation, and as an effect of refraction (k from 0.4 to 0.9 needed, within the measured range). It does not support flatness; it shows that single-ended low-sight designs cannot decide shape. - Concave variant (Koreshan): Never properly tested by a neutral party; the single run was by the interested party, its instrument tolerance leaves room for a systematic error equal to the claimed effect, and the last stage was an optical sight. It contradicts the flat model. - Open design that would settle it: a long equal-height trio over water with simultaneous reciprocal vertical angles to measure k (Hirt's method), repeated at several times of day. Neither side has produced it.

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Claim 2. The earth is stationary: it neither rotates nor orbits

a. Mathematics. Internally the zetetic arguments are not equations. Where numbers appear they are mostly sound arithmetic with the wrong premise (Dubay items 97, 179-184: "adds speeds in different directions"; planes "should" be 2 or 3 times faster eastbound while the atmosphere co-rotates with the ground, which the same post asserts in item 23, so the post holds two incompatible models [read: Dubay deep read, 3f]). The TFES Ring Laser page misreads a Brillouin-gyroscope caption: "the angular rate change for N-S is close to twice the Earth's rotation rate (2x15 deg/h)" is a difference between pointing the sensitive axis north and then south, +15 to -15 deg/h = 30 deg/h, and the same caption says the E-W change is "near zero", which is the correct pattern for a rotation sensor; the page omits that [read: Ring Laser deep read, section 6; [calc] earth rate 15.04 deg/h].

b. Consistency with experiment. Take the evidence in order of directness. 1. Sagnac interferometer, Michelson-Gale 1925 [read: deep read, all]. A light loop of 2010 ft x 1113 ft at latitude 41 deg 46', pipes evacuated to about 1/30 atmosphere. Prediction of a rotating earth: Delta = 4 A omega sin(phi) / (lambda V), with A the enclosed area, omega the earth's angular velocity, phi the latitude, lambda the wavelength and V the speed of light. [calc] A = 207,836 m^2, omega = 7.292 x 10^-5 rad/s, lambda = 5700 A, gives 0.2363 fringe, matching the paper's 0.236 +/- 0.002. Observed 0.230 +/- 0.005 from 269 readings in 13 sets. The 13 set means (0.193 to 0.255) have standard deviation 0.0204 and standard error 0.0057 [calc]; a no-rotation null (0 fringe) is therefore rejected at about 40 standard errors of the statistics, and the correct sign (counter-clockwise beam retarded) is observed. TFES's "borderline significance" rests on Correa's different mean and on single readings, not on the reported averages. Caveat: systematic errors are only described qualitatively (image superposition corrected by measuring image positions; no estimate for temperature, residual air, pipe settling) [read]; the paper's claim is agreement "within the limits of observational error". It was a single run at a single latitude and, as far as the folder shows, was not replicated in that form by others. Michelson himself stated the same prediction follows from "a stationary ether as well as ... relativity" [read], so it measures rotation relative to the local inertial frame, not "aether versus relativity". 2. Ring lasers. The same principle at much higher precision. The Sagnac beat frequency is 4A/(lambda P) times the rotation component along the ring normal. For a horizontal ring the component is omega sin(phi), so the signal is proportional to the sine of latitude, zero at the equator, with opposite sign in the southern hemisphere [calc]. For a 4 m x 4 m ring at lat 49.1 deg N and 632.8 nm: 348.6 Hz [calc; the geometry of G is [web] confirmed, the 348 Hz figure is [memory, medium] and is only a consistency check]. A rotating flat disc has the same vertical rotation vector everywhere, so it predicts no latitude dependence and no sign flip. This latitude dependence is the discriminator between "a flat plane rotating about a vertical centre" and "a rotating sphere". The TFES page's "noise" argument concerns that the earth-rate signal sits beneath other signals (tilts, seismic rotation, backscatter) and is extracted by averaging [read]; the G-ring dataset it quotes has "all known geophysical signals ... removed" (a residual, not the raw rate) [read: Ring Laser deep read, 4]. The page offers no mechanism that would produce a Sagnac split with the correct latitude and orientation dependence. 3. Foucault pendulum, 1851. The plane of swing precesses at 15.04 deg/h x sin(latitude): 11.3 deg/h at Paris (48.85 deg), 10.0 deg/h at 41.8 deg, 15.04 deg/h at a pole (period 23.93 h), zero at the equator, reversed sense in the south [calc]. The TFES page gives no rate data at all; its evidence is historical difficulty of launching a plane-swinging pendulum (Airy, Kitchell 1851: elliptical motion), Longden's 1919 wire-anisotropy effect (a real error source), and motor-driven museum pendulums [read: Foucault deep read]. These are real systematic errors that experimenters (Airy included) knew how to control; they are not evidence for a null. The South Pole station anecdote (rotation "twice what is expected", 12-hour days) is from a light-hearted station trivia page with no data and no stated cause; I record it as a single uncorroborated anecdote of an uncontrolled build, to be read in full before weighting [read]. A repeated, controlled measurement of precession rate vs latitude is what the claim needs and what the Foucault literature provides [memory, high; not in the folder]. 4. Coriolis. The TFES page is a collage of quotations. Its own sources say (i) the artillery table H exists (it does not deny it); (ii) Reich's 1831 mine-shaft drop gave an eastward deflection "almost exactly" the predicted over an inch [read]; (iii) Shapiro and Trefethen found the bath vortex follows hemisphere when the water is settled for 24 h [read, and web check of the Trefethen paper's existence]. Its Eotvos paragraph confuses the equivalence-principle torsion balance (a difference between two bodies, so any common Coriolis/centrifugal term cancels) with a Coriolis detector [read: Coriolis deep read, section 6]. Dubay's vertical-cannon story (item 20: "14 seconds up, 14 down ... within 2 feet") has no experimenter, date or wind data; a vertical shot with 28 s flight time at 45 deg lat lands about 1.85 m (6 ft) west by Coriolis alone (Omega cos(phi) g T^3 / 6 [calc]), so even the anecdote, taken at face value, does not exclude rotation. 5. No orbital motion. Airy's 1871 water-filled telescope: if starlight enters a water-filled tube, a stationary aether would make the tilt n times larger (27.3 arcsec for n = 1.333 instead of 20.49 arcsec [calc]); Fresnel's 1818 partial drag (coefficient 1 - 1/n^2 = 0.43 for water) cancels the difference to first order, and special relativity gives the same coefficient. Airy found no change [memory, high; web fetch failed]. The TFES page expects the n-times tilt, which a moving-earth theory with Fresnel drag does not predict; its own quote from Johnson (Arago/Fresnel) states the drag [read: Airy's Failure deep read, section 4, 7]. Michelson-Morley (1887): expected fringe shift 2 L v^2 / (lambda c^2) = 0.43 for L = 11 m, lambda = 500 nm, v = 29.8 km/s [calc]; observed under about 0.02 [memory, high]. That is a null for motion through a stationary aether, explained by relativity; it was followed by many independent null and positive tests (Kennedy-Thorndike, Ives-Stilwell, Sagnac) [memory, high]. A stationary earth in a stationary aether would need the MGP rotation signal to be explained as rotation relative to the aether, and annual stellar aberration (20.49 arcsec, same for all stars; the value used by Bradley 1728) and parallax (Bessel 1838) to be explained otherwise [memory, high]. The folder holds none of these primary papers.

One honest qualification. Rotation experiments measure rotation relative to the local inertial frame. Whether the earth turns inside fixed stars or the universe turns around a fixed earth is, in general relativity, a coordinate choice with the same local forces (Thirring/Mach-type frame dragging) [memory, medium]. The TFES Foucault page uses this ("Mach's principle"). That keeps "the earth does not rotate" from being strictly false in a kinematic sense, but it is not the flat-earth claim: it requires an enormous rotating mass distribution (the whole universe, with ordinary stars at light-year distances moving faster than light [calc: angular rate 7.3 x 10^-5 rad/s x 4.2 ly = 3.1 x 10^-4 ly/s, far above c]), and no flat-earth source writes down such a model.

c. Tested? MGP (Michelson, Gale, Pearson 1925); ring lasers since the 1960s-2000s (G at Wettzell, C-II in Christchurch, others) [memory/web partly]; Foucault since 1851, repeated worldwide; Airy 1871, Hoek 1868 [memory, high]. Not "dismissed without testing": the flat-earth side has not itself run a controlled Foucault or ring-laser measurement; the main counter-claims are about experimental noise and reinterpretation.

d. What would have to change? All of: Newtonian rotating frames (Coriolis in weather forecasting, ballistics tables, the Eotvos correction in shipboard gravimetry), GPS (the Sagnac correction of order 100 ns for a fixed satellite is in the folder's PTTI paper [read: Piester et al. 2007 deep read]), VLBI earth-orientation work (the WGS 84 standard, with omega = 7.292115 x 10^-5 rad/s as a nominal mean and measured fluctuations of order 3 ms in UT1 [read: NGA deep read, section 5]), and optics/relativity.

Verdicts (claim 2, split). - Earth does not rotate (relative to the local inertial frame): Tested, not supported. Rotation is measured with predicted magnitude (MGP 0.230 vs 0.236 fringe), sign and, in ring lasers, the sin(latitude) dependence. - Earth does not orbit the sun: Tested, not supported by aberration, parallax and spectroscopic Doppler [memory, high]; the specific Airy and Michelson-Morley "proofs" are Tested, not supported as proofs of rest (Fresnel drag, relativity). - Rest versus rotating universe as a pure kinematic reframing: Not testable as stated locally; no flat-earth source supplies a model.

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Claim 3. Sun and moon are small and near; sunrise and sunset are perspective (or curved-light) effects over a plane

a. Mathematics. Rowbotham's sun is about 32 mi across, about 3,000 mi up: angle = 32/3,000 = 0.61 deg, roughly the observed 0.53 deg [calc/read]. The model fails on other counts. Perspective cannot set the sun. For a sun at height H = 3,000 mi over a plane, its elevation at horizontal distance d is arctan(H/d): 45 deg at 3,000 mi, 25.8 deg at 6,213 mi, 13.6 deg at 12,426 mi, still 6.8 deg at 25,000 mi, and it takes d = 10 million miles before the elevation falls to one arcminute [calc]. Sunsets would never occur on a plane of earth's size, and the sun's angular size would shrink by a factor of about five between noon and the farthest reach of the day. (Blount and Smith's reply, "globules of water magnify the setting sun", is a qualitative statement with no measurement [read: Blount-Smith deep read, 7].) The sun's height is inconsistent between latitudes. At an equinox the sun is overhead at the equator; on a plane the elevation at latitude phi (ground distance 69.1 mi per degree) is arctan(H/(69.1 phi)). Matching the observed 90 - phi elevation gives H = 3,938 mi from 7.2 deg (the Eratosthenes baseline), 3,109 mi from 45 deg, 2,394 mi from 60 deg, 975 mi from 80 deg [calc]. A single height H cannot fit; with H = 3,940 mi the plane predicts 43.5 deg at 60 deg latitude where 30 deg is observed. Cited southern evidence in the movement's own journal (Revell, Tuakau, 1893: sun's course, Southern Cross circling a southern point) contradicts a single north-centred disc and forced the 1904 two-vortex, figure-8 model [read: Review and Blount-Smith deep reads]. In that pamphlet the speed arithmetic contains slips (moon "180 miles per minute" vs its own computed 2,281 mph; adding the earth's orbital speed to the moon's in the heliocentric frame and calling the result absurd) [read: Blount-Smith deep read, 9].

The curved-light replacement (TFES "Electromagnetic Acceleration"). The only equation is an image: y = (3/4)(beta x^4/c^2)^(1/3), "not valid for short-range experiments", with beta an undetermined "Bishop constant" and no derivation [read: EA deep read, 2]. It is dimensionally consistent if beta is an acceleration [calc/read], but it has no numerical value, so it predicts nothing. To make sunsets, rays must bend upward at roughly the earth's own curvature, a radius of order 6,400 km, i.e. a transverse acceleration c^2/R = 1.4 x 10^10 m/s^2 [calc]; that is a sag of 1.25 m over LIGO's 4 km arm [calc] with no such deviation reported [memory, medium]. Worse, upward-bending rays make distant objects appear lower (that is how the page explains the lowering sun, ship hulls and horizon dip), which is the same sinking the zetetic Bedford observations deny. Claims 1 and 3 therefore use opposite light-physics.

b. Experiment. Sun and moon distances are measured independently of any shape assumption by radar ranging, lunar laser ranging and parallax (reflecting arrays since 1969; AU by radar since 1961) [memory, high; not in folder]. Total solar eclipses show the moon's shadow of about 100 mi width crossing the earth [memory, high]. Lady Blount's one observational test of straight versus curved light (the tilt of the moon's illuminated limb, 29 Oct 1904) is a standard perspective effect of a great-circle terminator on the sky [read: Blount-Smith deep read, 9]. Hewitson's diary records a neutral hearer of Rowbotham's 1866 Preston lecture calling him "honest & intelligent & ingenious" [read: research note]; that is a character note, not evidence on the sun.

c. Tested? Rowbotham gave no triangulation figures; the Blount-Smith pamphlet gives none either [read]. The experiments that would show it (simultaneous sun-elevation at three stations) have been done since Eratosthenes with the result in my table.

d. What would change? Every measure of astronomical distance, the Doppler/aberration geometry, the heat budget is NOT an objection: a 32-mile disc at 3,000 mi and 5,772 K gives sigma T^4 (r/H)^2 of about 1.8 kW/m^2, close to the measured 1.36 kW/m^2 [calc; corrected per arbiter section 1, which found the earlier remark wrong as stated].

Verdicts (claim 3). - Perspective sunset over a plane with a 3,000-mile sun: Refuted by calculation. The elevation never reaches the horizon; one height cannot fit multiple latitudes. - Curved-light (EA) replacement: Not testable as stated (undefined constant, "not valid for short-range"), and where it can be tested (bending sign vs Bedford claims; rate needed for sunset) it contradicts claim 1 and local laser/optical experience. - Two-vortex ether currents carrying the sun (1904): Historically superseded but instructive: a patch to cover the southern sky, with qualitative support only.

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Claim 4. Gravity is not a pull from the earth's mass; the earth accelerates "upward" at 9.8 m/s^2

a. Mathematics. The Universal Acceleration (UA) page asserts a constant 1 g upward acceleration for the earth and "the observable universe", resting on the equivalence principle: locally, an accelerating frame and a gravitational field cannot be told apart [read: UA deep read, 2]. Taken seriously with special relativity, which the page invokes: at/c after one year is 1.03, so v = 0.72 c; after 10 years 0.995 c; after 6,000 years gamma = 6,194 and v/c = 1 - 1.3 x 10^-8 [calc]. The kinetic energy of the earth would then be (gamma - 1) M c^2 = 3.3 x 10^45 J [calc], roughly 5 x 10^7 times the sun's total output over the same period (7.2 x 10^37 J; 1.2 x 10^34 J is one year's output) [calc; corrected per arbiter section 4 item 2], with no source (the page says "dark energy" or a "Davis plane" of exotic matter, "in progress"). The page shifts between UA and a Davis model (infinite plane, finite attractive g, consistent with Gauss's law), which are different physics. The page's three-line relativity argument (constant 1 g in the earth's frame, decreasing for an inertial observer) is textbook constant-proper-acceleration, but it never names the inertial observer [read].

b. Experiment. The decisive differences from gravity are in gradients. A rigid uniformly accelerating frame has proper acceleration a(h) = g/(1 + g h/c^2), so the vertical gradient is -g^2/c^2 = -1.07 x 10^-15 s^-2 [calc, Rindler frame; [memory, high]]. The measured free-air gradient of gravity is about -3.09 x 10^-6 s^-2 (g falls by 3.09 microm/s^2 per metre) [memory, high; consistent with 2g/R = 3.08 x 10^-6 s^-2 [calc]], about 3 x 10^9 times larger. Gravimeters (and tower, aircraft and satellite measurements) see it. UA also gives no Cavendish attraction between lead spheres (the page lists the Cavendish experiment as "inconsistent short-range attraction" with no argument [read]), no tides except by re-adding gravity ("Celestial Gravitation") [read], no variation of g with latitude (9.78 m/s^2 equator, 9.83 pole [memory, high]), and no Kepler's third law for artificial satellites: a GPS orbit of semi-major axis 26,560 km has period 11.97 h from T = 2 pi sqrt(a^3/GM) [calc], as observed [memory, high]. Eotvos-type tests of equivalence (10^-9 to 10^-13) test that equivalence, which both UA and gravity assume; they do not decide between them, and the TFES page cites none [read].

c. Tested? Gravity has been measured at every scale. UA has no measurement in the folder; the page cites no experiments. Blount and Smith (1904) replace gravity with ether currents and electric/magnetic circulation, but offer no field strengths; their arguments against Newton rely on the 1692 Bentley letter and misread arithmetic [read: Blount-Smith deep read, 8-9].

d. What would change? General relativity's treatment of gravity as spacetime curvature (UA borrows its equivalence principle), geodesy, celestial mechanics, satellite navigation.

Verdicts (claim 4). - UA as the origin of weight on a flat earth: Refuted by calculation (gradient 10^-15 vs 3 x 10^-6 s^-2; energy 10^45 J; Kepler's law for satellites). - Ether-current gravity (1904): Not testable as stated; no quantitative form. - The negative claim "Newtonian/relativistic gravity requires a spherical earth": the Davis-plane variant (uniform field of an infinite plane, 2 pi G sigma) is internally consistent with Gauss's law, but predicts zero vertical gradient: Tested, not supported by the measured gradient.

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Claim 5. The earth's shape is concealed by agencies, whose own documents show it

a. Mathematics. The "documents say flat earth" sub-claim is a reading problem. The deep reads show: NASA TM X-2514 (1972) states four times that the method is "limited ... to application where a flat, nonrotating earth may be assumed", and "this assumption limits the analysis to short-range, short-duration flights"; the same report counts the omitted earth rotation as 0.25 deg/min uncertainty (that is 15.04 deg/h, the sidereal rate) and says rotation "will cause readings on the gyro" [read: TM X-2514 deep read, sections 2-4]. Over its 9-second window the omitted term is about 0.04 deg against a 1-2 deg gyro error [calc]; over 10 km a tangent plane is off by d^2/(2R) = 7.85 m, 78 m at 30 km [calc]. NASA CR-4568 (1993) uses a spherical, nonrotating earth with inverse-square gravity; the "flat" case is the epsilon = 0 term of a perturbation expansion in epsilon = h_s/r_e, solved analytically; even there the range angle uses r_e (theta-dot = V cos(gamma)/r_e) [read: CR-4568 deep read]. The PTTI 2007 paper tried a plane troposphere and rejected it as "too large", adopting Niell's mapping function (a spherical-shell model with refraction) [read: PTTI deep read]. WGS 84's four defining parameters (a = 6,378,137 m, 1/f = 298.257223563, GM, omega) make a rotating oblate ellipsoid; the TFES WGS 84 page quotes no WGS 84 or GPS interface text and its central claim that WGS 84 "requires a flat coordinate system" is unsupported by its own quotations (projections are for mapping, GPS solves in 3-D Cartesian coordinates) [read: WGS84 deep read, 2-3; NGA deep read]. Lead Stories and AAP fact-checks quote NASA the same way [read: claims.md].

b. Consistency with experiment / independent checks. Dubay's flight-time items depend on an unspecified flat map; with the usual polar-centred map, Santiago to Sydney is 15,974 mi, Johannesburg to Perth 11,415 mi, Cape Town to Buenos Aires 10,725 mi, against globe great-circle distances 7,046, 5,164 and 4,276 mi [calc]. Non-stop Santiago-Sydney flights take about 13.5 to 15 hours [web: https://www.flightsfrom.com/SCL-SYD], i.e. a ground speed near 500 mph over 7,000 mi, not 16,000 mi, as a flat map would need at 1,100 mph. (Dubay items 43-48 say these routes make detours; I did not check each, but the flight-time test is not about route choice.) Dubay's statements about satellites and the ISS are assertions in the author's voice with no named document or dataset [read: Dubay deep read, section 1 caution].

c. Tested? The "agencies hide the shape" claim is not a tested physical proposition; the specific NASA-phrase claim was checked against the primary text (deep reads) and fails. Independent confirmations that do not rest on NASA: the Piester paper (PTB, NICT, KRISS time laboratories) with a geostationary-satellite link and a Sagnac correction of the order of 100 ns [read]; any ham-radio or GNSS receiver (GPS period 11.97 h [calc]). I did not find, in the folder, an independent (non-agency) satellite-tracking dataset, and I say so.

d. What would change? Not a physics change but a social one: coordinated falsification across national agencies, airlines, shipping, surveyors, amateur radio operators and competing powers.

Verdicts (claim 5, split). - Specific: NASA/Army reports say the earth is flat and nonrotating: Tested, not supported. The phrase is a stated modelling approximation in two reports, a perturbation sub-problem in one, and a rejected model in a fourth. - WGS 84 is a flat-map system: Tested, not supported (definition read in the NGA standard). - General: shape is concealed, space travel faked: Not testable as stated (unfalsifiable as formulated); the specific consequences that can be tested (flight times, satellite orbits, Sagnac corrections) are Tested, not supported.

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Claim 6. Scripture describes a flat, stationary, enclosed earth

a-d. This is a theological and exegetical claim; physics can test only its physical consequences (claims 1-4). The Biblical-literalist motive is explicit throughout the sources (Hampden 1869 contains none of the Bedford wager, correcting an older digest [read: claims.md]; Hampden's 1885 letter: "If this man's experiment on the Bedford canal was founded on fact, then the whole of the Scriptures are false" [read: Wallace deep read, 8]). That quotation is worth keeping: it shows the claim is held independently of the measurement outcome, which is relevant to how the Bedford result was received. Ancient Near-Eastern cosmography with a firmament was a reasonable pre-Greek position [memory, medium]; the sphericity arguments (Aristotle's lunar-eclipse shadow, ship hulls, stars changing with latitude) are ancient [memory, high; Dubay items 114 and 190 are accounts of ancient cosmologies, not evidence].

Verdict (claim 6). The theological content is Not testable as stated by physics. The physical content (dome, fixed flat earth) is Historically superseded but instructive; physical tests are those under claims 1-4.

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3. The Investigator's findings, weighed (kept whatever the verdict)

• Rowbotham, Experimental Proofs (1870): his own account of 5 April 1870 (18 in telescope, turf boat, board 6.5 ft) and his procedural objection that the agreed three equal discs were not used. Physics: his own design is a low sight line, needing k = 0.41 for a globe [calc]. His objection to Wallace's trial design (three equal heights not used, "an oblong flag") is a fair question of procedure; Wallace's own account says the discs and heights were fixed beforehand and both referees saw them [read]. The folder does not hold Rowbotham's telescope power or the weather for the date; that limits the reading.
• Lady Blount, "Collapse of the Globular Theory" (1905): read directly. Camera "less than two feet above the ground-level" (the letter says the telescope was two feet above the water); lens focal length 16-17 ft; a dark chimney midway marked A; 15 ft sheet [web/read]; Clifton's own letter lists "unfavourable" atmospheric conditions and shimmering vapour; his closing sentence concedes "unless rays of light will travel in a curved path". The expected hidden height is 12.1 ft, not "over 20 feet" (Section 2). Photographs themselves are not in the folder (OCR of a reproduction only). A genuine unresolved item is the reflection of the sheet in the water: a mirage-type image can show reflections too; I do not know of an analysis of that photograph [memory, low].
• Hewitson diary, Preston 1866; Clifton's letter; Carpenter's referee report in The Field, 26 March 1870; Walsh's decision: all kept as records of what each party reported. Carpenter, Hampden's referee, signed the sketches showing the pole above the line [read: Wallace deep read]; Walsh's finding "five feet, more or less" [read: sites.md] is close to the expected 5-6 ft. Hampden's later claim "this Mr. Wallace saw with his own eyes" the absence of curvature [read] is a party statement.
• Hampden v. Walsh (1 QBD 189, 1876): wager-law ruling; no finding about the experiment [read: sites.md]. The libel convictions (1871-75), on Wallace's own account in 1905 and the Investigator's newspaper leads (Chelmsford Assizes March 1875 etc.) are history of people, relevant to the "dismissed without testing" question: the experiment was done, under agreed terms, and the dispute then turned to litigation and ad hominem charges on both sides (Hampden's "cheat and swindler" letters; Wallace's own admission of "an ethical lapse" in betting) [read].
• Koreshan Flaming Sword (1897) and Florida State Archives N2009-3: the field notebooks of the survey would be there; not examined. This is the record that would let a reviewer reconstruct the error budget (settling, temperature, tide staff transfers). Absence of such an analysis in 1897-1900: the geodetic establishment seems not to have engaged (the survey's own account says critics "were not brave enough"; elsewhere it says Copernican critics attended a trial) [read]. Competing explanations: (a) critics ignored a small religious colony's work; (b) the work did not meet the standards of geodesy; (c) the data were inaccessible beyond the colony's own book. I cannot decide between them from the folder.
• Voliva press record (AP 1921, TIME 1931/1933; $5,000 standing offer, WCBD radio): a documented public challenge with no recorded successful claimant [read: Schadewald]. Under SOURCE HONESTY: absence of a taker is not evidence of the claim's truth (a challenge that the challenger judges) nor of its falsity; no neutral adjudicator is named.
• Skiba 2017 balloon launch (15 Nov 2017): closes the gap in claims.md: team reports "very slight curve", camera barrel distortion and cloud, result inconclusive; raw footage said to be on the "Explosive Truth" channel (not checked) [read]. Wide-angle lenses (fisheye) make a flat horizon look curved or not depending on where in the frame it sits, so a fisheye/non-fisheye comparison is the right design; the published result is not a measurement. I cannot weigh it beyond "no result".
• Chicago skyline press: ABC57 and the Washington Post call the Michigan photo looming/mirage (fata morgana); a physics expert's explanation (Rennie) is in the folder [read]. The photographer's data and the lake's temperature profile are the missing records.
• Wikipedia/other "related work" (Goudey 1930, "Rectangle" 1899 Zetetic Cosmogony): not read; neither bears on my verdicts. Misattribution of the 1899 book to Rowbotham on the Internet Archive is noted by the Investigator.

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4. What would settle things

• Claim 1: simultaneous reciprocal vertical-angle measurements of k (Hirt's method with lines of 6 to 10 km over water at several hours), plus an equal-height trio. Predicted: s = 6.0 ft x (1 - k) for a globe and -6.0 ft x k for a plane (the ray's curvature; zero only if k = 0), so the test is the 6.0 ft difference at the measured k (corrected 2026-10-10, see arbiter claim 1 and A21).
• Claim 2: ring lasers at several latitudes (including the southern hemisphere), with published raw data: Sagnac frequency proportional to sin(latitude) with a sign flip in the south.
• Claim 3: three simultaneous sun-elevation measurements at known distances on one meridian at an equinox (my table).
• Claim 4: a gravimeter on a tall tower: gradient -3.09 microm/s^2 per m versus -10^-15 s^-2.
• Claim 5: an independent non-agency record of satellite passes (amateur radio, optical).

5. Summary of verdicts

Privacy note: no personal details of the project owner appear here; the README finding aid in the folder is private and was not used as evidence.