Flat-Earth: Arbiter (Step 3)

Inputs read: claims.md, physicist.md, mathematician.md, contrarian.md, sites.md (index and leads), facts.json and deep reads as cited by the reviewers, the Michelson-Gale deep read (re-read for the set count). Tags: [read] from a project document or a reviewer's quoted reading of it, [web] with URL, [memory] with confidence, [calc] my own arithmetic (numpy, project venv; script in /tmp, not kept).

Source gap: none for the claims themselves. Caveats that carry into the verdicts: Rowbotham 1865/1881, the 1893-97 Zetetic Review and most NASA reports were deep-read only in part; five NASA/PTTI reports were read in depth, about a dozen others from digests and phrase search only; Skiba's videos are auto-captions; the Clifton negative, Oldham's full paper, Koreshan field notebooks and the Skiba balloon footage are not held. Where a verdict leans on [memory] alone (stellar aberration and parallax, lunar and radar ranging, free-air gravity gradient, Michelson-Morley null) I say so; none of these is in the folder.

Overall result in one paragraph: all three reviewers agree on every central verdict except the labelling of three sub-claims (section 3). The one genuinely open empirical question is small and narrow: how large the refraction coefficient k was on the days of the low-sight-line Bedford-type sightings. It was never measured. The strongest flat-earth claim (zero curvature) fails against the one pre-agreed, both-sides-signed equal-height test (Wallace 1870) and its repeat (Oldham 1900-01), and against calculations from the model's own geometry (southern distances, sun elevations). That the "open" question exists does not rescue the strong form.

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1. Recomputations where reviewers differed or I could check cheaply [calc]

R = 3958.8 mi. Hidden height = (d - d_e)^2 / (2R(1-k)) with d_e = sqrt(2R h_eye/(1-k)). k is the refraction coefficient (k = 0 straight ray).

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2. Claim by claim

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

Where they agree. Rowbotham's "8 in x miles squared" is the correct small-angle drop (d^2/2R); his own arithmetic is mostly right (11 ft 8 in, 10 ft 2 in, 14 ft, 40 in); the three real slips are Whitby 102 (112), Lower Farn 67 (21.7) and the Grimsby refraction step, plus Mont Fréjus 52 (should be 42.7 ft). Recurring faults: treating "level" as "straight"; applying the refraction allowance to the wrong quantity; treating computed lighthouse ranges (Findlay) as observations; mixing the tangent drop with the chord sagitta (Carpenter, Dubay); omitting the target's own horizon (Dubay items 78-79). Wallace's equal-height design is robust to uniform refraction, because uniform refraction scales both offsets by (1 - k) and leaves the 1:2 ratio. [QE revision 9.1b adds the inventor's own rebuttal of the design and my answer to it.] Carpenter's "equal steps down means a straight line" is a mathematical error. Single-ended low-sight-line sightings need k = 0.4 to 0.92 on a globe, which lies inside Hirt et al.'s measured range near the ground (-4 to +16 over grass at 1.8 m; +1 to +18 about 5 m above water in work they cite) but far above the textbook 0.13. Nobody measured k on the days of any historic Bedford, Clifton or Chicago sighting.

Where they differ. 1. Label for the low-sight-line sightings. Physicist: "Established as an observation, and as an effect of refraction". Mathematician: "Never properly tested for the alternative (k unmeasured)". Contrarian: "Never properly tested". I side with the mathematician and contrarian on the second half: that the visibility is refraction is a plausible and physically possible explanation, supported by the mainstream press and optics experts quoted in the folder and by Clifton's own "aqueous shimmering vapour", but in no run was k measured, so it was never tested. The observation that distant objects are sometimes seen beyond the geometric horizon is Established, and every party (including the meteorologist and optics expert quoted by the Skiba material) concedes it. 2. Whether a flat earth with a definite metric is "Refuted by calculation". Only the mathematician says so. I accept it, restricted: it applies to a flat model whose distances are given, for example the north-centred azimuthal map used by the Flat Earth Society. Southern distances come out 2.1 to 2.6 times too long, and scheduled flight times on those routes agree with the globe. It does not apply to a model with no stated metric, nor to the concave variant. This is a calculation on the model's own map against measured distances and times; flight times are data, so one could also call it tested, and I record both. The result does not depend on any refraction argument. 3. Wallace 1870 as a measurement. The physicist and mathematician lean on "5 ft" as an umpire's finding. Precisely: Wallace gives no instrument reading of the offset; he gives sketches signed by both sides' referees and a predicted 5 ft 8 in, "perhaps about five feet" after refraction. [QE revision, section 9.1a: this sentence was too strong. Wallace's 2 April 1870 letter derives "about 5 1/2 ft" at the middle signal and "22 ft in all" at the far one from the sketches, and the signed sketch itself can be scaled against its own 4-ft disc spacing; I get about 6 ft. The offset is a readable number, though from a woodcut of a rough sketch.] The "five feet, more or less" is the umpire's printed decision in The Field (26 March 1870) [web: https://people.wku.edu/charles.smith/wallace/zCarpenter1870Field1.pdf, via the Investigator]; the umpire (Walsh) was the stakeholder, and Hampden's later characterisation of him as Wallace's nominee is contested: Hampden had authorised him in writing (Epsilon WCP5561) [web: https://epsilon.ac.uk/view/wallace/letters/WCP5561]. Carpenter, Hampden's referee, signed the sketches "under protest", objecting that the large telescope was not levelled and had no cross-hair, but did not dispute what the sketch showed. Hampden declined to look. So the evidence is: sketches signed by opposing referees, an umpire's decision, a winner's account 35 years later. Weighed, it still favours curvature, but it is not a numerical measurement and uniformity of refraction over the six miles was assumed, not measured. 4. Oldham. All agree it is a 23-line abstract ("about six feet") with no heights, weather or photographs. It confirms the design's outcome; it cannot be audited.

Arbiter's weighing. The flat-earth case here is a set of true observations plus an interpretation. The curvature side's best evidence is the Wallace/Oldham ratio test; the flat side's best point is the fair one that refraction was invoked, not measured (the Blount-Smith retort "they can blow both hot and cold" is a legitimate logical point). The weakest part is Rowbotham's quantitative layer (lighthouses, datum arguments), which has demonstrable errors, all in one direction. The 1838 observation also exists in two versions by one author (3 ft flag, observer in the water, 1865; 5 ft flag, 1881), and Rowbotham's own 1872 preface calls some first-edition evidence "not entirely satisfactory" [read: 1881 p.v]. That candour is to his credit and is kept in the record.

Final verdicts, claim 1 (split). - Strong form: the earth's water surface is a plane over miles, so the earth is not a globe of about 25,000 miles circumference: Tested, not supported (Wallace 1870, Oldham 1900-01; with the stated caveat that refraction was not measured in either). - Flat earth with a definite metric (north-centred map): Refuted by calculation (southern distances x2.1 to x2.6; flight times). - Low-sight-line sightings as proof of flatness (Rowbotham 1838/1870, Clifton 1904, Nab): the observation is Established; that they exclude curvature is Never properly tested (not dismissed without testing: several tests were run; what was never tested is k). Required k = 0.4 to 0.92 is physically possible over calm water in an inversion but unmeasured. - Rowbotham's lighthouse table, datum and Mont Fréjus arguments as quantitative proofs: Refuted by calculation (arithmetic errors, computed ranges read as observations); the datum/levelling argument also Internally inconsistent. - Koreshan concave earth (1897): Never properly tested (single interested-party run; quadratic shape is real in its data, exponent 2.09 over 1 to 4 1/8 mi; a constant 0.12 arcsec per-step bias would produce the same curve; last 1.6 mi optical; no control baseline; no independent replication). It contradicts the flat model. - TFES "dismissed without testing": does not hold for Bedford (a pre-agreed test was run). The contrarian's separate point stands: the academic non-replies to Carpenter's challenge (Gilman, Baird, Proctor's postscript) were dismissal without engagement, not tested-and-failed.

What would settle it. Repeat Wallace's equal-height trio over the Old Bedford/Hundred Foot stretch at three heights, with simultaneous temperature profiles at two or more heights (Hirt eq. 2 gives k from dT/dz) and reciprocal vertical angles from both ends, in calm and breezy conditions and at several hours. Prediction: sagitta 6.0 ft x (1 - k) on a globe; on a plane, -k x 6.0 ft (the ray's own curvature; zero only if k = 0). Both fall by 6.0 ft per unit of k, so the discriminating test is the 6.0 ft difference between them at the k measured on the day (corrected 2026-10-10 per A21 and primer section 9 item 2; a plane with k about -1, light bending upward, reproduces Wallace's result, so k must be measured independently). A Rectilineator control run along an independently surveyed baseline would test the Koreshan bias.

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Claim 2. The earth is stationary

Agreement. MGP: prediction 0.236, observed 0.230 +/- 0.005, 269 readings, all 13 set means positive within 0.04 of 0.23; TFES's +0.26 mean and "-0.04 to +0.55" are Correa's single-reading figures, not the paper. Foucault: 15.04 deg/h x sin(latitude); the TFES page offers no rate, only real launch and wire artefacts. Ring lasers: the TFES page misreads the Brillouin caption ("twice the Earth rate" is a +15 to -15 deg/h difference between N and S orientation; E-W near zero is the correct pattern), and gives no mechanism for a Sagnac split with the right latitude and orientation dependence. Airy 1871: a moving earth with Fresnel drag (1 - 1/n^2 = 0.43 for water) predicts a null; the page's premise is wrong. Michelson-Morley does not by itself select rest. Coriolis: the page's own sources (Reich, Shapiro, Trefethen, firing-table H) show demonstrations.

Differences. 1. Orbit/Airy. The mathematician says "Refuted by calculation (as inference)"; the physicist and contrarian say Tested, not supported. These are about different objects. As an inference (Airy and Michelson-Morley prove rest) the argument fails on its premise, a calculation: Refuted by calculation. As a physical claim (the earth does not orbit), aberration, parallax and Doppler speak against it: Tested, not supported, but those tests are [memory, high] and not in the folder (Bradley 1728, Bessel 1838); the sources do not address them. I keep both labels, with that caveat. 2. Reframing. All three say that "earth at rest, heavens rotating daily" is kinematically equivalent for local rotation measurements (Sagnac, Foucault). I checked the physicist's [memory, medium] note on Thirring: Thirring (1918) found Coriolis-type dragging inside a slowly rotating mass shell, centrifugal-type forces were contested for decades, and the result was not accepted as fully vindicating Mach [web: https://arxiv.org/pdf/0905.0765; https://isidore.co/misc/Physics%20papers%20and%20books/Zotero/storage/A6CRVCRA/Pfister%20-%202007%20-%20On%20the%20history%20of%20the%20so-called%20Lense-Thirring%20eff.pdf, search summary, originals not read by me]. So the qualified statement holds: locally the equivalence is respectable, globally it requires a rotating cosmos that no flat-earth source models, and stars at light-year distances would then move faster than light (physicist's arithmetic, 3.1e-4 ly/s, checks as order of magnitude). Verdict Not testable as stated for the pure kinematic reframing. 3. Trefethen 1965. Citation confirmed by all three (Nature 207, 1084-1085); a secondary mailing-list post says Sydney water drained clockwise [web: search of 2026-10-10 returned https://www.desy.de/user/projects/Physics/General/bathtub.html and https://link.springer.com/article/10.1038/2071084a0]. I did not read the paper. State the outcome as "reported in secondary sources". 4. Knodel/Campanella ring-gyro press report. A documentary-press report (Earth.com, Kottke) that two flat-earth proponents measured a signal of "15 degrees per hour" with a commercial laser gyroscope, which is the sidereal Earth rate. Single-source press evidence, no instrument record held. It is kept: it reports a detection by people who expected a null. 5. South Pole pendulum anecdote ("twice what is expected"): a single station-trivia page, no data or cause. (Correction 2026-10-10, A21: the same page, the 2001 build by Town, Bird and Baker, gives a final result: period 24 h +/- 50 min, clockwise seen from above, i.e. the predicted rate; 'no data' was wrong [web https://www.southpolestation.com/trivia/00s/southpolefoucault.html via Q21; saved work/themes/research/pages/southpolefoucault.html].) Kept in the record as unresolved anecdote of an uncontrolled build; the pendulum literature does not show doubled rates in controlled work [memory, high; not in folder].

Final verdicts, claim 2. - Earth does not rotate (relative to the local inertial frame): Tested, not supported (MGP 0.230 vs 0.236; Foucault law; ring-laser beat 348.6 Hz and sin(latitude) dependence). - Earth does not orbit: Tested, not supported ([memory, high] for aberration/parallax; not in folder). Airy and Michelson-Morley as proofs of rest: Refuted by calculation (as inferences). - Earth at rest as a coordinate choice: Not testable as stated. - "Coriolis never demonstrated": Tested, not supported. - "19 mi/s, 1,000 mph are absurd": Not testable as stated (argument from incredulity; speed is frame-dependent).

What would settle it. Ring-laser rates at several latitudes in both hemispheres with raw data published: proportional to sin(latitude), sign flip in the south, against zero for a rotating flat disc. A thread-released Foucault pendulum at two latitudes. Not obtained: Knodel's instrument data; firing-table (Table H) values set against stated dispersion.

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Claim 3. Sun and moon small and near; sunset by perspective or curved light

Agreement. On a plane, a sun at height H has elevation arctan(H/d); it never reaches the horizon, and its angular size would shrink as sin(elevation) (0.61 deg overhead to 0.11 deg at 10 deg elevation), which is not observed. One H cannot fit the equinox elevations at several latitudes (3,938 mi from 7.2 deg, 3,109 mi from 45 deg, 2,394 mi from 60 deg; the movement's own 1893 table gives 3,585, 3,105, 2,390). The 1904 figure-8 and two-vortex model was a patch for the southern sky; Blount-Smith's speed arithmetic has slips; moon-limb tilt is ordinary perspective of the terminator. The Electromagnetic Acceleration (EA) formula y = (3/4)(beta x^4/c^2)^(1/3) is dimensionally consistent for beta an acceleration but has no value of beta and no derivation; making a sunset needs beta of order c^2/R = 1.4e10 m/s^2; and upward-bending light would lower distant objects, the opposite of what claim 1 needs.

Difference. Only the physicist attached a heat-budget objection; it is wrong as stated (section 1). The remaining independent evidence (radar and laser ranging, eclipses, parallax) is [memory, high] and not in the folder; it is not needed to reach the verdicts below, because the model fails on its own geometry.

Verdicts, claim 3. - Sunset by perspective over a plane, sun about 32 mi across at 3,000 to 7,000 mi: Refuted by calculation. - Sun and moon sizes and heights as measured quantities: Tested, not supported (equal-latitude elevation table inconsistent by the movement's own data; southern observations). - Curved-light (EA) replacement: Not testable as stated until beta is fixed; where it can be tested it conflicts with claim 1's direction of bending. - Two-vortex ether currents carrying the sun (1904): Historically superseded but instructive. - A friend's "moon less than 300 miles" Theodolite-app triangulation (Skiba FEIC 2019, second-hand): Never properly tested (no angles, no baseline, unpublished).

Settle. Three simultaneous noon sun-elevation measurements along a meridian at an equinox; the reader can do it from published almanac data.

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Claim 4. Gravity is not a pull from the earth's mass

Agreement. The equivalence principle is local and textbook; the UA page uses it as global proof. Rindler gradient 1.07e-15 s^-2 vs measured free-air 3.09e-6 s^-2 (x2.9e9); no latitude dependence of g (NGA normal gravity 9.7803 at the equator, 9.8322 at the pole [read: NGA deep read]); satellite orbits (GPS period 11.97 h from Kepler's third law) unexplained; tides require a separate "Celestial Gravitation" that restores a pull; the "Davis plane" is used both as an explanation and as an alternative (and for an infinite plane gives zero gradient). Ether-current gravity (Blount-Smith 1904) has no equations; Newton's Bentley letter is accurately quoted.

Difference. Physicist: "Refuted by calculation" for UA (including the energy budget). Mathematician: "Tested, not supported" with an Internally inconsistent component. Contrarian: Not testable as stated locally, Tested, not supported non-locally. I rule: the decisive item is a measurement (the gradient, the latitude variation, orbits), so Tested, not supported; the energy budget is not decisive because UA never defines the inertial frame in which the energy is counted (and my correction shrinks it to about 5e7 times the sun's 6,000-year output). [QE revision 9.4: the gradient is now also a [read] measurement, Airy 1856.] The statement "UA is locally indistinguishable from gravity" is correct and Established as the equivalence principle. As a complete model the page is partly Internally inconsistent (Davis plane both ways; tides). The contrarian's gentler "Not testable as stated" for the local part is accepted for the local statement only.

Verdicts, claim 4. - UA as the origin of weight on a flat earth: Tested, not supported (gradient, latitude, tides, satellite orbits), with Internally inconsistent components as written. - Davis-plane variant: Tested, not supported (zero gradient). - Local equivalence of acceleration and a uniform field: Established (not in dispute). - Ether-current gravity (1904): Not testable as stated; Newton's discomfort with action at a distance is Historically superseded but instructive.

Settle. Gravimeter readings at two heights 100 m apart: about 31 milligal (3.1e-4 m/s^2) for gravity; about 1e-13 m/s^2 for a uniformly accelerating rigid frame. Any commercial gravimeter and a tall building do it.

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Claim 5. Agencies conceal the shape and their documents show it

Agreement. Five documents read in depth: NASA TM X-2514 (1972) uses "flat, nonrotating earth" as a stated limit ("limits the analysis to short-range, short-duration flights"), counts omitted rotation as 0.25 deg/min (15.04 deg/h) and says earth rotation causes gyro readings; the omitted terms are about 0.04 deg over 9 s and 7.8 m of plane error at 10 km, 78 m at 30 km. NASA CR-4568 (1993) uses a spherical nonrotating earth; "flat" is the epsilon = 0 term of an expansion and "deviated significantly". PTTI 2007: a plane troposphere rejected as "too large". The TFES WGS 84 page quotes no WGS 84 definition; its own quotations call the earth an ellipsoid; the NGA standard defines a rotating oblate ellipsoid (a = 6,378,137 m, 1/f = 298.257223563, omega = 7.292115e-5 rad/s). Lead Stories and AAP quote NASA, an interested party, but agree with the primary text. Dubay's institutional claims name no record. Skiba's own conclusion in 2016: "I cannot prove any conspiracy at work here".

Caveat all three share. The Reddit/Steemit list names about 17 documents; five were read in depth, the others by digest and phrase search. A sixth misreading is not excluded, and no reviewer found a real counter-example. This limit is recorded. [QE revision 9.5: the count was wrong. The Reddit list has 32 items and the Steemit list 15 (largely overlapping); the folder holds 22 of the reports, 5 deep-read and 17 checked by phrase search and digest; ten listed items are not in the folder. QE scanned every NASA/ARL/PTTI digest for "flat", "nonrotating" and "rotating": each hit is a stated simplifying assumption, none a counter-example.]

Verdicts, claim 5 (split). - "NASA/Army documents state a flat, nonrotating earth as a description": Tested, not supported (checked against the primary text, five documents; the plane is a stated, quantified local approximation). The error budget makes the phrase a calculable modelling choice (reviewers label this "Refuted by calculation"; I use the Step 2 label that matches a reading check). - "WGS 84 is a flat-map system": Tested, not supported; the page is also Internally inconsistent with its own sources. - "Agencies hide the shape and space travel is faked": Not testable as stated. Testable consequences (flight times, satellite periods, Sagnac correction of order 100 ns in the PTTI paper) are Tested, not supported.

Settle. An independent, non-agency record of satellite passes (amateur radio, optical tracking); the remaining unread NASA/Army documents on the list.

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

All agree: theological. Not testable as stated (physical content tested under claims 1 to 5); the physical cosmology of a dome is Historically superseded but instructive. Kept in the record: Hampden 1869 ("round" never applied to the earth), his 1885 remark that if Wallace's experiment was founded on fact "the whole of the Scriptures are false", and Skiba's statement of the order of his reasoning (faith first, test "inconclusive"). These show the physical claims were held independently of the measurement outcome, which bears on how the Bedford result was received on both sides.

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3. Disagreements settled (table)

4. Corrections to earlier documents (for the orchestrator)

1. Contrarian.md, claim 2 (b) and the TFES MGP deep read: "set sizes sum to 263, not 269" is wrong; set 6 is 26 observations (page image), so 220 + 26 + 23 = 269. Correct in the contrarian file; claims.md is already right.
2. Physicist.md, claim 4 (a): "roughly 10^11 times the sun's total output over the same period (1.2e34 J)" is wrong. The sun's output over 6,000 years is 7.2e37 J; the ratio is about 5e7. Fix in the physicist file and any entry that repeats it.
3. Physicist.md, claim 3 (d): the [memory, medium] remark that a 32-mile sun at 3,000 mi cannot supply 1.4 kW/m^2 at 5,700 K is wrong (E ≈ 1.8 kW/m^2 by the angular-size argument). Delete the claim or replace with: the geometry fails; flux is not the objection.
4. Mathematician.md, claim 1.8: Johannesburg-Perth is about 10 h scheduled, not 11 h [web above]; conclusion unchanged.
5. Deep read of the TFES Bedford page: "16.7 ft, not 11 ft" and "8 in x 18.2 = about 15 ft" are wrong (11.7 ft flag top; 12.1 ft Clifton). All three reviewers agree; apply.
6. claims.md claim 1: "Wallace 1870 and Oldham (middle mark about 6 ft above the sight line)": only Oldham says "about six feet". Wallace gives sketches and a prediction of "perhaps about five feet"; the 5 ft figure is the umpire's printed decision. Reword the "8 inches times miles squared" rule as "about 8 inches times the square of the distance beyond the observer's horizon, unless refraction lifts them".
7. claims.md Corrections (Wallace): the pool was £1,000 (two £500 stakes) per The Field, 26 March 1870; Wallace's "£500" is Hampden's share. Add. The TFES statement that a court found Wallace "cheated" is unsupported by Hampden v. Walsh, 1 QBD 189 (wager law only) and by Wallace's own account; "cheat and swindler" are Hampden's words.
8. sites.md leads, "Walsh Wallace's nominee": mark as Hampden's characterisation; Hampden authorised him in writing (WCP5561).
9. sites.md leads, Clifton "not an interested party": he worked for Dallmeyer (a seller of the camera), the zetetic account calls him a "globularist", and his own letter says conditions were "very unfavourable" with shimmering vapour. Two accounts differ on who commissioned the photograph.
10. claims.md claim 2 counter-records ("Knodel gyroscope drift"): say it is a press report by flat-earth proponents of the sidereal rate, single source, no instrument record.
11. Trefethen 1965: the outcome (clockwise in Sydney) rests on a secondary post; paper not read.

12. Rowbotham 1838: two versions (3 ft flag with the observer seated in the water, 1865; 5 ft flag, 1881). Record both.

13. (QE revision) arbiter.md claim 1, difference 3: "Wallace gives no instrument reading of the offset" is too strong; see section 9.1a. Wallace's 2 April 1870 letter derives about 5 1/2 ft (middle signal) and 22 ft (far signal) from the sketches, and the sketch scales to about 6 ft. Also claims.md: "no neutral record of the signed sketches is in the folder" is wrong; The Field of 26 March 1870 (research/files) holds them with both referees' countersignatures.

14. (QE revision) primer.md lines 3 and 262, arbiter.md section 5 (Oldham row): "R. D. Oldham" and "Geological Survey of India context" are wrong; the author is H. Yule Oldham, a Cambridge geographer.
15. (QE revision) physicist.md claim 1 (c): "Naylor ... cited, not held" is wrong; Naylor's August 1894 Bedford repeat is held (Earth Review, pp.216-217 of the PDF). Cite it as "1894 (Naylor, printed about 1896)", not "1870s". Naylor's own globe figure ("21 ft above" the railway bridge) is arithmetically wrong; the consistent figure is 38 ft at k = 0 (section 9.1c).
16. (QE revision) arbiter.md claim 5 caveat and section 7: the "about 17 documents" count; see section 9.5.
17. (QE revision) arbiter.md claim 2, difference 4: the gyroscope was Knodel's; Campanella's separate four-mile light-through-holes test is a different experiment (section 9.1e).
18. (QE revision) the Hottentot letter's "Coulcher: about 20 ft" (Review p.34): not in Coulcher's printed 1870 material; it matches Wallace's "22 ft in all". The "contradiction" with Walsh's "five feet" is a mix-up of the mid-point rise (6 ft) with the far-signal drop (24 ft); both fit one globe (section 9.1a). Carpenter's 1894 remark that the drawings were "unattested" conflicts with The Field, which prints the level-telescope views countersigned by both referees and says Fig. 6 was signed by Carpenter.
19. (QE revision) Rowbotham's Palmerston reading (1881 p.71): Palmerston's 1857 letter itself says the ball keeps its west-to-east motion and the deviations "may in practice turn out to be very small"; Rowbotham's "his Lordship did not allow for" it misreads the letter. Rowbotham's cannon prediction (8,400 ft) is 600 ft/s x 14 s, not 600 mph x 28 s (24,640 ft); the 1865 air-gun (16 s, 5,600 ft) and the 1881 powder cannon (28-30 s, 8,400 ft) are told as one experiment. The 1881 "Experiment 3/4" labels in Chapter III repeat Chapter II's numbers for different experiments.
20. (QE revision) the Harton figure is a net gradient: Airy's 1/19,286 is gravity-with-depth through rock of density 2.5, not the free-air gradient. Any text that quotes it as "the free-air gradient" should say so (section 9.4).

5. Absence of evidence: where the record goes dark

6. What would settle it (summary)

1. Claim 1: Wallace-type equal-height trio with measured k (simultaneous temperature profiles, reciprocal angles); plus a Rectilineator control run for the Koreshan bias.
2. Claim 2: ring laser rates at several latitudes in both hemispheres with raw data; a controlled Foucault run at two latitudes.
3. Claim 3: three simultaneous noon sun-elevations on one meridian at an equinox.
4. Claim 4: gravimeter at two heights 100 m apart (31 milligal versus about 1e-13 m/s^2).
5. Claim 5: independent non-agency satellite-pass record; the remaining unread NASA/Army documents.

7. Open questions

• How large was k on the days of Rowbotham 1838/1870 and Clifton 1904? Inversions over cold, calm water make k = 0.5 to 0.9 possible (Hirt's equation: k = 0.5 needs about +0.05 K/m); nobody measured.
• Is the Koreshan quadratic a real curvature measurement or a repeated tiny instrument bias? The near-identity of the two magnitudes (0.118 arcsec per 12 ft) is not a coincidence a reader should wave away; the 228-ft out-and-back "0.0001 in" closure (if as described) argues against a down-bending bias, the later 0.375 mi return (0.25 in) does not.
• What did the Clifton negative actually show, and was the reflection of the sheet a mirage image?
• What did the South Pole pendulum build do after modification?
• Does the Machian rotating-heavens description, taken seriously with all fictitious forces, reproduce the observed latitude dependence without a separate mechanism? Locally yes (kinematic equivalence); globally nobody has written the model.
• Which of the remaining Reddit-list NASA/Army documents say "flat, nonrotating earth", and in what context? Five of about seventeen were read in depth.

8. Final verdict table

Privacy: no personal details of the project owner appear; the folder's finding aid (private) was not used as evidence.

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9. QE revision (2026-10-10)

Why. qe.md gave MINOR: no verdict likely to change, six experimental records read from digests only, one author misnamed, and the inventor's own rebuttal of the 1870 test missing from the arbiter. Deep reads R1 to R6 have since been done (deep/ files: the Earth Review second read; Rowbotham 1881 Chapters III-V; Koresh and Morrow optical tests; Airy 1856; Rowbotham 1865 sections 2-3 and the moonlight passage; IS-GPS-200N). For R7 I read the saved files in research/files myself (Westlake's two 1870 letters, Carpenter's Field letters 2 and 3, Hampden's Field letter and Weston letter, Chambers's Journal of 30 July 1870, Scientific Opinion of 27 April 1870, Rowbotham's 1870 Experimental Proofs, and, after OCR, The Zetetic of July 1872 and The Field of 26 March 1870 with its figures).

Result in one paragraph. No verdict is reversed. Every claim keeps its split verdict, and most are better evidenced. Four of my own statements were wrong or too strong and are corrected (section 4, items 13 to 20): that the 1870 test recorded no numerical offset; that Oldham was R. D. Oldham; that the gravity gradient was a [memory] item; and that the NASA/PTTI list had "about 17" documents. Two new "Refuted by calculation" lines come from the inventor's own text (the 1881 sun-height and the vertical gun). One new line cuts against the Koreshan optical evidence (the mid-stake test). The one open empirical question, the size of k on the days of the low-sight-line sightings, is still open, and the new records make it larger, not smaller: the Koreshan tests alone add about 20 rows that a globe can accommodate only with k of 0.4 to 1.0 (Naylor adds one at 0.8 to 0.9), and nobody measured k in any of them.

Tags as before. [calc] is my own arithmetic (numpy in the project venv; I re-ran the Koreshan k values, the Coriolis drifts, the Harton ratio and the GPS offset and they match the deep readers). No new web checks were made: nothing below rests on a medium- or low-confidence [memory] fact that a verdict depends on. Where a deep reader marked something [memory, medium] I carry the tag.

9.1 Claim 1 (water level, no curvature)

a. The 1870 sketches do carry a number, and it is the globe's. Corrects difference 3 above. - What the record holds. The Field, 26 March 1870 [read: research/files/wku-zCarpenter1870Field1.pdf], gives all three signals at 13 ft 4 in above the water (a 6 ft by 3 ft oblong on Old Bedford Bridge, a 1-ft red disc on the middle staff, the Welney Bridge signal). The telescope was also at 13 ft 4 in. A second disc stayed on the middle staff 4 ft lower (9 ft 4 in). That second disc is a scale bar: it is drawn 4 ft below the upper one in the same view. Fig. 6 (large telescope, from Welney; "Drawn from rough sketch made on the spot by Mr Coulcher, and signed by Mr Carpenter") therefore shows the angular offset between the middle disc and the far signal in units of 4 ft at 3 miles. - My measurement [calc: pixel measurement on a 400 dpi render of Fig. 6]: the upper disc to the centre of the far signal is about 1.49 disc-spacings, about 5.9 ft at the middle signal's range. A globe predicts (6 - 3)/(2R) = 78 arcsec, which is 6.0 ft at 3 miles for k = 0 and 5.2 ft for k = 0.13. A flat surface predicts zero (equal heights lie on one line through the eye). The sketch's discs are not drawn exactly to scale with their spacing (about 25 percent off), so I put the uncertainty near plus or minus 1.5 ft. The measurement excludes zero, and with that uncertainty it excludes k above about 0.3 for that afternoon (offset = 6.0 (1 - k) ft); it does not fix k more closely. - This number does not depend on the cross-hair, so Carpenter's objection ("it was not levelled") does not touch it. It needs only that the two signals were at equal height, as Walsh's decision, Carpenter's own report and The Field all state. - Wallace's own reading, The Field 2 April 1870 [read: R1 deep read, which quotes the WKU transcription; the same figures appear, unattributed, in Chambers's Journal, 30 July 1870, read directly]: "about 5 1/2 ft. at the middle signal ... equal to 11 ft. if measured at the distant signal", and with the depression below the cross-hair an equal amount "22 ft. in all, leaving less than 2 ft. for refraction". Wallace was the winner and so an interested party, and his 22 ft leans on Carpenter's sketch for the cross-hair part. The mid-point figure agrees with my own scaling of the sketch. - The Hottentot letter's "Coulcher said about 20 ft" (Review p.34) matches Wallace's 22 ft rather than anything of Coulcher's held. Its alleged "contradiction" with Walsh's "five feet, more or less" mixes two quantities: the mid-point rise above the end-to-end chord (6.0 ft at k = 0) and the far signal's drop below the level line (24 ft at k = 0, 20.9 ft at k = 0.13). They differ by a factor of 4 by geometry and fit one globe [calc, R1]. - Rowbotham scaled the Troughton-level view (Field Fig. 7) the same way and found the far signal only about 10 ft and the middle disc about 2 ft below the cross-hair, against 24 and 6 expected [read: Experimental Proofs 1870, pp.10-11]. His scale is the middle staff's 4-ft spacing, but the far signal lies at twice the range, so a given picture distance is worth twice as many feet there; his 10 ft becomes about 20 ft, close to the 21 ft that k = 0.13 gives. My own crude reading of the woodcut gives the middle disc about 2.4 ft and the far signal about 9 ft (mid-scale feet) below the hair, which points to a constant offset of roughly 4 ft in the cross-hair setting. That is consistent with Carpenter's complaint that the cross-hair cannot be trusted and is why I rely on the disc-to-signal separation instead. It is a reading of a rough woodcut, and no verdict rests on it.

b. The inventor's rebuttal of the 1870 test (the omission QE found). Rowbotham's Experimental Proofs (1870) [read: research/files/wku-zParallax1870ExperimentalProofs.pdf, pp.8-12] says the agreed design was three equal discs, one immediately by the telescope. In the event "at the end of six miles instead of a disc an oblong flag was placed; a disc was erected in the middle position only; and nothing whatever was fixed close to the telescope." He concludes "the money was neither won nor lost" and that the stakes should be returned. He adds that spirit-levels have collimation error and that a good theodolite would have been better. B. Chas. Brough made the same case to Wallace in The Zetetic of July 1872 [read: OCR of research/files/tfeslib-The_Zetetic...July_1872.pdf]: the signal "which should have been placed near the telescope was omitted", so the appearances "were necessarily changed". Westlake, Wallace's friend, wrote twice to The Field (2 and 9 April 1870) [read]: his first letter said the stations were not equidistant in Coulcher's diagrams; the second corrected an error and argued that an eye on a straight line sees all its points coincide, so any separation shows curvature. Hampden answered in The Field and the Weston-super-Mare Gazette (16 April 1870) [read]. He had "Mr Wallace's engagements ... in his own handwriting" and refused to read the diagrams as curvature: "A B represents what I assert to be the dead flat of the canal." - Weighing. The procedural point is partly right. The telescope's cross-hair was a poor third point (Carpenter said so at the time and signed "under protest"), and the agreed disc beside the telescope was not set up. The Scientific Opinion text of the wager [read: 27 April 1870] says Wallace had to prove "the convexity and curvature to and fro ... by actual demonstration and measurement" to the satisfaction of Walsh and Carpenter, or of the umpire they might appoint, and Walsh's decision records that Solomons the optician was consulted "at the request of Mr Hampden". Neither fact settles the procedure argument. - But the "lamps" analogy (Rowbotham, Brough) works only if the eye is above the lamps. Here the telescope was at the signals' own height, 13 ft 4 in. On a plane all equal-height signals then lie on one line through the eye and coincide, whatever the tilt of the instrument; a tilt shifts only the cross-hair. The sketches show the middle and far signals separated by about the globe's 78 arcsec. To fake that on a plane needs a height error of about 6 ft at the middle staff, against stated heights of 13 ft 4 in. - Carpenter's argument "equal steps down the field of view mean a straight line" is wrong, and so was Westlake's first claim that the steps were unequal. Equal-height objects on a globe fall below the level line by an angle proportional to distance, so level line, middle signal and far signal are equally spaced (1.30 and 2.61 arcmin at k = 0). A straight sloping surface would put the two signals on one point and leave only the cross-hair displaced. The primer's check question 4 asks exactly this. - Hampden's April 1870 threat to Walsh and Wallace ("I will serve you both with a writ"), his repeat offer of £1000 a side, and his Weston letter ("Either the Bible or science is a lie and a fraud") are kept; see 9.6. - Verdict: strong form stays Tested, not supported. The caveat I gave before (refraction was not measured) stays, but the sketch now supplies a rough measurement that the offset on 5 March 1870 was close to the k = 0 value, which argues against strong looming on that day at 13 ft over 6 miles. That is a different regime from the near-water, low-eye sightings below.

c. Naylor, August 1894 (the flat side's own levelled repeat). [read: deep R1, section 8; Earth Review PDF pp.216-217; printed about 1896.] - Instruments: surveyor's theodolite, Dumpy level, telescopes; four days of weather "unsatisfactory"; no host or other member named; no instrument reading is given in figures. The heights are his: Old Bedford Bridge 17 ft, Welney Bridge 13 ft ("6 miles distant"), the Great Eastern Railway bridge 19 ft to the girder top and 15 ft underneath (from a company letter of 31 August 1894 that he cites and I have not seen), 12 miles from the start. The boat observation was from 2 ft 6 in. - What he reports: with the level fully adjusted Welney Bridge sat "generally a little below the cross hair", and the railway bridge appeared as a dark band above Welney's parapet, with a train making it "more than double its breadth". From the boat the railway bridge was "distinctly seen underneath the arch of Welney Bridge". He reports that before both bubbles were set the bridge's position varied "considerably above" and below the hair, and that "no two positions ever gave the same results". - Recomputed [calc, R1]: on a globe with k = 0 the grazing line over Welney would pass 57 ft above the water at 12 miles, 38 ft above the girder top; at k = 0.13, 32 ft. The girder top shows only if k is at least 0.79, the clear gap beneath it at 0.875. From the boat (eye 2.5 ft) the girder top needs k of about 0.63, the underside about 0.69. Naylor's own globe figure ("21 ft above") is wrong: he subtracted the 96-ft drop from a water-level tangent without the 17-ft eye height, which understates his own case. - Open points that decide how much it counts: the datum for the heights; whether the six and twelve miles are straight and as stated (Rowbotham puts Old Bedford Bridge "at Salter's Lode", Walsh's decision says the six miles run "between Welney Bridge and Welch's Dam", opposite ends of Welney); the weather at the moment; the level readings (a "little below the hair" fits both models, 0.43 arcmin on a plane against 2.4 to 3.0 on a globe, and he says almost imperceptible changes of level moved the picture "very considerably"). His optics claim, that a cross-hair deflects rays so objects can "never be the real" position, is wrong; the cross-hair only marks a direction. - Weighing: this is an interested-party account by a committed zetetic, single-source in the folder, with the only reported sightings that look like the strong zetetic case on a 12-mile path. It is documented and quantified enough to say what k it needs (0.8 to 0.9, which happens in strong inversions), and not enough to decide. Never properly tested (k unmeasured, geometry unverified); it joins the low-sight-line group.

d. The Koreshan optical tests, 1896-97. [read: deep R2; Koresh and Morrow, PDF pp.84-106, read from page images.] Summit canal (25 July 1896), Lake Michigan (16 August), Roby (23 August), Naples beach and bay and the Gulf (January to March 1897). The party is the Koreshan Unity's own staff, unnamed except for a few outside witnesses in Florida (Capt. Gilbert, the Walkers, Hart, Williams, Anderson) whose statements are second-hand in the book and mostly unsigned here. Minimum k that a globe needs, from the deep read's table and my recheck [calc]: - Summit, 5 miles, telescope 6 in, target 29 in (top) and 7 in (bottom): 0.69 and 0.87. Its "reflections of the targets on the water": 0.97. Water to bridge No. 2 at 6.5 miles: 0.98. - Lake Michigan hulls at an estimated 12 miles: 0.90 from a 10-ft pier, 0.97 from the beach; Roby liner at 15 miles or more: 0.99. These distances are the authors' estimates. - Gordon's Pass to Doctor's Pass, 6.5 miles, 12-in telescope, 5-ft target: 0.63. Naples Bay, 4.5 miles, 2-in telescope, target bottom 4.5 in above water: 0.92. Sanibel Light at 34 miles (book): 0.75. - Together about 20 rows need k from 0.36 to 0.99, most between 0.5 and 0.95, against the textbook 0.13 and Hirt et al.'s measured +1 to +18 about 5 m above water (in work they cite) and -4 to +16 over grass at 1.8 m [read: Hirt, as in claim 1 above]. Naked-eye losses and the telescope's recovery of hulls are what one would expect from resolution and haze as well as from refraction: at Summit the targets vanished to the unaided eye at 15 in but the telescope at 6 in saw them, so what hid them from the eye was not geometric [read: R2]. - The mid-stake test (Naples Bay, 5 March 1897) is the one measurement of shape. Taken at face value it needs an apparent sag of about 11 in, so k of about 1.27 on a globe (ducting) [calc]. But the Koreshan model's own 8 in/mi^2 concavity would put the cross-bar about 30 in below the line to the target top, not "in line" [calc: R2]. The reported result fits neither model as stated; the stake height and tide state are ambiguous in the text. Verdict line: as quantitative support for the stated concavity, Tested, not supported; the concave earth as a whole stays Never properly tested. - Retained and stated fairly: the observations were repeated morning and afternoon on 3 March, at several telescope heights, over salt water as well as canals, and the authors invite any surveyor to escort. None records air or water temperature or time of day for Summit and Naples Bay; none shows a different result on a different day. The Gordon Pass to Doctor's Pass and Naples to Sanibel distances may be shorter than stated (about 5 and 26 miles, [memory, medium], not checked by me), which would lower k to about 0.35 and 0.54; no verdict depends on this.

e. Smaller items, all stated as sources give them. - Heliograph, 1894 (Review pp.218-219, via Herald of Glad Tidings and Harper's Weekly): Uncompahgre (14,418 ft) to Mt Ellen (11,410 ft), 183 miles. The zetetic claim is that "nearly 6 miles" of curvature hid the station. The tangent drop at 183 miles is 4.23 miles; the two horizon distances sum to 278 miles, so over a sea-level sphere the peaks see each other; the straight line clears a 7,000-ft plateau by about 230 ft at k = 0 (terrain between not checked) [calc, R1]. Refuted by calculation (the drop-from-sea-level error, with the observer's height omitted). The Harper's caption ("actually hidden ... by the Curvature") is only seen as reproduced. - Boston Stump (290 ft, "visible 40 miles", Answers 1896, Review p.204): the Review charges 1,067 ft of drop as if from sea level; from a 30 to 60 ft masthead the hidden height is about 520 to 740 ft, so the claim depends on the observer's height and k, neither given [calc, R1]. - Roy's pickets (Review p.34, second-hand via a correspondent "Enquirer", citing Trig. Survey vol. 1 p.175, not seen): thirty pickets 100 ft apart looked straight in the afternoon and concave upward in the morning. Over 2,900 ft the earth's own bulge is 0.05 ft, so this is refraction changing between morning and afternoon. This is the documentary source I lacked for "k varies by time of day". It is a reported observation; the original is to be obtained. - Campanella, 2019 (Earth.com on Behind the Curve, press report; single source): two styrofoam sheets four miles apart with holes at the same height; the light was "not visible by Campanella". The sagitta over 4 miles is 2.67 ft at k = 0, so the result depends on the hole height, which the report does not give. A flat-side equal-height test that is reported as supporting curvature, not evaluable beyond that. It is a different experiment from Knodel's gyroscope (corrections item 17). - Stretton, 1905 (Ashby Canal; Wikipedia citing English Mechanic, 20 January 1905; secondary): a theodolite on a cabin roof "showed a dip ... of about eight inches" at one mile, the tangent drop being 8.0 in. A report from the curvature side, secondary; English Mechanic 1905 is a record to obtain. - Plymouth 1864, two accounts: Rowbotham's committee report (Eddystone light invisible from 5 ft at 14 miles, deep read 1865 item 4) and, in Chambers's Journal (30 July 1870), J. N. Hearder's account that a telescope 84 ft up on the Hoe showed "the whole of the Eddystone", but "ten feet above the water's edge nothing could be seen but the lantern" at about 16 miles. The two differ in distance and detail; Hearder's is second-hand through a magazine that took Wallace's side. Neither gives measured heights or k. - Middleton's 1871 plumb-line proposal (Review p.235): posts and wires joined at 90 degrees to plumb-lines, comparing two plumb distances at the ends. Each local step follows the level surface, as spirit levelling does, so on a globe it would also give equal plumb distances; the plumb-lines at the ends differ by 5.2 arcmin and nothing local can check "parallel". As described it cannot tell convex from flat. It was proposed, not run [calc, R1]. It is therefore not a settling test, and I do not add it to section 6. - Rowbotham 1881, Chapter IV (shape and size) [read: deep, Chapters III-V]: the Atlantic cable and time methods give 16,262 mi for a circle at latitude 50 N; the globe gives 16,006 (1.6 percent apart), so these data match a globe and were read as a disc by assuming the plane. The southern circle (23,400 mi) rests on one almanack distance (1,315 nm against 1,165 nm great circle) and a slip of longitude (Adelaide-Sydney taken as 23 degrees; it is 12.6). His radial scale changes by a factor of 2.3 between the northern and southern data, and 52,800 mi should read 32,800. This adds to Refuted by calculation for a flat earth with a stated metric, and it is the inventor's own arithmetic.

f. Overall for claim 1. The split verdicts stand as in section 8. The weight of the flat-side record on refraction is larger than I had counted (Rowbotham 1838-70, Koreshan 1896-97, Clifton 1904, Naylor 1894), and the record of the 1870 sketch is better than I had said. They pull different ways on k: the 13-ft, six-mile equal-height offset points to a k near 0, the low-eye water-level sightings to 0.4 to 1.0. Both can be true if near-surface air differs from air at 13 ft, which is what Hirt's measured profiles allow, but nobody measured it. The settle test in section 2 stays as written; to the paired heights it should add one low-eye run over the same stretch, so the k at 2 ft and at 13 ft are measured together.

9.2 Claim 2 (earth stationary): Rowbotham's own experiments

[read: deep R3 (1881 book pp.62-104) and R6 (1865 PDF 68-80).] - Vertical gun. The 1881 book says a cast-iron cannon fired straight up, ball back "only 8 inches from the gun" after 30 seconds, "the greatest deviation ... less than 2 feet", average time 28 s. No calibre, charge, place, date or witness. The 1865 book has an air-gun, 16 s and "within a few inches", with a 5,600-ft prediction; the 1881 text has a different gun, time and prediction with the "8 inches" and "twice on the mouth" outcomes carried over, and does not say it changed. His predicted 8,400 ft equals 600 ft per second times 14 s; 600 mph over 28 s is 24,640 ft, so the printed prediction is internally wrong by a factor of about 3 [calc, R3]. More basic: his own Fig. 46 grants that a ball dropped from a moving mast keeps the ship's speed, and the same inertia applies to a ball thrown up. In a closed cabin it lands in the hand; the open-air cases he cites involve drag. - The globe's actual prediction is the Coriolis drift: x = Omega cos(phi) g T^3/6 [calc, re-run]: 0.30 m at 16 s, 1.6 m at 28 s, 2.0 m at 30 s at 52 N without drag, about 1.2 m with a modelled round shot. The reported average miss (0.2 m) and maximum (0.6 m) are smaller than that, but a 0.3 m/s breeze alone moves such a ball about 1.4 m and 0.1 degree of barrel tilt several metres, and the report gives no wind or tilt. So the test rules out the 1.5-mile shift that nobody predicted and cannot test the 1 to 2 m shift that the globe does predict. - Spring gun and the Palmerston letter. The spring-gun claim is stated as a certainty with no figures. Palmerston's 20 December 1857 letter [read: p.70-71] does allow for the ball keeping its west-to-east motion and says the deviations "may in practice turn out to be very small"; Rowbotham's "did not allow for" misreads it (corrections item 19). The sideways drift for ranges of a mile is 0.5 to 1.3 m and the east-west range difference about 0.55 percent [calc, R3], so the artillerymen's "no difference observable" at ordinary ranges is compatible with rotation. The outcome of the proposed one-mile-circle firing is not reported. - Grindstone and clouds: a boundary-layer drag demonstration, which supports co-rotation of the air; opposite-moving cloud strata are differences of tens of m/s on top of about 463 m/s, as a rotating globe expects. His own conclusion ("the atmosphere revolves also") is the globe's position. - Star tubes (1865 pp.74-76; 1881 pp.79-87): two parallel tubes a yard apart; a lag between the two knocks is claimed. Two parallel tubes aimed at the same far star see it at the same moment; a lag of 1 s corresponds to a 15 arcsec misalignment [calc]; on his own star distances (1,000 to a few thousand miles) a yard of baseline gives 0.03 to 0.12 arcsec, 2 to 8 ms of transit time, far below an audible signal. The test is differential, so anything common to both tubes, including the actual annual shift, cancels, and the six-month repeat shows only that the tubes did not warp. It cannot detect orbital motion. The parallax values he quotes (Henderson 0.98 arcsec, Bessel about 0.54) are published measurements of the effect he calls absent. "The same meridian time" six months later cannot be sidereal (a star transits about 3.9 minutes earlier each day [memory, high]). - Rowbotham's surface speed at London of 700 ft/s (1865) is low; about 940 ft/s is right for 51 to 52 N [calc]. - The Schoepfer lecture and the pendulum table (Review pp.78-82, reprinted from Scientific American; original not seen): the table's "20,000 vibrations in about 2,000 seconds" implies a period of 0.1 s, a pendulum of a few millimetres, so the printed seconds do not match the premise; the Richer/Cayenne clock is dated 1867 where the well-known observation is 1672 [memory, high], and the printed figures for it are mutually consistent only to about 20 percent. The "1,250 ft per second" equatorial figure is 18 percent below the 1,520 ft/s the earth's size gives. A Fellow of the Royal Astronomical Society's letter (23 October 1896) gives the Foucault precession at 5 degrees latitude as 1.307336 degrees per hour, which is exactly 15 sin 5; it says the pendulum is impractical there, not that the effect is absent. - Skiba's 2015 concessions (QE item 12: he could not refute the Coriolis effect or the lunar eclipse in a "Top 10" list): [read: digest only; not re-read by me]. Kept in the record with that limit. - Verdicts: "Coriolis never demonstrated" stays Tested, not supported. The gun and star-tube experiments as proofs of no rotation or no orbit: Refuted by calculation as inferences, because as set up they cannot discriminate; the report of the gun result itself is unverified and stays in the record. No change to the rotation or orbit verdicts.

9.3 Claim 3 (small near sun and moon)

• Rowbotham's sun-height from London and Brighton [read: deep R3, R6]. 1865: "considerably less than 4,000 miles" with the Ordnance Survey pair London 55 deg 18 min and Ackworth 53 deg 2 min, 151 miles apart. The difference, 2 deg 16 min, is within 3 percent of the globe's 2 deg 11 min for 151 miles (66.6 miles per degree against 69.1) [calc]; his plane height from it is 2,508 miles, and the pair fits a globe about as well as a plane. His second 1865 pair (45 and 38 degrees, 800 miles) does not fit a globe (a globe expects 11.6 degrees for 800 miles), no stations are named, and 800 miles north-south is longer than mainland Britain.
• 1881: 61 and 64 degrees over 50 miles on 13 July 1870 give a sun about 700 miles up. The same inputs give 751 miles by exact trigonometry; the height varies as 1/(altitude difference), so a 1-degree error changes it by a factor of 1.5 to 3. The latitudes of London Bridge (51.5 N) and Brighton (50.8 N) and the sun's declination on that date give noon altitudes of about 60.4 and 61.1 degrees, a difference of 0.69 degrees, not 3 [calc, R3; coordinates and declination formula [memory, high]]. London's 61 is fine, Brighton's 64 is about 3 degrees too high; read consistently, the flat model gives about 3,560 to 3,580 miles. With his 700-mile sun the noon altitude at London would be 19 degrees, against 60 observed. The 1865 and 1881 results by the same method differ by 3 to 4 times, and the book revises its limits ("under 4,000" and "6,000" in 1865, "700" and "1,000" in 1881) without comment. Single source, no observer named. Verdict: Refuted by calculation for the 700-mile figure as printed; the corrected inputs reproduce the "one H cannot fit" result in section 2.
• The movement's own concession. Naylor, "Zetetic Refraction No. III" (Review p.175, c.1895-96) [read: R1]: "it may be freely conceded, that these angles far more nearly correspond with the common theory than with Zeteticism". His escape is that "Zetetic refraction" makes apparent angles "accidental or emperical", not determinable by an a priori rule, which makes the sun-angle question not testable as stated. The direction of bending he assumes is the reverse of the textbook one [memory, high]. G.M.'s equinox-noon challenge (Review p.173) gives implied heights of 3,585, 3,105 and 2,390 miles at 30, 45 and 60 degrees; George Revell's New Zealand letters of 1893 (sun in the north at noon in June, "not more than 30 degrees" on 11 July) match ordinary geometry for about 37 S [calc, [memory, medium] for the latitude]. The editor's reply to Revell's question, that "the light of the sun travels faster in some places than the sun itself", is an editorial characterisation, not an observation.
• Moonlight and heat (Rowbotham 1865 pp.103-107; QE item 16) [read: R6]. The chain is quotations (Lardner, Dickens's periodical, De La Hire, Forbes by Noad) and one cooling report ("Lancet", 14 March 1856, "more than 8 degrees", not located). Full-moon light is about 5e5 times weaker than sunlight [memory, high]; concentrating it 6,000 times gives about 1.2 percent of ordinary sunlight. The "no heating" results are therefore what a moon that reflects sunlight predicts, and they do not distinguish a self-luminous moon. A thermometer under a clear night sky can read below air temperature by radiating to the sky [memory, high], offered as one explanation of the cooling report, not as a verdict on it. "Damp and putrefactive" moonlight has no citation. Skiba's thermometer test (80.9 against 89.6 degrees, shadow warmer; QE item 16) [digest only]. Verdict: moonlight "cold, damp, putrefactive": Not testable as stated for the unsourced assertions; "moonlight cools a thermometer": Never properly tested (one unlocated report, one uncontrolled test, no replication). The moon's being self-luminous is not decided by this evidence.
• Not read in depth (digest only): Faulkner's star-trail analysis (Answers in Genesis, a critic and an interested party), FE101's Indonesian Eratosthenes experiments ("could not get a consistent figure for the Sun's distance"; a critic's site reporting flat-side data). Both are kept in the record and may be weighed by the reader.

9.4 Claim 4 (gravity): two [read] measurements replace [memory]

• Airy, Harton Colliery, 1856 [read: deep R4, PDF pp.35-37, 43-47, 58-60, page images]. Two pendulums, interchanged, 1,256 ft 1 in apart in depth: gravity below to above = 1.00005185 plus or minus 0.00000019 (Airy's probable error, which he says may be doubled but not trebled); a seconds pendulum gains 2.24 s a day below. Mean rock density 2.50 gives a mean density of the earth of 6.566 (6.565 after Stokes's addendum). A uniformly accelerating rigid floor predicts a gradient of g^2/c^2 = 1.07e-15 s^-2, which over 382.9 m is 4.2e-14 of g. The measurement is about 1.2e9 times that, and about 136 standard errors from zero even with Airy's doubled error [calc].
• Caution the deep reader gave and I keep: Airy's number is the net of height and rock. Free-air alone is 2g/R = 3.08e-6 s^-2, which over 383 m is 1.2e-4 of g (Airy's first term); the rock slab subtracts, and the net is 5.2e-5. So the Harton ratio is not "the free-air gradient"; it is a measurement that needs both an inverse-square fall-off with height and a mass-attraction term, and the UA gradient supplies neither. The free-air value itself stays [calc from textbook, not from Airy]. Against the modern mean density 5.51 [memory, high] Harton's excess is about 34 percent larger than predicted; Airy lists temperature, mounting unsteadiness and a rounded rock density as sources of doubt, and the reason for the overshoot is not in the pages read. It is an open point that does not touch the sign or the size of the gradient.
• GPS, IS-GPS-200N (1 August 2022) [read: deep R5, PDF pp.33, 117-118, 125-128; interested party: the US GPS operator, who also issues WGS 84]. Satellite clock rates are offset by "-4.4647E-10" so they appear at 10.23 MHz to a ground observer; the relativistic term uses F = -2 sqrt(mu)/c^2 = -4.442807633e-10 s per sqrt(m) with mu = 3.986005e14 m^3/s^2. I re-ran the check: the potential difference (geoid W0, mu, r = 26,561,750 m) gives +5.2996e-10, the velocity term -0.8349e-10, net +4.4647e-10, equal to the printed number to five digits. W0 is [memory, medium] and r is nominal, so I do not treat this as independent of the issuer. A constant g carried up to orbit height gives 2.20e-9, five times too large [calc]. Kepler's third law with A_REF = 26,559,710 m gives a period of 11.966 h (the physicist's [memory] 11.97 h, now with a [read] value). The document does not say how the offset was verified in orbit; a sceptic may call it a tuned parameter, but the reproduction from first-principles inputs shows it is not free. Independent clock tests (Hafele-Keating 1971, Gravity Probe A 1976, Galileo's eccentric-orbit satellites 2014-15) are [memory, medium] and not in the folder.
• Verdict: UA as the origin of weight: Tested, not supported (unchanged), now with a documented measurement of the gradient and a second, orbit-scale check. The Davis plane, the local equivalence (Established) and ether currents stand as before.

9.5 Claim 5 (agencies)

• Count. The Reddit list has 32 items and the Steemit list 15, largely overlapping; the folder holds 22 reports, 5 read in depth and 17 checked by phrase search and digest; ten listed items (two CIA, NOAA, IRIG 106-17, NAVAIR, seven ARL reports) are not in the folder [read: QE section 4, Reddit and Steemit digests]. QE scanned all 22 digests for "flat", "nonrotating" and "rotating": every hit is a stated simplifying assumption in context [read: QE]. The earlier "about 17" count is replaced. The other ten are a record to obtain.
• IS-GPS-200N contains no "flat" in its 248 pages and no "Sagnac" by name [read: deep R5, whole-document search]. It uses the WGS 84 oblate ellipsoid (R_E = 6,378,137 m, J2 = 0.0010826262), subtracts the earth's rotation rate 7.2921151467e-5 rad/s to give Earth-fixed coordinates, and carries Coriolis and centrifugal terms in the satellite acceleration. The document states a rotating oblate earth plainly; whether that is true is not decidable from the operator's own text, which is why the independent checks (non-US systems, amateur tracking) are the settle test as before.
• TFES Aviation page quotes a 1979 New Scientist letter from the RAF College saying navigators are taught a fixed celestial sphere. That is the standard convention of a celestial sphere for position-finding [memory, high]; I did not read the letter. It does not state a flat or nonrotating earth. Kept in the record.
• Verdicts unchanged.

9.6 Claim 6 and the historical record: what stays in

• Hampden to the Weston-super-Mare Gazette, 16 April 1870 [read]: "Either the Bible or science is a lie and a fraud." Same letter: "The whole of last week was spent in a series of experiments, the fullest particulars of which will shortly be before the world"; that publication is not in the folder (Rowbotham's 1870 turf-boat run is the nearest). He calls Walsh's verdict "scandalously precipitate". In The Field he says "You were nominated by him" of Walsh, which the signed wager text qualifies (the referees named in it are Walsh and Carpenter; the umpire was to be chosen by them), and he adds Coulcher's "oath" to the list he is defying.
• The libel and threat record, kept as pertinent history that cuts against the flat side and recorded as sources give it [read: sites.md, summarising the Investigator]: Stratford magistrates, July 1871 (a week's imprisonment for want of sureties, Daily News, via Epsilon WCP1947); committal, October 1872 (London Standard); Chelmsford Assizes, March 1875 (The Times, 8 March 1875); six months in Chelmsford Gaol (Schadewald; Chelmsford Chronicle, 19 February 1875). The 1876 civil case decided only wager law. People-history, not evidence on the shape of water.
• Records held as leads and not examined (add to section 5): Goudey, Earth Not a Globe (Boston, 1930), and the Winship Zetetic Cosmogony (Durban, 1899, with Port Natal observations). Also the Flaming Sword (January to May 1897) PDFs, Earth no. 51 (OCR: a column on "The Earth's Curvature" repeating the 8-in rule, no new data) and Lady Blount's "Collapse of the Globular Theory" (read: Clifton's letter, quoted in section 5, says the telescope was "two feet above the level of the water" and the day "very unfavourable"). The camera-height wording in Lady Blount's text ("less than two feet above the ground-level") and the letter differ slightly; I follow the letter.

9.7 Verdict changes and additions, in one table

9.8 Still open after this revision

• Whether k was large on the days of the low-sight-line sightings: no measurement exists. A paired low-eye and 13-ft run with simultaneous temperature profiles remains the test.
• Naylor's geometry (distances, straightness, datum, the GER crossing) and any record of the other party members; the Koreshan notebooks and the Summit sketches (mentioned in the book, not reproduced); Harper's Weekly of 20 October 1894 for the heliograph profile; English Mechanic 1904-05; The Field and The Future for any Coulcher figure; Hampden's promised "series of experiments"; the Lancet 14 March 1856 report; the remaining ten NASA/ARL/CIA documents on the lists.
• The reason Harton overshoots the modern density, and the observation series and temperature coefficient on Airy's pages 6-34 and 48-57, which the deep reader did not read.
• Not re-read by me (digest only, as QE records): Skiba's 2015 concessions, Faulkner's star trails, FE101's Eratosthenes report, Schoepfer's source tables.