Arbiter: Kelly-AG ("The Sagnac Effect and Uniform Motion")

Role: Step 3. I read claims.md, facts.json, the deep read, physicist.md, mathematician.md, contrarian.md, sites.md and research/ notes, re-read Wang et al. 2003 (research/files), and recomputed the numbers on which the reviewers differ (project .venv, NumPy). Tags: [read] document or saved file; [web] URL; [memory] recalled with confidence; [calc] my computation.

Source gap

The project rests on ONE primary document: Kelly_2.pdf, 13 pages, undated, written after 2003 (our PDF copy was made 16 Apr 2011, after Kelly's death on 30 July 2005) [read]. Kelly's other work (IEI Monographs 1, 3, 4; Infinite Energy 2001; Phys. Essays 2000/2003; the 2005 book "Challenging Modern Physics") was not obtained. Statements about those rest on the Investigator's summaries. Monograph 2 (1996) and the 2000 Hafele-Keating page are saved in research/files but were only read for leads. Where I rely on [memory] alone it is marked. Equations garbled in the text layer were checked by algebra, not by page image (all three reviewers did the same); the one affected detail is the "4nA" versus "4 pi n A" slip on p.12, which is probably an extraction garble.

Background for the reader (short)

Sagnac effect: two light beams sent round a closed loop in opposite directions, with source and detector fixed to the loop, arrive at different times if the loop rotates: dt = 4Aomega/c^2 (A enclosed area, omega angular speed in rad/s, c light speed). General form: dt = (2/c^2) times the loop integral of (u . dl), u being the velocity of each bit of the loop and dl a step along the light path. For a rotating rigid loop, Stokes' theorem turns this into 2Aomega. For a rigid loop moving with one constant velocity V, the integral of V . dl round a closed path is V . (integral of dl) = 0, because the path returns to its start. All three reviewers and I agree on this, and it decides claim 1.

Corrections to the numbers (where reviewers differ, recomputed)

Further small errors in the paper that all reviewers agree on: "forty years" for Dufour-Prunier versus cited 1937-42 papers; the Delta t / 2 Delta t labelling on p.12 and the primes t', t'' that change meaning between p.3 and p.12; Kelly's "orbital angle" figures (2.3e-10 degrees for Michelson-Gale; the physicist gets 7e-11) are in any case beside the point (see claim 1 and 4).

Web checks done by the arbiter

• Stedman et al. 1995 abstract: confirmed, "frequency resolution of 1 part in 3 x 10^21" [web: https://opg.optica.org/ao/abstract.cfm?uri=ao-34-24-5375]. Upgrades the physicist's and mathematician's "via search summary".
• Von Laue 1911 first SR description of the Sagnac effect; Harress experiment; Einstein's 1914 rebuttal of Harzer; Langevin 1921/1937 [web: https://en.wikipedia.org/wiki/Sagnac_effect, fetched]. Upgrades the von Laue and Einstein items. Wikipedia is a secondary source. What it says about Einstein is that he "directly rebutted" Harzer's claim; it does not say whether Einstein named Sagnac.
• Wang et al. 2003: the quoted sentences are in the saved paper [read: research/files/wang-2003...pdf, p.2]: the FOG "travelled with the mechanical conveyor and its uniform motion did not cause any phase shift because the FOG is only sensitive to the rotational movement"; fitted slopes 0.03200 (predicted, rad per m^2/s) versus 0.03229 +/- 0.00365 measured. About 11% scatter in slope, as the physicist said.
• Brillet and Hall 1979: rotating-table laser Michelson-Morley test, fractional length change (1.5 +/- 2.5) x 10^-15 [web: https://www.semanticscholar.org/paper/Improved-Laser-Test-of-the-Isotropy-of-Space-Brillet-Hall/477a2c6f8bc16410f63b7386e6d87c978d6a78bf, search summary]. Upgrades the physicist's [memory, medium] for the claim 5 verdict. It limits anisotropy of the speed of light in the laboratory frame; it is a test of the claim in its local-measurement form.
• NOT web-checked (still [memory]): Post, Rev. Mod. Phys. 39, 475 (1967) stating that a Sagnac device in pure translation gives no shift (the passage is quoted by Kelly on p.9 [read], so the point does not depend on my memory of Post); Alvager et al. 1964 pion-decay source-independence test [memory, medium]; GPS Sagnac correction of order 100 ns [memory, high]; Hafele-Keating confirmations by later experiments [memory, medium]; stellar aberration objection to "light follows the Earth" [memory, medium]. The final verdicts below do not turn on any of these alone.

Corrected claim list

(Revised after QE: see the "QE revision" section at the end, which changes some labels below. Where the two differ, the QE revision governs.)

Claims 1-6 of claims.md stand as statements of what the paper says, with these corrections: claim 4's "better than 1 part in 10^20" should read "frequency resolution" (and is Kelly's wording, not a test of the formula); claim 3's "about 13 m/s" holds at 1 m radius only; claim 1 should say that the paper's own formula gives zero for rigid translation.

Claim 1. The Sagnac effect applies equally to bodies in uniform straight-line motion

Agreement: all three reviewers split it the same way. Weak form (a segment of moving medium, with co-moving source and detector inside a closed loop, adds 2vdl/c^2): supported, predicted by the standard line-integral formula. Strong form (a rigid body or interferometer in uniform translation shows a shift): Refuted by calculation. Disagreement: only on labelling the weak form (physicist: Established; mathematician and contrarian: Tested, supported by one experiment). Stronger argument: the mathematician's and contrarian's labelling is the more careful, because the weak form has one experiment from one group (Wang, Zheng, Yao, Langley, Phys. Lett. A 312, 7, 2003; PRL 93, 143901, 2004) with ~11% slope precision and no independent replication of the conveyor measurement that any of us found. It is predicted by the standard formula, so I treat it as consistent with accepted theory and tested once. Why the strong form fails, with the numbers: Kelly's own p.11-12 result dt = 2D/c^2, D = loop integral of u dl, gives D = 0 for u = V constant. His large-disc argument (pp.9-10) fails: for a fixed small loop on a larger disc at fixed rim speed v, omega = v/R goes to 0 and the shift 4Aomega/c^2 goes to 0; for a full circle at fixed rim speed it grows with R (4pirv/c^2) and does not tend to a translation limit. Worked example (contrarian): a belt loop with two 1 m straight runs moving in opposite directions at 1 m/s adds 2vL/c^2 per run, 4.5e-17 s total; moving the whole belt apparatus at 1 m/s changes nothing. Kelly (p.10) also misdescribes Wang as sending light out and back along a straight line; the experiment used a closed fibre loop and Wang's own text reports a null for translating the whole gyroscope. Kelly's quotation of Post (p.9, "conceptual discontinuity") describes the same zero. Strongest case for Kelly, kept in the record: Wang's zero-area and figure-8 configurations show the shift follows fibre length times speed, not enclosed area, so the area formula Aomega is not the fundamental statement and Kelly's line-integral form (derived without the ether, in the form of his polygon proof) matches it. That is a real and interesting result (the contrarian's "anomaly-flavoured experiment"), but Wang and co-authors did not claim a conflict with special relativity [read: Wang p.2 and PRL abstract per contrarian]. Open: a hollow-core fibre (vacuum) version of the conveyor test was proposed by Wang et al.; no report found. Kelly's light-at-c-relative-to-the-lab rule applies to vacuum or air paths; in glass the index-independence Wang found is the known Fresnel-drag outcome [memory, medium]. Final verdict (split): weak form: Tested, supported (one group, ~11%, no independent replication found); consistent with accepted theory. Strong form: Refuted by calculation (and the one relevant experiment is a null). What would settle it: (calculation) none needed; (experiment) an independent conveyor run with a hollow-core fibre and a second group, plus a gyroscope on a uniformly moving frame (already routine, null).

Claim 2. Light travels at c relative to the laboratory, independent of source speed; this alone gives the Sagnac result for any path shape

Agreement: the algebra is correct (eqs 1-12, binomial polygon step with second-order terms cancelling, circulation 2omegaA; SymPy by the deep reader and hand checks by all). Both circular derivations are the same equations, so the second is not an independent check. "The correct result proves the assumption" (p.3) is affirming the consequent; special relativity (SR) in an inertial lab uses the same premise and gives the same first-order result and the same lab-frame 4Aomega/(c^2 - v^2). "First general derivation that does not assume an ether" (p.10) is wrong: Post (1967), whom Kelly cites, gives the line-integral form without the ether, and von Laue did the SR derivation in 1911 [web: Wikipedia above]. Disagreement: verdict labels. Physicist: Established, with "laboratory" wording internally inconsistent. Mathematician: formula Established, "proves/differs from SR" Internally inconsistent. Contrarian: narrow form Established, broad form (rules out SR) Not supported because Sagnac data do not discriminate. Which is stronger: they describe different parts of one point. The inference "proves" is a logic error (mathematician, physicist); the broad claim's failing is that it is non-discriminating (contrarian). Both hold. I keep "Internally inconsistent" for the "proves" step and "Not testable as stated" for Sagnac as a discriminator, because the two theories give identical first-order predictions and the second-order difference (relative size v^2/c^2, about 1e-15 at 13 m/s) has never been resolved in a Sagnac apparatus [memory, medium]. The "laboratory" wording issue is real and was kept by all: for Michelson-Gale and ring lasers the laboratory is the spinning Earth; light does not travel at c relative to a rotating lab (that is the Sagnac effect itself). Kelly's successful calculations use Earth's spin relative to a non-rotating Earth-centred frame, which is what Monograph 2 (1996) says: light follows the Earth's orbit and gravity but not its spin [web: Investigator, research/files]. So the project paper's wording is the weaker statement, Monograph 2 the better one. That Earth-centred non-rotating frame is also the frame GPS uses [memory, high]. Final verdict (split): the derived formula and "c in an inertial or non-rotating frame": Established (and not original to Kelly). "The correct result proves the assumption": Internally inconsistent (logical fallacy). "Therefore time and distance are absolute / SR is excluded": Never properly tested in Sagnac terms and not decided by this paper's evidence; the decisive tests (Ives-Stilwell, Kennedy-Thorndike, muon lifetimes, clock flights) lie outside the documents [memory, high for existence]. What would settle it: a second-order test of lab-frame light speed on a rotating apparatus, where Kelly's absolute-time picture and SR differ; existing Michelson-Morley-type results on rotating tables (Brillet and Hall 1979, (1.5 +/- 2.5) x 10^-15 [web]) are the closest record. Kelly's follow-up, which the paper does not give, is the explicit difference he predicts.

Claim 3. SR has no role in the Sagnac effect; the effect appears at rim speeds of about 13 m/s

Agreement: the order-of-magnitude point is correct (first-order Sagnac versus second-order v^2/c^2 SR corrections; at 13 m/s the correction is about 1e-15 [calc: v^2/c^2 = 1.9e-15]). The "13 m/s per metre" scaling is inverted. SR is not a high-speed-only theory; Kelly's p.4 limit v approaching c with "speed 2c" strays into a regime he excludes; the claim that authors "apply gamma in the denominator then the numerator, cancelling" refers to unnamed papers and is not checkable. Disagreement: physicist labels "contradicts SR" Refuted by calculation (SR predicted the effect); mathematician and contrarian label it Not testable as stated (no distinct prediction). Which is stronger: "Not testable as stated" fits better for the weak statement in the paper ("SR has no function"), because Kelly's treatment and SR's lab-frame treatment give the same first-order formula. The physicist's "Refuted" applies only if "contradicts SR" is read as "SR could not predict a Sagnac shift", and that reading is refuted by history (von Laue 1911 [web: Wikipedia], Langevin, Post). I adopt a split that keeps both. Hafele-Keating critique (Kelly 2000, from the USNO 1971 report): per-clock readings East -196/-54/+166/-97 ns, West +413/-44/+101/+26 ns against published averages -59 and +273 ns [web: Investigator, research/files/kelly-2000...htm]. These raw numbers are kept in the record. They were not checked against the USNO report by any reviewer. The scatter among individual clocks is as large as the effect, a legitimate observation about that experiment's statistics. It is a separate claim (about SR's clock predictions) from the Sagnac formula, and later flights and GPS are independent tests [memory, medium; not web-checked]. Final verdict (split): "The effect is first order and needs no relativistic correction": Established. "SR has no role / Sagnac contradicts SR": Not testable as stated in the Sagnac setting (identical predictions); if read as "SR cannot treat the effect", Refuted by the historical record (von Laue 1911). What would settle it: a second-order Sagnac measurement (relative 1e-15 at tens of m/s, or v^2/c^2 terms in a fast rotor) distinguishing 4Aw/(c^2 - v^2) with or without the rim-clock factor sqrt(1 - v^2/c^2).

Claim 4. Michelson-Gale 1925 is an ordinary Sagnac test (projected area, sin latitude); ring lasers confirm the formula to better than 1 part in 10^20

Agreement: the projection argument is correct and well explained; 0.236 reproduced by all; the measured mean 0.230 (spread +0.55 to -0.05) is honestly reported by Kelly; Marett, an amateur experimenter with no commercial stake, recomputes 0.2364 versus 0.230 +/- 0.005 [web: http://www.conspiracyoflight.com/Michelson-Gale/Michelson-Gale.html, via Investigator]. The "10^20" is a frequency resolution (web-confirmed above). Other defects (agreed): Earth-spin fringe of a 1 m disc (see table), 4250 km, ring-laser lock-in story misapplied to Sagnac's passive interferometer, and the "orbital angle" argument (pp.9-10) is a category error: whether a frame is non-rotating is decided by its rotation rate against local gyroscopes or light loops (Earth spin 7.3e-5 rad/s, orbital rate about 2e-7 rad/s [memory, high]), not by the angle swept relative to the Sun. Disagreement: none on the main verdict. Mathematician calls the "10^20" and "1e-5" sub-claims Refuted by calculation; the physicist and contrarian call them misstatements. The numbers are indeed wrong, so I accept "Refuted by calculation" for the two figures only. Final verdict (split): Michelson-Gale and ring lasers as ordinary Sagnac tests with the sin(latitude) projection: Established (tested and replicated many times, by ring lasers and fibre gyros). "Novel" label: incorrect (Michelson-Gale's own analysis already used the normal component of Earth's rotation). "1 part in 10^20 accuracy of the formula": Refuted by calculation / misreading of a resolution. "Earth-spin 1e-5 fringe for 1 m disc": Refuted by calculation (about 1e-6). "Orbital-angle argument that the lab is as inertial as the geocentre": Internally inconsistent. What would settle it: nothing remains open on the formula; the interpretive point (rotation relative to local inertial frames, versus relative to an Earth-centred absolute frame) is not settled by Sagnac data, which fit both (Marett's preferred-frame reading and the mainstream reading are experimentally equivalent here).

Claim 5. Light does not travel at c relative to a moving disc on straight segments; so Sagnac, Harress and Pogany contradict constancy of light speed in the moving frame

Agreement: Kelly's c +/- v is correct as coordinate speed in a rotating description (also contained in SR and GR treatments). The inference from a closed-loop time difference, measured with one clock at one place, to the one-way speed on one straight segment does not follow, because one-way speed depends on how distant clocks are synchronised and that cannot be made consistent round a rotating loop (the Sagnac time gap itself). The straight segment on a disc is not inertial (centripetal acceleration v^2/r), so Einstein's polygon-clock argument (p.8) is about second-order clock rates, not first-order synchronisation. Disagreement: physicist "Refuted by calculation" for the contradiction; mathematician "Not testable as stated / misreads SR's domain, second order Never properly tested"; contrarian "Not testable as stated". Which is stronger: the contrarian's and mathematician's. A convention-dependent one-way speed has no experiment that can refute it, so "Refuted by calculation" over-reaches; the thing that is wrong is the inference. Where SR claims something measurable, local isotropy of c, the rotating-table laser tests (Brillet and Hall 1979, limit about 2.5e-15 [web: Semantic Scholar link above]) agree with SR. I note that no independent one-way light-speed test with independent clocks on a disc is on record in the documents. Final verdict (split): observation that a rotating observer's coordinate light speed is c +/- omega*r: Established. "Therefore the experiments contradict SR": Not testable as stated (a logical overreach from a round-trip difference); the local-isotropy form is Tested, not supported (rotating-table laser tests agree with SR). What would settle it: a direct one-way speed test is limited by synchronisation convention. The decisive discriminating experiments are the second-order ones listed under claim 2.

Claim 6. Einstein never mentioned the Sagnac or Michelson-Gale tests, though they bear on the speed of light

Agreement: not a physics claim. Kelly's phrasing is "This author has located no reference by Einstein", a report of his own search with no stated method. The quotations: Silberstein (1921) speaks only up to 1921 (Michelson-Gale is 1925) and did not name the Sagnac test in the quoted line [read: p.4]; Turner (1979), edited by Hazelett, collects Ives's relativity-critical papers (the characterisation of a source with a stake on one side) [memory, medium]. Counter-evidence: Einstein published rebuttals of Harzer's reanalysis of Harress's rotating-prism experiment in Astronomische Nachrichten 199 (1914) [web: https://en.wikipedia.org/wiki/Sagnac_effect; bibliographic record https://onlinelibrary.wiley.com/doi/10.1002/asna.19141990104 per contrarian]. Harress's experiment is classed today as a Sagnac-type rotating-ring experiment. Whether Einstein ever wrote the names Sagnac or Michelson-Gale remains unverified. Von Laue (1911) and Langevin dealt with the effect within SR [web: Wikipedia above]. Disagreement: labels only (physicist: Not testable; partly contradicted historically; mathematician: Never properly tested for the narrow form; contrarian: unresolved on the literal names). Final verdict: as physics, Not testable as stated (an authorial silence cannot support or refute a theory). As history, split: the narrow form (Einstein never named Sagnac or Michelson-Gale) is unverified, with no counter-example found; the broad form (Einstein ignored rotating-interferometer experiments) is contradicted by the 1914 Harress notes. What would settle it: a search of the Collected Papers of Albert Einstein index and correspondence for "Sagnac" and "Michelson-Gale".

Summary table

What would settle it (short list)

1. Strong form of claim 1: already settled by the calculation; a hollow-core-fibre conveyor run and an independent group would extend the weak form.
2. Claims 2, 3, 5 (absolute time versus SR): second-order tests on rotating apparatus; the existing rotating-table laser tests (Brillet and Hall, 2.5e-15) and Ives-Stilwell-type tests are where Kelly's picture and SR differ, not Sagnac.
3. Claim 6: an index search of Einstein's collected papers and correspondence.
4. Hafele-Keating raw numbers: compare Kelly's per-clock figures with the USNO 1971 report (Proc. 3rd PTTI Meeting, pp.261-288) and with later independent clock-flight data.
5. Reception: the 1996 Irish Times letters (Irish Times archive) and the Infinite Energy 2001 paper, to see what critics actually argued.

Open questions

• Dating: when was the project paper written and where (if anywhere) published? The PDF is a 2011 copy of an undated text; Kelly died in 2005.
• Which frame does Kelly mean by "the laboratory"? The project paper and Monograph 2 differ; the claim 4 explanation needs the Earth-centred non-spinning frame.
• Does the Hafele-Keating scatter Kelly reports survive a reading of the USNO report, and how does it compare with later flights?
• Is there a second experiment, by an independent group, of Wang's moving-fibre result, and what does a vacuum (hollow-core) version show?
• What exactly did the 1996 Irish Times correspondents argue, and was Kelly's offer of a public debate declined, ignored, or never relayed? Only one sympathetic source (Cowan's memoriam, GED 16(6), 2005; Natural Philosophy wiki) reports it; the letters are not located.
• Vigier (Phys. Lett. A 234, 75, 1997) built a photon-mass reading of Sagnac citing Kelly's 1995 monograph; full text not opened. A professional physicist took the analysis seriously; this is not endorsement of the anti-SR conclusion.

Absence-of-evidence analysis

Where the record goes dark: 1. Kelly's own later output stops with his death on 30 July 2005 [web: Irish Times obituary, Investigator]. This is expected. The undated project paper surfaced as a PDF copy in 2011, and no publication venue is known. 2. The 1996 Irish Times debate: a months-long letters controversy and an unaccepted debate offer are documented in one published, sympathetic source (Cowan's memoriam; Natural Philosophy wiki). The letters themselves were not found (the archive is subscription; not tried). The newspaper's own 2005 obituary independently says Kelly provoked "much academic debate, some of it acrimonious" [web: https://www.irishtimes.com/news/pioneering-engineer-who-helped-transform-the-esb-1.482657]. Competing explanations for the missing record of the dispute: (a) ordinary: letters pages are unindexed and the archive is behind a paywall; (b) the opposing arguments were routine textbook replies (rotation versus translation; SR predicts Sagnac) and so left no separate trace; (c) Kelly's challenge was posed to a lay forum where experts did not engage in kind; (d) suppression of publication. Evidence for (a), (b): the substance of the standard reply is in the literature (von Laue 1911, Post 1967). Evidence for (c): the debate offer "never taken up" as reported by Cowan (sympathetic, single source). Evidence for (d): none found; Kelly published in Infinite Energy, Galilean Electrodynamics, Physics Essays, the IEI monographs and, per Vigier, in Phys. Lett. A through a citing author. What would decide: the 1996 Irish Times letters, IEI minutes and any referee correspondence. 3. No published refutation of Kelly's specific claims by name was found, and no experiment was run to test his distinctive claims (absolute time, Earth-frame light). That silence is real but weak: the Sagnac data that he relies on were accepted long before him, and the discriminating tests (second order) were done by others on other grounds. It is "never tested by him or about him", not "tested and failed" in the Sagnac setting, and the mainstream response was mostly that his first-order results are already in SR. 4. Kelly's companies (HDS Energy; Top Tech Ireland) leave no trace in the Investigator's search except the Google Patents siphon family DE1528915A1 (1965 priority). The contrarian judges this a normal pattern for a retired engineer. I agree on the present evidence: no sign of suppression, absorption or classification, and nothing shows publication was blocked. Company-register searches (Irish CRO) remain unreached (sites.md "Not yet tried") and would decide between commercial dormancy and any other reading. 5. The Hafele-Keating critique appears only on a website copy and as a single 2000 paper from Kelly; no response from Hafele or Keating was found. Whether a rebuttal exists is unknown.

QE revision

Trigger: qe.md verdict MINOR (2026-10-04). Inputs: qe.md; the three new QE deep reads appended to deep/Kelly-2-1a1021.md (pp.6-8, pp.9-10, pp.10-12; page images p.6, p.7, p.8, p.12 were rendered by the deep reader); two new web checks by me. Tags as above. Net effect: no central verdict changes direction. Four labels change (claim 1 weak form, claim 2 summary row, claim 4 orbital-angle, and the Wang wording), and four items of Kelly's evidence and argument that the first pass omitted are now in the record and weighed.

Web checks added (2 of the 8 budgeted for the QE round)

• Michelson 1913, "Effect of Reflection from a Moving Mirror on the Velocity of Light", Astrophys. J. 37, 190-193: the search record says he tested the emission (ballistic) theory, which predicts c + 2v for light reflected from a mirror moving at v, and concluded that "within the limit of error of experiment (say 2 per cent), the velocity of a moving mirror is without influence on the velocity of light reflected from its surface" [web: https://en.wikisource.org/wiki/Effect_of_Reflection_from_a_Moving_Mirror_on_the_Velocity_of_Light, search result summary; I did not open the full text]. This upgrades QE's [memory, medium] and the deep reader's [memory, low]. It matches Kelly's "accuracy 1:50".
• Saburi: a search for a Japanese Sagnac or ring-laser paper by Saburi found nothing identifying Kelly's "Saburi (0.9 m)" [web: search, no useful hit]. It stays unidentified (the deep read agrees: no reference number, no year, no result quoted).

1. Michelson 1913 rotating-mirror test (new in the record; bears on claim 2)

What Kelly says [read: page image p.7, deep read B]: light beams bounced off mirrors rotating at 1800 rpm; he says Michelson "proved from the resulting fringe shift" that (1) light does not bounce like a tennis ball off a moving racquet, (2) light does not take up the mirror's movement, (3) "the light actually ignores the whole rotating apparatus. It moves solely with respect to the laboratory". He calls it "a clear confirmation" and gives the accuracy as 1:50. He adds that Michelson made a factor-of-2 error that was cancelled by an omission of similar size, "uncovered by a colleague who has been corresponding with this author". Kelly gives no layout, no shift size and no definition of 1:50. The factor-of-2 statement is documented in one source, Kelly's report of private correspondence; no document or calculation for it is given and none was found. It is recorded as Kelly's report, with no second source. Weighing: the web record shows what the experiment tested: the dependence of reflected light speed on mirror speed, against the emission theory, to about 2% [web, above]. Conclusions (1) and (2) follow from that and are accepted physics; special relativity (SR) makes the same prediction because it also takes light speed to be independent of the source's motion. Conclusion (3) goes further than that experiment. An experiment on reflection from a moving mirror does not establish that light "moves solely with respect to the laboratory" for a Sagnac loop with a co-rotating source and detector, and it cannot tell "c relative to the lab" from SR's "c in every inertial frame". Strongest case for Kelly: it is a real experimental result, directly on source-independence, and he cites it correctly as confirming that half of his premise. It is consistent with claim 2, and does not discriminate. Effect on verdicts: none beyond claim 2's label (below). Michelson 1913 is a supporting experiment for the source-independence part of claim 2: Established as an experimental result (about 2%); non-discriminating between Kelly and SR.

2. Ring-laser standing-wave argument (new; bears on claim 2 and the "small scale" qualifier)

What Kelly says [read: page image p.7]: in a circular ring laser the standing waves "stay stationary in relation to the laboratory" (cites Martin; text says 1996, reference list says IEEE Spectrum 1986); when the ring rotates the nodes pass an observation post at a rate proportional to the rotation rate, and for a square or triangle the rate differs from that for a circle; "This phenomenon is further confirmation of the proposal in this paper, that light, in small scale experiments, travels relative to the laboratory (Anderson, 1986)" (Scientific American 254, 86-91). The attribution to Martin covers only the first statement; the "confirmation" sentence reads as Kelly's inference with a citation attached [deep read C3]. Weighing: the picture that the standing wave is fixed in space (inertial) while the ring turns under it is the usual textbook account of the ring-laser beat [memory, medium; not web-checked]. It is the same non-discriminating situation as claim 2: the standing wave is fixed relative to a non-rotating frame, which is the "non-rotating Earth-centred frame" reading already adopted in the claim 2 section above. The qualifier "in small scale experiments" is Kelly's, appears once, is not defined and is not derived anywhere in the paper. It sits awkwardly with the M-G pipes (0.207 km^2, which Kelly counts as success) and with the paper's headline. I record it as an unexplained qualification of claim 2: the paper does not say what scale separates "light travels relative to the laboratory" from anything else. Formula check: the page image confirms df = 4Aomega/(lambda*P) (the text layer lost omega and lambda) [read: page image p.7]. Kelly's omega is "the angular rotation of the earth", without sin(latitude) here; for his Bilger square (0.75 m^2, P = 3.46 m, 632.8 nm assumed [memory, medium-low], 43.5 deg) the deep reader gets 69 Hz with the sine and 100 Hz without [calc by deep reader, not rerun by me]. Kelly gives no measured beat. Other p.7 points kept: Macek and Davis (1963) accuracy "1 in 10^12"; his "twelve orders of magnitude improvement on M-G" cannot be reconciled with the figures printed beside it; the 277,000 area ratio checks (0.207 km^2 / 0.75 m^2 = 276,000). The lock-in passage (Sagnac's 1913 result seen only thanks to vibration; a steady apparatus would have given zero) is Kelly's assertion with no source; lock-in belongs to active ring lasers, and Sagnac's was a passive interferometer [memory, medium], so the passage is not shown to apply to Sagnac's setup. It is kept in the record as an unsupported claim by Kelly, not as refuted.

3. Einstein quotations and the "selective quotation" charge (new; bears on claims 3, 5 and 6)

Kelly's argument [read: page image p.8]: Einstein (1905) extended the clock-slowing result to polygonal and closed curved paths ("the travelled clock ... will be 1/2 t v^2/c^2 second slow"); Einstein (1916) later wrote that "special" means restriction to uniform translation; Einstein (1919): "The rotating observer notes very well that of his two equivalent clocks, that placed on the circumference runs slower than that placed at the centre." He concludes that "authors can selectively quote Einstein's writings, whenever there is a seemingly insurmountable difficulty with SR theory", and that many references wrongly say SR cannot be applied to circular motion, "but Einstein applied that theory to those situations in the basic paper on SR". Weighing, fairly to both sides: - Kelly is right that Einstein 1905 gave the closed-path clock result and applied the lab-frame SR clock-slowing to curved paths; that is also what the clock-flight analyses use, and SR does treat accelerated motion as seen from an inertial frame. The "SR cannot be applied to rotation" statement, as a blanket statement, is therefore wrong, and the reviewers already say so (SR handles rotation as seen from an inertial frame). - The 1916 sentence is a definition of "special" (which frames are equivalent), not a withdrawal of 1905. "Changed his mind" is Kelly's interpretation [deep read D2]. The 1919 quotation has no reference in Kelly's list and could not be traced; it is recorded as unverified, not as false. - The charge cuts both ways: Kelly himself quotes the 1905 passage with an ellipsis and omitted words. I record this as an observation, not as a verdict on his honesty. No author is named in the charge, so it cannot be checked. - Relation to claim 6: it supports the 1914 Harress notes (Einstein did address rotating-apparatus experiments) as a counter-example to the broad form of claim 6. - The 1905 passage and Kelly's use of it also bears on claim 3: if the 1905 SR clock-slowing applies to a clock on the rim, then SR does have a (second-order) role, as the physicist said, and Kelly's item 5 on p.12 ("Time and distance aboard a spinning disc are identical with time and distance in the stationary laboratory") contradicts his own use of Post's dilation factor on p.10 [deep read B4]. That is an internal tension in the paper, new in the record. It does not change the claim 3 label ("Not testable as stated" for "SR has no role", since the first-order predictions coincide); it sharpens the reason.

4. Harress and Pogany (p.8)

Kelly gives no results for either [deep read E]: Harress (ten prisms round a disc; thesis, Jena, 1911, unpublished per Kelly's own reference) and Pogany (a square path; reference list has 1926 and 1928 papers, text says 1928). His inference, that light on straight polygonal segments of a moving disc "does not travel at c relative to the moving disc", rests on the same closed-loop-to-one-way step already ruled on in claim 5. The prisms are glass, a refracting medium; later re-analyses discussed dragging [memory, medium-low, not checked]. No change to claim 5.

5. Orbital-angle / GPS-consistency argument (pp.9-10): label change for claim 4

Kelly's own words [read: p.9]: "The non-rotating centre of the earth is acceptable by adherents of the theory of SR as a suitable place to set up a satisfactory Inertial Frame ... But the surface of the earth (the laboratory in this case) is not considered as an Inertial Frame for the Bilger et al. test ... Pretending that SR does not apply to rotation, while at the same time applying it daily to experiments like the Global Positioning System ... is indefensible ... a very biased selection of what is termed an 'Inertial Frame'." He supports it with a table of "orbital angles" swept by the Earth's centre during each experiment. Reply: the accusation of inconsistency has a fair core and is stated here beside the ruling. Mainstream treatment does use an Earth-centred non-rotating frame for GPS and does treat the Sagnac term as the correction for the rotation of the Earth-fixed frame, so it does not say "SR cannot touch rotation"; the Sagnac term is applied in GPS as a known correction [memory, high for existence]. But Kelly's way of choosing a frame is wrong by calculation: a frame is non-rotating or not according to its rotation rate against local gyroscopes or light loops (Earth spin 7.3e-5 rad/s, orbit about 2e-7 rad/s [memory, high]), not according to the angle swept in the transit time. The quantities he compares are angles, not rates, and mix a 40-hour flight with light transits of nanoseconds [deep read p.9-10, section B note and I.9]. Number checks from the new deep read [calc by deep reader; I recomputed the Bilger ratio only]: Hafele-Keating 1.6 deg orbital angle in 40 h: correct (1.64). GPS 2.9e-6 deg: not reproduced (1.5e-6 for one circuit, 3.05e-6 for a round trip). M-G 2.3e-10 deg: not reproduced (7.2e-11). Bilger 1.66e-13: "turned on its axis" is a wording slip, the figure is an orbital angle (1.3e-13 by their count, 26% high). Sagnac 2.8e-13: not reproduced (4.5e-14). The printed ratio "5 x 10^6" (GPS to Bilger) conflicts with his own figures (2.9e-6 / 1.66e-13 = 1.7e7) and with the 1e7 ratio (GPS to Sagnac) on the same page, which would make Bilger twice Sagnac when his figures make it 0.59 times. The 8,750,000 m disc diameter does not match 43 deg 29' S (about 9,245 km). The qualitative ordering (the GPS and clock-flight "angles" are millions to trillions of times larger) survives these slips. Label change (QE P3): "Internally inconsistent" for the argument itself was a stretch, as QE says: the argument does not contradict itself, it compares the wrong quantity. New verdict: the orbital-angle argument: Refuted by calculation (compare rotation rates, which the very interferometers in question measure). The ratio "5 x 10^6": Internally inconsistent with Kelly's own printed figures (this narrow sub-claim keeps that label). The wider charge that the frame choice is applied unevenly: Not testable as stated as phrased (no author named), and answered by the rate criterion above.

6. Other label and wording corrections from QE

• Claim 1 weak form (QE P1): "Tested, supported" is not on the Step 2 scale. On the scale, the weak form is predicted by accepted theory and was measured once, in agreement within the stated precision. Verdict: Established, qualified: one experiment, one group (Wang, Zheng, Yao, Langley, Phys. Lett. A 312, 7, 2003), slope 0.03229 +/- 0.00365 against the predicted 0.03200 (about 11% scatter), no independent replication found. The qualification stays attached everywhere the label is used.
• Wang's ride-along gyroscope (QE A1): Wang et al. state that the fibre-optic gyroscope (FOG) "travelled with the mechanical conveyor and its uniform motion did not cause any phase shift because the FOG is only sensitive to the rotational movement" [read: research/files/wang-2003..., p.2]. That is a design statement with a stated reason, not a separately reported null measurement. The wording in the claim 1 section ("the one relevant experiment is a null", "Wang's own text reports a null for translating the whole gyroscope") is corrected to: "Wang et al. state that the FOG's own uniform motion produced no phase shift, which is what the line integral predicts." The strong-form verdict stays Refuted by calculation: it rests on Kelly's own formula (D = 0 for constant u) and on Post's quoted statement, not on the Wang statement. Corollary for the primer: the FOG translates with the conveyor; it does not go round the loop. Kelly's own description of Wang ("light beam sent out on a straight line on a moving platform and reversed", and "that defence is now shown to be groundless") is a three-sentence account with no numbers [read: p.10]; the experiment used a moving fibre segment inside a closed fibre loop. The claim that the "rotation defence" is groundless rests on this one paper.
• Claim 2 label (QE P2): the body said "Not testable as stated", while the verdict line and summary table said "Never properly tested". One label is kept: for "therefore SR is excluded", Not testable as stated in Sagnac terms, because the two theories give identical first-order predictions. The wider question is not left untested: the second-order and isotropy tests exist elsewhere (Ives-Stilwell, Kennedy-Thorndike, Brillet and Hall [web]).
• Stedman et al. 1995 (QE spot check 7): my web check was of Stedman, Li and Bilger, Applied Optics 34, 5375, a companion paper by the same group and instrument. Kelly's cited sources are Bilger et al., IEEE Trans. Instrum. Meas. 42, 407 (1993) and 44, 468 (1995) [read: p.13]. I did not open those. The conclusion (the figure is a frequency resolution, not the accuracy of the Sagnac formula) rests on the companion paper's abstract and is probably right for Kelly's source too; I flag it as the same group, not the same paper.
• Vigier (QE A2): in the absence-of-evidence analysis, "published in Phys. Lett. A through a citing author" is corrected. Kelly did not publish in Phys. Lett. A. Vigier did (Phys. Lett. A 234, 75, 1997), and cites Kelly's 1995 monograph [full text not opened]. Kelly's own outlets remain Infinite Energy, Galilean Electrodynamics, Physics Essays and the IEI monographs.
• "4nA" (QE S2): resolved from the page image of p.12 by the deep reader: the printed text is "D = 2 omega A = 4 pi n A" and "2 Delta t = 2D/c^2 = 8 pi n A / c^2" [read: page image p.12]. The garble is in the text layer, not in Kelly's printing. My "probably an extraction garble" in the Source gap note is now confirmed. The Delta t versus 2 Delta t bookkeeping contradiction is in the printed page, as the reviewers said. Note also the printed denominator "3 x 10^-18" on p.6 (should be 10^+18, a sign slip; 4.37e-16 s is right).
• Sagnac area (new detail): the deep read gives the fringe from each Kelly area at 436 nm and 2 rev/s [calc by deep reader; wavelength and 866 cm^2 are [memory, medium], not web-checked by me]: 666 cm^2 gives 0.051 with reversal; 866 cm^2 gives 0.067; 0.86 m^2 gives 0.66. Only 866 cm^2 matches the roughly 0.07 fringe of standard accounts. 0.86 m^2 exceeds the whole 50 cm disc (0.196 m^2) by 4.4 times, so p.1 cannot be right as printed. This agrees with the table above.
• "First general derivation without an ether" (p.10-11): hedged by Kelly ("As far as could be ascertained"), with no literature search shown. General-circuit derivations without an ether exist (von Laue 1911 [web: Wikipedia, above]; Post 1967, Kelly's own reference [2], which he quotes). The deep read also notes that Kelly's own text admits the result is the same as for an ether at rest in the lab; what is new is the labelling of the assumption, not the mathematics. Verdict unchanged (claim 2).
• Gamma-cancelling charge (p.10): Kelly names no publication; it is his description of unnamed authors and an interested position. Not checkable; kept as his statement. The size argument (dilation is second order, Sagnac first order) is correct arithmetic; chaining Post's two remarks gives dilation about (v/c)^2 of the Sagnac effect, about 1e-17 at Sagnac's rim speed [calc by deep reader].
• Saburi: unreferenced and unidentified (no hit on the web). The "M-G (600m)" figure fits only the long side of the 2010 ft x 1113 ft rectangle (about 613 m x 339 m).
• Doppler point (p.12 item 3): Kelly says a lab observer sees a negligible Doppler effect and Sagnac's on-board camera saw none; consistent with the Post figures he quotes (Doppler is v/c of the effect, about 1e-9 fringe at Sagnac's speeds [calc by deep reader]). No change.
• Retention items R4 (QE): Kelly's own Faraday/unipolar-induction work (IEI Monographs 5 and 6, 1998; research/files) and Essen's 1977 Hafele-Keating critique (Creation Research Society Quarterly 14, 46, cited by Kelly 2000; in the contrarian's review) are the inventor's own experimental work and an earlier critique he built on. They are peripheral to Sagnac and not weighed here; they stay in the record for the primer's reading list, and the Hafele-Keating raw numbers section above stands unchanged.

Verdict changes (summary)

What the QE round leaves open

• Michelson 1913 full text, to check Kelly's three conclusions and the claimed factor-of-2 errors (Kelly's correspondent is unnamed).
• Whether the 1919 Einstein quotation exists as quoted (no reference given).
• The CCDS (1980) and ITU (1990) statements on the Earth-centred inertial frame, cited second hand by Kelly.
• Everything in the earlier "What would settle it" and "Open questions" lists is unchanged.