Thompson-JJ (J. J. Thomson): Arbiter (STEP 3)

Arbiter, 2026-10-09. Inputs read: claims.md, physicist.md, mathematician.md, contrarian.md, sites.md (including "Leads for review"), and the Corpuscular Theory and Conduction page images that decide the Kaufmann table (rendered by me, see claim 2). The three reviews rest on the eight deep/ reads; I did not re-read those, but I recomputed every number on which the reviewers differ. Source tags: [read] project documents, [web] with URL, [memory] with confidence, [calc] my own arithmetic this session (NumPy, scratch directory, not a deliverable).

Source gap note

There is no source gap for the central claims: all eleven documents are primary works by Thomson with a readable text layer (mostly OCR of scans). Three limits that later readers must carry forward:

1. Coverage by digest only: Conduction of Electricity through Gases Chapters I-XX (about 660 pages), Electricity and Matter Chapters I-IV and VI, Corpuscular Theory Chapter I (its deep read was overwritten) and Chapters IV-V, Positive Rays earlier chapters, Vortex Rings Parts I and IV (the kinetic-theory and chemical-combination parts of claim 6), and the textbook. Nothing in this arbiter checks the mathematics of those parts.
2. Not obtained: Thomson's 1897 papers, the 1913 Nature letter (preview only), his 1922 Proc. Roy. Soc. A paper (title and date confirmed, result unread), Kaufmann's original papers, and the Strutt, Merton, Egerton and Allison-Harkins papers. Statements about them rest on the Investigator's bibliography and secondary summaries, and are marked so.
3. Several verdicts lean on [memory, high] facts that no reviewer web-checked: Laue-Friedrich-Knipping 1912, Duane-Hunt 1915, Moseley 1913, the Geiger-Marsden 1909 scattering result, Millikan 1909, Aston's neon-22 (1919) and Ne-22 abundance (about 9%). They are textbook history and I treat them as reliable, but they are not web-cited in this record. A conclusion that rests on [memory] alone is flagged where it occurs.

Corrected claim list

(Corrections to claims.md; the originals stay in the record as the Step 1 wording.)

1. Cathode-ray corpuscles (electrons) are the same from every source, negative, with e/m about 1.7 x 10^7 emu/g (modern 1.759 x 10^7), constituents of atoms, and the emitters in the normal Zeeman effect. Thomson's charge as printed in the 1906-07 books (1.0-1.2 x 10^-20 emu, modern 1.602 x 10^-20) was 25-35% low. QE revision: his own first e/m (1897 deflection) was 7.7 x 10^6, about 2.3 times below the modern value, and his 1898 cloud charge was 6.5 x 10^-10 esu, about 35% above it (see QE revision). The number of corpuscles per atom is a separate claim (4). Priority is shared with Wiechert, Kaufmann and Zeeman-Lorentz.
2. The field of a charge moving slowly adds the inertia m = (2/3) e^2/a (emu); Thomson says the whole inertia of the corpuscle is of this kind, that it rises with speed as Kaufmann's radium data are said to show, that a is about 10^-13 cm, and that mass is "bound ether" carried by Faraday tubes. He states in the same 1906 book (Conduction Art. 355, and the preface of the Corpuscular Theory) that corpuscles cannot carry all of an atom's mass. His table of calculated against observed mass ratios cannot be reproduced from his own model, and the three books do not label its columns alike (QE revision: two of three label 3.09 ... as Kaufmann's, the 1906 Conduction labels it the other way; the question is open until Kaufmann's own table is seen). His equation (1) is printed correctly in Electricity and Matter and misprinted in Conduction.
3. Roentgen rays are thin pulses from a suddenly stopped charge, and make matter conduct by splitting molecules into ions. Thomson and Stokes (1897-98) take the pulse to be non-periodic and of assumed thickness (about a millionth of an inch).
4. The atom is a uniform sphere of positive electricity holding corpuscles in rings; their number is said to be about the atomic weight, "supported" by three counting methods. Correction to claims.md: the three methods do not agree with each other or with that number (see claim 4); the best of them, worked with the modern charge, gives about half the atomic weight, the atomic number.
5. The positive-ray parabola method weighs atoms and molecules; in 1913 it showed a mass-22 line beside neon 20, a mass-3 line which Thomson attributed to a triatomic hydrogen (H3), and helium and neon appearing after cathode-ray bombardment of solids, which he linked to possible disintegration, saying "few will be prepared to accept it until every other explanation has been shown to be untenable".
6. Vortex rings in a perfect fluid interact by computable laws, and (Part IV) a gas of them makes definite predictions about Boyle's law, thermal effusion, molecular speed against temperature and valency. QE revision: the effusion and speed predictions were tested and not supported; see QE revision. Correction to claims.md: n vortices on a circle are linearly stable for n up to 6, neutral at linear order for n = 7 (Thomson's printed "unstable" is a rounding artefact), and linearly unstable from n = 8; nonlinear analysis has since shown the heptagon is stable (see claim 6).
7. Added by QE revision (Corpuscular Theory Ch. I): Thomson also claims that at very low pressure every gas gives the same two positive carriers, e/m about 10^4 and 5 x 10^3, i.e. one and two hydrogen-atom masses. And (Ch. IV, supplementary item) the classical free-corpuscle model of metals needs about 6 cal per degree per cc of silver against 0.6 cal measured, which he states as a contradiction.

Where the reviewers' disagreements were settled by recomputation

Kaufmann table, the three-way difference. [Partly superseded by the QE revision below: the 'resolved' conclusion here was too strong; the e/m-product test supports the Conduction labels only to about 4%, and two of Thomson's three printings label the columns the other way. The recomputed numbers stand.] All three reviewers see that Thomson's two books print the same two columns with opposite labels; the physicist left it unresolved, the mathematician and contrarian favoured the Conduction labelling. I rendered both pages. Conduction p.655 (PDF p.668) prints columns "p' (observed by Kaufmann)" = 3.1, 2.42, 2.0, 1.66, 1.5 and "p (calculated)" = 3.09, 2.43, 2.04, 1.83, 1.65 [read: page image]. The Corpuscular Theory p.33 (PDF p.48) prints the second column "values found by Kaufmann" = 3.09, 2.43, 2.04, 1.83, 1.65 and the third "alpha calculated" = 3.1, 2.42, 2.0, 1.66, 1.5 [read: page image]. The decisive evidence is Kaufmann's own e/m table printed in Conduction (0.63, 0.77, 0.975, 1.17, 1.31 x 10^7): a constant slow-speed e/m times the observed ratio must be constant. Times 3.1, 2.42, 2.0, 1.66, 1.5 it gives 1.95, 1.86, 1.95, 1.94, 1.97; times 3.09, 2.43, 2.04, 1.83, 1.65 it gives 1.95, 1.87, 1.99, 2.14, 2.16 [calc]. The Conduction labelling is therefore favoured by this test [see QE revision: the Electricity and Matter printings agree with the 1907 book, not with Conduction, so 'right' and 'interchanged' are not established]. Consequences, recomputed with c = 3.0 x 10^10 cm/s for the five speeds 2.85, 2.72, 2.59, 2.48, 2.36 x 10^10 [calc]:

Thomson's calculated column is 7.5-13% above his own stated model at every speed, and within 2.5-3.5% of gamma. The observed column is 8-12% above his model at the first three speeds, within 1% of it at the last two, and 3-7% from gamma. So three statements hold together: the rise of mass with speed is real; Thomson's claim "the observed and calculated values do not differ by more than 10 per cent" is true of his tabulated numbers; but the tabulated "calculated" numbers are not the output of the model he describes, and (with scatter of 10% in the data) neither his model, Abraham's, nor gamma is singled out. How he obtained his column is unknown. The mathematician's and contrarian's reading of the swap is confirmed; the contrarian's remark that his calculation is "10% high" at the two lowest speeds is right under this labelling; the Corpuscular Theory deep read's "8-12% above his model at the top three speeds" described the observed column, not his calculation.

Seven vortices. The closed-form spectrum, with growth exponent squared proportional to -k(n-k)[2(n-1) - k(n-k)], gives largest values -4, -8, -12, -9, 0, +32, +80 for n = 3..9 [calc]: n = 7 has an exactly zero root, n = 8 the first positive one. Confirmed (mathematician, deep read).

Barkla count. sigma_T x (2.687 x 10^19 molecules per cc) x 14.4 electrons = 2.57 x 10^-4 per cm [calc], against Barkla's 0.00025 per cc of air: with the modern electron charge the datum is met by 14.4 electrons per air molecule (the sum of the atomic numbers of N2 and O2 mixed in air), not by 25-28 (the atomic weights). Confirmed (physicist, mathematician, contrarian agree).

Energy budget for claim 5. Reviewers gave [memory, medium] values. I web-checked them: S_alpha (the energy needed to take an alpha particle out) is 10.47 MeV for sodium-23 (Audi-Wapstra table, via search result; https://www.nndc.bnl.gov/ensnds/23/Na/23na_a_aP.pdf lists the Na-23 alpha data) and, from the mass excesses of K-39 (-33806.8 keV, https://atom.kaeri.re.kr/cgi-bin/nuclide?nuc=K-39), Cl-35 (-29013.5 keV) and He-4 (2424.9 keV), 7.22 MeV for potassium-39 [web via search summary 2026-10-09; arithmetic [calc]]. A 30 keV electron (beta = 0.33) carries 0.29% of the Na value and 0.42% of the K value; a 100 keV one carries 1% and 1.4%. Energy conservation alone forbids the removal, whatever the mechanism, so the retagged fact [memory, medium] is now [web].

Claim-by-claim

Claim 1. Corpuscles: universal, negative, e/m about 10^7, constituents of atoms, Zeeman emitters

Agreement: all three: mathematics consistent (Zeeman splitting He/m exact; 0.012 nm at 10^4 gauss and 500 nm [calc by physicist]); consistent with all later measurements; replicated many times. Differences: none of substance. The contrarian and physicist note shared priority; the contrarian adds that universality of the emitted particle is not evidence of how many are inside an atom, which I keep for claim 4. a. Maths consistent (Chapter I charge value 1.03 against Chapter VII 1.2 x 10^-20 emu is a book inconsistency, and the printed "e = 10^20" is a misprint for 10^-20). b. Consistent with e/m, Zeeman sign and magnitude for normal triplets; anomalous patterns need spin (Lande, Uhlenbeck-Goudsmit [memory, high]). c. Tested by Zeeman and Lorentz, Wiechert, Kaufmann, Thomson (1897) and Millikan (1909) [memory, high]; replicated. d. Nothing would change; it is the textbook. Verdict: Established.

Claim 2. Electromagnetic mass

Agreement: the slow-speed formula, the 4/3 problem (U = 3/4 m c^2 in Thomson's numbers [calc]), the failure of Conduction eq. (1) to reduce to its own slow limit (12.5 against the correct 0.0067 at v/V = 0.01 [calc by mathematician]), the circular radius (a is whatever makes the field mass equal the measured mass; 1.1-1.9 x 10^-13 cm), and that under relativity a mass rising as gamma says nothing about whether the mass is electrical. Disagreement: the physicist and mathematician split the verdict into four parts, the contrarian into three and rates "velocity dependence of electron mass" Established; the physicist and mathematician say the tested Thomson velocity law is not supported. Stronger argument: the physicist and mathematician. Thomson's tabulated agreement was not produced by his stated model (table above), the data (10% scatter) did not distinguish it from alternatives, and the later better data (Bucherer 1908 onward [web: https://en.wikipedia.org/wiki/Kaufmann%E2%80%93Bucherer%E2%80%93Neumann_experiments, search summaries; Wikipedia is a secondary source]) favour gamma. The contrarian's "Established" is right about the fact that mass rises with speed, which I list separately. What would settle: re-derive the table from the printed model and then from raw Kaufmann plates (done for the first step above; the second needs the 1901-03 data). b. Consistent with experiment only qualitatively; the electron is point-like to below about 10^-18 m [memory, medium; not web-checked; all three reviewers lean on it, but the verdict does not depend on it, because relativity and the 4/3 problem already remove the need for a]. c. Tested qualitatively 1901-09, quantitatively later; the all-electromagnetic strong form was never tested on its own terms. d. The electron would need finite size and an ether to carry "bound mass"; relativity's mass-energy relation would be a feature of electromagnetism only. Investigator's finds kept: the tubes-of-force and "dual structure" electron in Structure of Light (1925) and Beyond the Electron (1928) [web per sites.md, not read by any reviewer]; Rayleigh's 1942 account of the "specks of great intensity" argument. Verdict (split). - Field momentum adds (2/3) e^2/(a c^2) of inertia to a moving charge, and that inertia rises with speed: Established (as classical electrodynamics, with the 4/3 problem unresolved by Thomson). - Thomson's tabulated velocity law as quantitative agreement with Kaufmann: Tested, not supported (not reproducible from the printed formulas; later data favour gamma). - The corpuscle's whole inertia is electromagnetic, a about 10^-13 cm: Historically superseded but instructive. - "Bound ether" as a physical substance: Not testable as stated. - Extension to the mass of atoms: Refuted by calculation, by Thomson's own counting in Art. 355.

Claim 3. Roentgen pulses and ionisation

Agreement: ionisation (1896 note, observed by others the same week [read: 1896 note p.3]) and bremsstrahlung via the Larmor formula are right; Thomson's "pulses, not waves" lost to crystal diffraction. Disagreement: the physicist and mathematician call the strong form "Historically superseded but instructive"; the contrarian calls it "Tested, not supported" (Laue 1912 was a real test). Stronger argument: the contrarian, because the choice matters: a controlled experiment (Laue, Friedrich, Knipping, then the Duane-Hunt cutoff and characteristic lines [memory, high; not web-checked]) was run and the exclusive pulse picture failed; "superseded" would suggest it was only replaced. All three agree it was reasonable in 1897-98 and Stokes himself concluded the rays were transverse. The contrarian's further point stands in the record: the unsettled wave-or-particle question was real, and localised absorption (photoelectrons) is closer to Thomson's "specks" than to a diffuse wave. Worked number (physicist [calc]): a 30 keV electron stopped within 10^-8 cm radiates about 1 eV, a fraction 3.5 x 10^-5, the right order for tube efficiency [memory, medium]. Minor mathematics: the pulse thickness is assumed, not derived; the pulse magnetic-force formula lacks a factor e (misprint); Art. 363 drops the Schott term and fails for pulse widths below 2a. What would settle: nothing further for the strong form. For the "specks" idea, a comparison of the 1925 Faraday-tube model's predictions with photon statistics (an open historical question, not an experiment now needed). Verdict (split). - X-rays make gases and insulators conduct by ionising molecules: Established. - Continuous X-rays are radiation from decelerated charge (Larmor power): Established. - Roentgen rays are non-periodic pulses and not waves (strong form): Tested, not supported (crystal diffraction 1912), though reasonable for 1897-98. [Verdict unchanged 2026-10-09, but its grounds are refined in QE revision section 10: the deciding tests are the characteristic lines and the Duane-Hunt cutoff, which crystal diffraction made measurable, not diffraction as such.] - The "specks of great intensity" localisation argument: Historically superseded but instructive.

Claim 4. The uniform positive sphere, counting, rings and the periodic law

Agreement: the model's mathematics is internally consistent with errata (equilibria Q = 0.9, 2.1, 3.6, 5.4 e^2/a for N = 1-4; ring stability only to 5; the ring table has 13, 8, 3 twice and no 23, swaps the valencies of the 62 group, uses greedy rings that differ from the lowest-energy planar structures for N = 9, 13, 16, 17, 19, 21, and its outer-ring boundaries at 58/59 and 67/68 do not survive; Thomson calls the sum-of-valencies 8 "quite accidental"). The plum-pudding sphere failed on alpha scattering (Geiger-Marsden 1909, Rutherford 1911 [memory, high; not web-checked]). Disagreement: (i) the label for "number = atomic weight": physicist "Refuted by calculation"; mathematician and contrarian "Tested, not supported". (ii) the label for the ring/periodic-law idea: physicist "superseded", mathematician "not testable as stated", contrarian "Tested, not supported". (iii) the contrarian adds the LaFave 2013 "Thomson problem" correspondence as "Plausible, untested". Stronger argument: (i) both labels are true and compatible: Barkla's own datum, worked with correct constants, gives 14 electrons per air molecule [calc above], a calculation from accepted physics that rules out N = A, and Moseley (1913) then tested the question directly [memory, high]. I give both. (ii) The mathematician's "not testable" is too weak: Thomson's quantitative ring scheme makes testable claims (the period lengths, the 10-member period for outer ring 21, the sum of valencies), and it fails them on its own tables and against the real periods 2, 8, 8, 18, 18, 32 [memory, high]; the physicist and contrarian are right that it was tested against known data and not supported. Its core principle (shell recurrence determines chemistry) lives on in quantum shells, and that is why it remains instructive. (iii) LaFave is one published paper by one author (J. Electrostatics 71:1029, 2013; arXiv:1403.2591), read by no reviewer beyond its abstract [web: https://arxiv.org/abs/1403.2591]. It concerns N point charges on a sphere's surface, a different problem from the 1904 rings in a uniform sphere; its numerical resemblances to shell filling are reported fairly and do not rescue the plum-pudding model. I keep it as "Plausible, untested" only as mathematics of the Thomson problem, not as a claim about atoms. The three counting methods, recomputed by the reviewers and agreed: Method I gives 21.5 corpuscles per air molecule with Thomson's e (he rounds to 25 for nitrogen's 28), 14 with modern e; Method II gives 2.2-3.6 per unit atomic weight, with Crowther's value giving 0.27 and beta-ray values 0.01-0.02, which he sets aside; Method III gives about 1 for hydrogen. The contrarian's observation stands: each method has an escape clause and the rounding was steered toward the prior (not alleged as fraud). What would settle: already settled by Barkla with modern constants, and by Moseley, and by Rutherford scattering. For LaFave, a test of whether the Thomson-problem energy patterns predict anything the quantum shell model does not. Verdict (split). - Uniform positive sphere of positive charge with corpuscles inside (plum-pudding): Tested, not supported (alpha scattering 1909-11). - The number of corpuscles equals the atomic weight, "supported by three counting methods": Refuted by calculation (Barkla's datum with the modern e gives about A/2, shown above), and tested again by Moseley; the "agreement" of the three methods is not supported by recomputation. - Ring stability mathematics (equilibria, instability beyond 5): internally consistent as mathematics, with the printed errata above; the ring table: partly wrong (errata, non-ground states). - Rings explain periodic law, valency and spectral series quantitatively: Tested, not supported. - The idea that chemical periodicity reflects recurring electron shell structures: Historically superseded but instructive (mechanism replaced, principle survives).

Claim 5. Positive rays: mass 22, mass 3, helium and neon from bombarded solids

Agreement: the method and the parabola algebra (mass 22 sits sqrt(22/20) - 1 = 4.9% from neon in deflection [calc]); neon-22 (about 9.25% of neon [memory, high; not web-checked]); mass 3 is today H3+, formed by H2+ + H2 giving H3+ + H [memory, high; web: Kragh 2011, https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1600-0498.2011.00237.x, abstract only]; Thomson's controls are real (helium grows with bombardment time; salts dissolved and evaporated 10-12 times with undiminished helium; split-aluminium blank; yield depends on the salt) and his own statement is cautious, not a claim of proof; the energy needed to remove an alpha is millions of electron-volts against tens of keV. Disagreements, and what I found: (a) Neutral H3 / stored gas. Physicist: neutral H3 "Tested, not supported", stored-gas nature "Never properly tested". Contrarian: neutral H3 "Tested, not supported" resting on Kragh's summary only, which he says would stay "Never properly tested" on primary evidence. Math: "Tested, not supported". I agree with the physicist's split and the contrarian's caution: what is documented is that the neutral molecule was abandoned by the mid-1930s (Kragh 2012 Phil. Trans. A 370:5225, abstract, [web per sites.md]); I have no primary report of an independent test of the stored mass-3 gas with its weeks-long storage and destruction by light plus oxygen, so that behaviour is unexplained, not refuted. Thomson's text records its own negative: "No lines which could be ascribed to X3 were detected" [read: contrarian, Positive Rays p.147]. Neutral H3 is not a stable ground-state molecule [memory, medium; not web-checked in this session, though Kragh's abstract says it was abandoned]. (b) Helium and neon from bombarded salts and metals. The physicist labels the experimental reports "Tested, not supported by later negative experiments" and refutes transmutation by the energy budget; the contrarian separates the targets. The contrarian's distinction is the stronger argument: Strutt (Proc. A 89:499, 1914), Merton (A 90:549, 1914), Egerton (A 91:180, 1915), Harkins and Wilson (1915) and Allison and Harkins (1924) concern the Ramsay and Collie-Patterson discharge-tube and X-ray-bulb claims, not Thomson's own bombardment of solid salts and metals [web per sites.md; Nelson's bibliography at https://www.alchemywebsite.com/nelson2_6.html; none of the papers read by any reviewer or me]. I found no independent replication or refutation of Thomson's solid-salt protocol. I also checked that the one possible direct test, his own 1922 paper on "the gases given off by deflagrated metals", exists (title and July 1922 date confirmed [web search 2026-10-09], Proc. A 101:290, https://royalsocietypublishing.org/doi/10.1098/rspa.1922.0044) but its result is unread by every reviewer and by me (a search summary offered a [memory]-style guess that he found no helium; I do not use it). The sources for the discharge-tube episode say: Redgrove (1922), "failed to be satisfactorily confirmed"; a Royal Society referee file for Collie-Patterson-Masson calls their results "currently unexplained" [web: https://makingscience.royalsociety.org/items/rr_21_53]; Nelson (a sympathetic alternative-science author) writes "The matter never has been resolved"; Baly and Riding (1925) reported small rare-gas yields from a discharge in oxygen with a nitride anticathode and said they confirmed earlier observations of Collie, Patterson and Masson [web search summary only, physicist; a lead, not read]. Both sides published; none of this was suppressed, and the New Energy Times list (an interested party's catalogue) carries no Thomson or Collie entry. The standard explanation is atmospheric and occluded helium in glass and solids; no reviewer found a source that demonstrates that explanation for these particular experiments, so I hold it as the field's explanation, not as a documented demonstration (correction 4 below). (c) Transmutation. Physicist and contrarian: "Refuted by calculation" for the strong form; mathematician says only "Tested, not supported". The energy budget (recomputed above) is decisive for electron energies of 30-100 keV: at most 0.3-1.4% of what is needed, by energy conservation alone, and the "loosened alpha" has no basis since Na-23 and K-39 are stable against alpha emission (S_alpha positive, 10.47 and 7.22 MeV [web]). But Thomson did not assert transmutation: he named it as a view that needs every other explanation excluded. The refutation therefore applies to the strong form, not to what he claimed. What would settle: (1) read the 1922 Proc. A paper and the Strutt, Merton, Egerton and Allison-Harkins papers; (2) a modern bombardment of the same salts in helium-free ultra-high vacuum, with He-3/He-4 isotope analysis and blank runs of the same salts, reagents and glass; (3) detection of the residue atoms (beryllium minus helium = 5, carbon minus helium = 8) which Thomson himself named as the decisive test; (4) the 1910-22 notebooks at CUL (MS Add. 7654). Verdict (split). - The parabola method of mass analysis: Established. - The mass-22 line beside neon (Ne-22 isotope; his "new element or inseparable form of neon" hedge anticipates isotopes): Established. - The mass-3 line as a triatomic hydrogen species: the ion H3+ Established; a stable neutral H3: Tested, not supported (secondary source, Kragh's abstracts; physics memory [medium]); the nature of his weeks-stable stored gas: Never properly tested. - Helium and neon appear in the analyser after bombardment of solids (his own protocol): Never properly tested (no independent neutral replication or refutation found; a contamination or occlusion explanation is standard but not demonstrated in the record; whether his own 1922 test settled it is unread). - Helium and neon from discharge tubes and X-ray bulbs read as transmutation (Ramsay, Collie, Patterson, Masson, Baly): Tested, not supported in the published negative tests as reported by secondary sources, with a later partial positive report (Baly and Riding 1925, lead only). - Transmutation of Na or K into helium by tens-of-keV electrons (strong form, not Thomson's own claim): Refuted by calculation.

Claim 6. Vortex rings (1883)

Agreement: the far-field method and most results are sound (inverse-cube deflection, sin 3-phi radius rule, linked-ring frequencies); errata: eq. (71) three times too small (reversing the p.75 comparison; confirmed [calc, mathematician]), eq. (74) needs k^4, sphere total angle lost 1/u, misprints in the n = 5 coefficient, a density dropped from a Part III bound; "seven unstable" is a rounding artefact. Disagreement: the mathematician labels "seven unstable" "Internally inconsistent" and the contrarian ("six is the greatest number stood") and physicist do not; the contrarian says "stable for n up to 6 ... unstable above 7" and calls "up to 6 stable" a result that stood. Stronger argument: the mathematician's. Thomson's own exact equations give a zero root at seven, so his printed verdict contradicts his own equations. Web check, done by the mathematician and contrarian and by me: for n < 7 a ring of identical vortices is linearly stable and for n > 7 linearly unstable (Thomson 1883), at n = 7 the linearised problem is degenerate; Cabral and Schmidt (1999) showed the heptagon is Lyapunov stable by going to fourth order, and Montaldi and Tokieda obtained the same by another route; a 2008 Phys. Rev. Lett. water-vortex experiment confirmed the stable and unstable ranges (the heptagon is in a narrow band or critically stable) [web search summary 2026-10-09: https://rcd.ics.org.ru/RD2004v009n04ABEH000294/ ; https://link.aps.org/doi/10.1103/PhysRevLett.100.174503; Havelock 1931 attribution secondhand, not confirmed; the Kurakin-Yudovich 2002 attribution is from a less authoritative page]. So the heptagon is stable, not unstable: Thomson's "six is the greatest number" is wrong at seven but right in spirit for eight and up. The vortex-atom as a theory of matter: superseded (needs a frictionless ideal fluid; no spectra, no e/m; the electron took over after 1897) [memory, high]. Not assessed: Parts I and IV (the kinetic-pressure and chemical-combination claims) rest on digests only. The "gas of vortex atoms reproduces kinetic-theory pressure" component is therefore listed without a verdict from anyone. Verdict (split). - Ring-interaction mathematics: internally consistent once the printed errata are corrected (an established piece of vortex dynamics; the physical rings are real fluid objects). - Seven vortices on a circle are unstable: Internally inconsistent (zero root at seven; the heptagon is stable [web]). - The vortex atom as a theory of matter and chemistry: Historically superseded but instructive.* - Gas of vortex atoms reproducing kinetic pressure: not assessed (digest only).

Final verdict table

What would settle it

Open questions

1. How did Thomson obtain his "calculated" ratios 3.09, 2.43, 2.04, 1.83, 1.65? They are neither his stated model nor, exactly, gamma.
2. What was the result of his 1922 deflagrated-metals analysis, and did he ever report the residue test he named as decisive?
3. Was any independent test run on his solid-salt helium protocol (as opposed to the discharge-tube claims)?
4. What was the stored mass-3 gas, if it was not neutral H3?
5. Is the LaFave correspondence between the Thomson problem and shell filling anything more than numerical resemblance?
6. How do Parts I and IV of the Vortex Rings essay (kinetic pressure, chemical combination) fare? No one has checked them.
7. Did Thomson's 1925-28 tube-and-ring models (anchor-ring light quantum, dual-structure electron) make any quantitative prediction? Not read by any reviewer.

Absence of evidence: where the record goes dark

A. Thomson's own bombardment helium after 1922. The record shows him still giving two explanations in 1921 and naming the residue test, publishing a 1922 paper on deflagrated metals, then nothing on helium from bombarded solids that any reviewer found. Competing explanations: (1) he concluded contamination or occlusion and dropped it (for: the 1921 text already leans away from transmutation; against: he published no statement to that effect; the 1922 paper is unread); (2) the work was overtaken by Aston's mass spectrograph (1919) and nuclear physics (for: Aston was his assistant and the method moved on; against: this explains why the work was displaced, not why the test he named was never done); (3) he did the residue test and it was negative or inconclusive and unpublished (for: the notebooks exist at CUL; against: no source says so); (4) the work was suppressed (no evidence: both sides published openly, Thomson himself led the opposition to transmutation, Nature, Proc. Roy. Soc. and the Chemical Society all carried the discussion). Interested parties: Thomson (also the senior judge of the question and head of the laboratory whose method was at stake), Aston, and the proponents Ramsay, Collie, Patterson, Masson and Baly each had priority or reputation at stake [web via Investigator: Morrisson, Modern Alchemy]. Deciding records: Thomson's 1922 paper; CUL MS Add. 7654 notebooks (NB35a, NB36); Rayleigh's 1942 Life, ch. IX (text saved, unread); the Strutt, Merton, Egerton papers and their referee files at the Royal Society.

B. The stored mass-3 gas. The observation was reported in 1913 and Thomson kept the name X3 until 1937 (a Charles University thesis snippet [web via Investigator]); the neutral molecule was abandoned by the mid-1930s (Kragh). The record does not say what the stored gas was. Competing explanations: (1) the observed stability, light-plus-oxygen destruction and palladium behaviour belong to an impurity or to a hydrogen-containing species mistaken for H3 (for: the null spectroscopic search recorded in his own text; against: no independent test of that gas); (2) the ion seen in the analyser (H3+) and the stored gas are different things (for: H3+ is stable only in the discharge; against: nothing documented); (3) an unreproduced result by an experiment-driven investigator with a gas of unknown composition; the record that would decide is Kragh's full text, the 1913 Bakerian lecture and the notebooks.

C. Why the 1906-07 books say nothing on Abraham, Lorentz 1904 or Einstein 1905. Not a gap in physical data but a silence in the text: the deep reads find no mention, while Kaufmann's 1905-06 data were read by Kaufmann himself against Lorentz-Einstein. Explanations: Thomson's Cambridge classical tradition (Navarro 2010, via sites.md), or simple oversight; the 1906 preface and Recent Researches would decide. Low stakes for the verdicts.

D. The record on the 1913 negative tests. The negative papers are known only by title through the Investigator's bibliography; a referee page flags the Strutt and Merton identifications with a question mark [physicist]. They are leads until read.

Web verification (budget 8, used 5)

Corrections to earlier documents (for the orchestrator)

1. claims.md claim 4 ("supported by three counting methods"): rewrite as "three counting methods, which Thomson reports as agreeing with N proportional to atomic weight; recomputation does not support the agreement, and Barkla's datum with the modern e gives 14 per air molecule, about A/2". (Physicist, mathematician and contrarian also say this.)
2. Kaufmann table, in claims.md claim 2, the Corpuscular Theory deep read (section 3, error summary item 3) and any later document: the observed column is 3.1, 2.42, 2.0, 1.66, 1.5 and Thomson's calculated column is 3.09, 2.43, 2.04, 1.83, 1.65, as Conduction p.655 prints them and as Kaufmann's own e/m table (Conduction p.654) requires; the Corpuscular Theory p.33 heads these columns the other way round. Thomson's calculated column is 7.5-13% above his own stated model and within 3.5% of gamma. Do not repeat "Thomson's alpha is 8-12% above his model at the top three speeds" as written in the Corpuscular deep read.
3. claims.md claim 6 and the Vortex deep read: add that n = 7 is neutral at linear order and that the heptagon is nonlinearly stable [web]; "seven unstable" is an error, and "six is the greatest number" is wrong at seven.
4. Positive Rays deep read, context paragraph, and any text that states the 1913 helium/neon episode "ended with contamination or occlusion" [memory, medium]: change to "contamination and occlusion are the field's standard explanation; the sources found say the claims 'failed to be satisfactorily confirmed' (Redgrove 1922), are 'currently unexplained' (Royal Society referee) and that 'the matter never has been resolved' (Nelson); no source found demonstrates the explanation for these experiments".
5. sites.md "Leads for review": add Baly and Riding (1925) as a lead (physicist, search summary only); mark Strutt and Merton (1914) as unread leads (physicist: the Royal Society referee file flags the identifications); add that Thomson's 1922 paper's result is still unread.
6. Physicist's "Corrections" item 4 and contrarian item 5 agree with the above; one wording point in the physicist's file: "Refuted by calculation" for the experimental reports of helium from solids overstates; only the transmutation reading is refuted, the observation itself is Never properly tested. Search for stale copies of "Tested, not supported" applied to Thomson's own bombardment helium in the primer, entry and Curator data when they are written.
7. claims.md claim 5: say that the 22 line is Ne-22 (an isotope) and that the 3 line is H3+ today; keep "does not claim is proved".
8. facts.json: carry the Barkla arithmetic (21.5 with Thomson's e, 14 with the modern e) and the 4/3 relation U = (3/4) m c^2 in Thomson's numbers.

QE revision (2026-10-09)

Inputs: qe.md (verdict MINOR) and the new deep-read sections written for it: Vortex Rings Part IV (deep/treatiseonmotionofvotexrings-0ee5cd.md), Electricity and Matter Ch. II Kaufmann table (deep/ELECTRICITY-AND-MATTER-1909-828b3e.md from line 248), Conduction Ch. XI Barkla/Bumstead (deep/Conduction...-23223e.md from line 235) and Ch. V-VI e/m and e values (from line 304), Corpuscular Theory Ch. I and Ch. IV-V (deep/The-corpuscular-theory-of-matter-ab57d0.md from line 556). I read those sections; I did not re-render page images, so page-image readings below are the deep readers' [read: page image]. Web: one search this session (below); web budget now 6 of 8. No verdict in the six central claims changes; sub-verdicts are added for Part IV, the positive-carrier claim and the metallic-conduction item, and the Kaufmann and Barkla statements above are corrected.

[corrected 2026-10-09 by the orchestrator after the QE recheck: this paragraph said deep reads 7 and 8 were "not done". That was wrong by the time of the recheck. Both have sections in deep/: read 7 in deep/ELECTRICITY-AND-MATTER-1909-828b3e.md, section "Deep read: Chapter VI end (PDF pp.167-179 ...)" (Le Sage by X-rays, the external-source argument, the 50,000-year radium estimate, the margin annotations in the project's copy of the 1904 printing); read 8 in deep/Conduction-of-electricity-through-gases-23223e.md, section "Röntgen rays, Marx's velocity and Haga-Wind diffraction" (pp.657-662). What they mean for claim 3 is weighed in section 10 below.] The original text read: "Not done: the QE's deep reads 7 ... and 8 ... have no section in the deep files ... Both remain open."

1. Kaufmann table: correction to my own earlier "settled" statement

The QE (S5) was right and I was wrong to call the labels resolved. Evidence [read: page images, deep reader]: Electricity and Matter Table II (1904, 1907, 1909 printings, one setting; PDF 1909 p.65) labels column 3.1, 2.42, 2.0, 1.66, 1.5 "determined by equation (1)" and column 3.09, 2.43, 2.04, 1.83, 1.65 "found by Kaufmann". The Corpuscular Theory p.33 agrees with it. Only Conduction (1906) p.655 reverses the two headers over unchanged columns. Two readings: Conduction swapped the headers in copying, or Conduction corrected an error. The pages cannot decide. My e/m-product test (observed ratio times Kaufmann's e/m constant) favours the Conduction labels, but only as a fit: column 3.1... gives products 1.92, 1.86, 1.95, 1.94, 1.97 (x 10^7; spread 5.5%, one outlier), column 3.09... gives 1.92 to 2.16 (spread 15.5%). Neither is an exact quotient by any one slow-speed e/m; with the 1.86 x 10^7 that Thomson's own table lists, column 3.1... is reproduced within 3-5% and exactly at one speed [calc, deep reader]. The test also assumed one common e/m of about 1.95, higher than Thomson's tabulated slow values (1.77-1.86); the QE point is accepted. Statement now: the three printings disagree; the e/m test favours Conduction; the model test at low speed and two of three printings favour Electricity and Matter; Kaufmann's 1901-03 tables (Gott. Nachr. 8 Nov. 1901, not in the folder) decide it. Recomputed facts that hold under either labelling: neither column is reproduced by Thomson's equation (1) (3.1... is 8-12.5% above it at the top three speeds and within 1.3% at the lowest two; 3.09... is 7.5-13% above it at all five), and the printed statement "do not differ by more than 10 per cent" is true of the two printed columns, not of model against data. The 3.09... column follows gamma within about 1% (V = 2.98 x 10^10), which Thomson could not have computed in 1903; if that column is Kaufmann's, then Kaufmann's reduced values were already gamma-like. That is a hypothesis for Kaufmann's papers, not a finding. Equation (1): the E&M printing (p.61) is correct, and equals the exact integral of the field momentum of a moving point charge; the Conduction printing (cos 2theta coefficient 1/2) is the misprint that fails the slow limit (1876 times the slow value at beta = 0.01). So the mathematician's slow-limit failure and my claim-2 wording "failure of Conduction eq. (1)" belong to the Conduction misprint, not to Thomson's formula. The conclusion for claim 2 (the tabulated agreement is not produced by the stated model) stands. Radius: with e = 1.2 x 10^-20 and e/m = 10^7 the radius is 8 x 10^-14 cm; E&M prints "about 5 x 10^-14" (which follows from e/m = 0.62 x 10^7), Conduction "about 10^-13". E&M also calls 1.2 x 10^-20 "electrostatic" units; it is electromagnetic [calc]. Kaufmann's electrical-mass fraction is "one-fourth" in E&M and "about 1/3" in Conduction. Claim 2 verdicts unchanged: velocity law Tested, not supported; field momentum Established; all-mass-electrical Historically superseded but instructive.

2. Barkla datum and the count (claim 4)

Conduction p.339 [read: page image] prints "about .0002" in the sentence and ".00025" in the equation, never reconciled. With Thomson's e = 1.2 x 10^-20 and e/m = 1.7 x 10^7, (8 pi/3) e (e/m)^2 = 2.9 x 10^-5, so .00025 gives Ne = 8.6 (he prints 10) and .0002 gives 6.9; with his ne = .4, N/n is 20 (not the printed 25) for .00025 and 16 for .0002 [calc, deep reader]. Modern constants (QE): 14.0 electrons per air molecule from .00025 and 11.2 from .0002, for n = 2.687 x 10^19 [calc, QE]; with Thomson's own n (about 3.6 x 10^19) the figure is about 10 [calc, deep reader]. All give about Z (14.4 for air), not A (29). My figure 14 per air molecule stands, with the range 11-14 depending on which printed datum is used; the rounding was steered further toward A than I wrote (charge, rounding of Ne to 10, and the 25% larger datum). Barkla's own figure must be taken from Phil. Mag. (6) 7, 543 (not obtained); the 1906 book's page is cited there as p.548. Verdict unchanged: N = A Refuted by calculation (as a claim that the count is the atomic weight). Thomson states the extension "if true for one element it would be true for all" conditionally.

3. Thomson's own e/m and e history (claim 1)

From the master table [read: page image, Conduction p.145]: Thomson 1897, 7.7 x 10^6 (deflection, which he calls the more reliable) and 1.17 x 10^7 (heating; "not so reliable"); Lenard 1898, 6.39 x 10^6; Kaufmann 1897-98, 1.86 x 10^7; Simon 1899, 1.865 x 10^7; Seitz 1902, 1.87 x 10^7; Becker 1905, 1.8 x 10^7. Modern 1.76 x 10^7 [memory, high]. His own first value was about 2.3 times low, and the method he criticised (using the cathode fall) gave the better answers; he concedes this via Seitz 1902. The "1/770" (Art. 59, from 7.7 x 10^6 / 10^4, with e = E asserted) and "1/1700" (Art. 78, from about 1.7 x 10^7 and e = E) both sit in the same book, unreconciled. Charge: Thomson 1898, 6.5 x 10^-10 esu (air), 6.7 (hydrogen); 1901-02 radium, 3.4; H. A. Wilson 1903, 3.1; modern 4.80 [memory, high]. Corpuscular Theory p.30 prints 3.1 x 10^-10 esu (the text layer's "8.1" is an OCR error). This corrects the primer sentence that Thomson's 1897 deflection measurement "agrees": it gave the right order and constancy across gases and electrodes, not the right value. Verdict unchanged: Established, with priority shared (Wiechert, Kaufmann, Zeeman-Lorentz). Minor internal inconsistencies noted by the deep reader: UV value 7.3 x 10^6 in Art. 67 text against 7.6 in the table; Simon's potential range 4860-11840 V against "about 1100 V" on the next page (page images not rendered).

4. Two universal positive carriers (new item, Corpuscular Theory Ch. I; claim 4 neighbourhood)

Thomson reports [read: page image p.35, p.38] that at very low pressure and strong field the deflection spot splits into two patches with maximum e/m about 10^4 and 5 x 10^3, "whether the tube is filled originally with air, hydrogen, or helium", and in every gas tried (air, carbonic oxide, oxygen, hydrogen, helium, argon, neon). He says it is "the most obvious interpretation" that all gases give two types of positive particle independent of the gas, of masses one and two hydrogen atoms, and that the 5 x 10^3 type has the e/m of the alpha particle. He states his reason for rejecting hydrogen contamination: an impurity of hydrogen molecules should give e/m 5 x 10^3, not 10^4. At higher pressures the carriers depend on the gas (hydrogen 10^4 and 5 x 10^3; helium 10^4, 5 x 10^3, 2.5 x 10^3). The text gives no spread, field or pressure values. Weighing: the later mass-analysis work, including his own 1913 parabola results in this folder, finds ions of each gas's own atoms and molecules (neon 20 and 22), so universality is not supported; the hydrogen-and-water desorbed from electrodes is the usual reading [memory, high; not web-checked, and I did not re-read the 1913 deep read for this point]. His own caveat deserves to be kept: "we know of no case where the mass of the positively charged particle is less than that of an atom of hydrogen". The alpha-particle identification (e/m 5 x 10^3 = doubly charged helium, with helium evolved from the same substances) is Established. Verdicts: universal H+ and H2+ from every gas Tested, not supported (by later mass analysis); alpha e/m 5 x 10^3 as He++ Established. He later dropped the first claim; no document in the folder records his dropping it (open).

5. Metallic conduction and the specific-heat paradox (supplementary item S1, Corpuscular Theory Ch. IV-V; not a central claim)

Thomson's own anomaly [read: page images p.98-100, deep reader checked]: the Rubens-Hagen reflection data need n > 1.8 x 10^24 free corpuscles per cc of silver, and at (3/2)-type classical energy a theta each (a = 1.32 x 10^-16 erg/K) those carry about 5.7 cal per degree per cc, against the whole metal's 0.58 cal (Dulong-Petit) [calc, deep reader]. He states it as a contradiction. It is the classical electron specific-heat problem, resolved by Fermi-Dirac statistics (Sommerfeld 1927); the electronic heat capacity of silver at room temperature is about 1% of the lattice value [memory, high/medium]. His Wiedemann-Franz result (4/3 form; pure metals within roughly -5% to +10% of the prediction in his Jaeger-Diesselhorst table, alloys, iron, platinum, bismuth up to 44% above) rests on the same classical equipartition, and the ratio contains no mass or charge sign, so it cannot identify the carrier (his Ch. V ends: the results "would hold if the carriers were bodies having a much greater mass"). The "at most only a part" conclusion (p.90) is drawn from the Peltier/free-path comparison and the melting data, before the specific-heat argument. Verdicts: the classical-gas corpuscle model of metals, as a complete account: Tested, not supported (by his own heat-capacity bound); the specific-heat contradiction as a statement: Established; the Wiedemann-Franz agreement as evidence for corpuscles: Historically superseded but instructive. Unchecked: a possible factor-9/4 slip in the second-theory ratio (p.102) is for the mathematician; the Hall-sign argument was recorded without a verdict.

6. Claim 5 record additions

• Pre-1913 transmutation thinking, from Thomson's own 1906 text [read: Conduction pp.333-344, page images]. Bumstead's lead/zinc heating (about twice, "nearly twice" in Art. 163; one cited paper, Phil. Mag. [6] 11, 292, 1906) leads Thomson to say Rontgen rays "may furnish a means of tapping the stores of inter-atomic energy", and to suggest that radium kept in contact with lead might gradually produce other elements; he floats these as questions. He reports "a large number of experiments" finding no residual radioactivity in metals after several hours of strong X-rays, and similar negative radium experiments with Bumstead (Proc. Camb. Phil. Soc. 13, 124-125, 1905). No metals, detector, sensitivity or intensities are given, so the sensitivity of the null result cannot be judged. Whether Bumstead's result held is not in the text; a later explanation by escaping secondary radiation is [memory, low] and not checked. Thomson's "explosion" argument (Art. 160): corpuscles of about 10^9 cm/s ejected by X-rays would need a pulse with X t = 60 and, for a pulse thickness of 10^-5 cm, an energy of about 0.7 cal per cm^2, "an altogether inadmissible amount", so the energy comes from the atom [calc 2.9 x 10^7 erg, deep reader]. So his 1913 caution about helium from salts continues earlier negative searches by himself, and his earlier view that X-rays trigger atomic instability.
• Neutral H3, web check done: the neutral molecule's ground state is repulsive and it exists only in short-lived excited (Rydberg-type) states, dissociating to H2 + H in about a picosecond for the lowest states [web: https://en.wikipedia.org/wiki/Triatomic_hydrogen ; Caltech thesis https://thesis.library.caltech.edu/6664 (both via search summary 2026-10-09, not opened)]. The [memory, medium] fact behind "stable neutral H3 Tested, not supported" is now [web] (search summaries; the pages themselves not read). It does not touch the stored gas, which remains unexplained and Never properly tested.
• Nelson's characterisation of X3 as "tritium" (an alternative-science author's reading, [web per sites.md]) is kept here: it points to a nuclear-origin reading of the mass-3 line. Against it: tritium was unknown until 1934 [memory, high]; the mainstream assignments are H3+ and HD+ [memory, high]; Thomson himself kept the name X3 until 1937 per the Charles University thesis snippet. C. N. Wall (Phil. Mag. 48:378, 1924), an extension of the Stokes-Thomson pulse theory, is kept as supporting information for claim 3 (not read; the physicist mentions it without judgement). Tolman 1922 and the Trinity College fonds THMJ/THMF are recorded as leads.

7. Claim 6 Part IV: verdicts from the deep read (replaces "not assessed")

Thomson says a full dynamical theory "must form the subject of a future paper"; Part IV collects "results which can be obtained with very little additional calculation" [read: p.133]. Paragraph 60 and parts of 58-59 were added after the essay was submitted (per the digest). | Prediction | Check | Verdict | |---|---|---| | Pressure of a vortex gas, pv = T/3 (Boyle) with a wall term giving pv "a little less" than Boyle, "agrees with Regnault" | The sign follows from his formula; the deviation comes from the wall term he calls small; he drops a molecule-molecule term he shows is positive; no density law; Regnault's hydrogen deviates the other way, air, nitrogen and carbon dioxide agree [memory, high; hydrogen detail not web-confirmed]; his claim that elastic spheres cannot explain any deviation was already wrong (van der Waals 1873). The 2/3 against 1/3 prefactor is unresolved in the text. | Not testable as stated (sign only; matches some gases) | | Mean speed of a monatomic vortex gas falls as temperature rises (restricted to monatomic gases) | Follows from thin-ring formulas [calc]; contradicted by Stern's silver-beam velocity measurements (1919-20) and by sound speed varying as the square root of T [web: Frontiers 2019 via search; memory, high] | Tested, not supported | | Thermal effusion p/p' = (t/t')^m with m > 1 (m about 1.5-1.9 on thin-ring estimates [calc]), proposed as a "crucial experiment" | Reynolds (1879, porous plates) and Knudsen (1909-10, narrow tubes) found p1/p2 = square root of T1/T2, m = 1/2, in the free-molecular limit [web: https://arxiv.org/pdf/2006.01574 eq. 7; https://arxiv.org/html/2602.21079v1, via search 2026-10-09]. The Poynting-Thomson Text-Book (1909, p.214 digest) states the square-root law [read: digest, not deep read] | Tested, not supported | | Paired/free time governs affinity, dissociation, dielectric strength | Qualitative; no value, no measurement procedure. Two paired rings stay together only if strengths are equal: follows [calc], with an m for m' slip | Not testable as stated | | Valency = number of linked rings, at most six; table makes C divalent, N, P, As univalent; figure-of-eight N for NO and NO2 | Rules applied inconsistently: HCN and CH3NH2 need mixed-atom primaries, and once those are allowed his arguments against tetravalent carbon (acetylene) and trivalent arsenic (cacodyl) fail [calc, deep reader]. "At most six" rests on the Part III seven-vortex instability, a rounding artefact (arbiter claim 6). Contradicted by the chemistry of the time and by IF7 (1930) [memory, high] | Internally inconsistent (as applied) | | Low-valency elements have simpler spectra | True for alkalis and hydrogen; chlorine's spectrum is rich [memory, medium] | Partly; not scored | Retained and fair to Thomson: Part IV is the only place the 1883 vortex atom meets laboratory numbers, and it made a definite, falsifiable prediction that differs from kinetic theory (with Reynolds' measurement already published four years before). He flags the experimental difficulty and the boundary effects himself. The vortex atom as a theory of matter stays Historically superseded but instructive. Part I (ring stability under all small displacements; elliptic vibration 0.289 of the circuit time) is still unassessed.

8. Scale labels (QE process point)

Where I wrote "internally consistent with errata" for the ring-stability and ring-interaction mathematics, the scale label is Established (as mathematics, with the printed errata listed). I have put this in the verdict table. "Not assessed" is kept only for vortex Part I.

9. Retention and process

Kept in the record (QE retention item): Wall 1924, Nelson's "tritium" reading, Tolman 1922, Trinity fonds. Not dropped by any reviewer for negative judgement. Still web-unchecked verdict dependencies: electron point-like to below 10^-18 m [memory, medium]; Laue, Moseley, Geiger-Marsden [memory, high]; the hydrogen deviation under Regnault; later explanation of Bumstead's lead/zinc ratio [memory, low]; Stern 1920 and Reynolds 1879 taken from the deep reader's search summaries.

10. Deep reads 7 and 8: what they mean for claim 3 (added 2026-10-09)

Inputs: the two deep-read sections named in the corrected note at the top of this QE revision. I read both in full. No web search was made for this section.

Read 8 (Conduction 1906, pp.657-662). By 1906 Thomson already knew of diffraction evidence and did not set it against his pulse theory. He reports Haga and Wind's V-slit broadening as effects "which would be produced by diffraction, and which have not been explained in any other way". He says light would need a wavelength of about 2 x 10^-8 cm to broaden the shadow that much. Then: "If we regard the Röntgen rays as due to discontinuous pulses, this will be the order of the thickness of the pulse" [read: Conduction p.662, page image; the deep reader leaves a small doubt between 10^-8 and 10^-6 in the exponent]. He also reports Marx's 1906 result that the rays travel through air at the speed of light, gives no number, and does not use it for or against the pulses [read: p.661]. A pulse from a stopped charge travels at the speed of light, so Marx's result fits his picture. Thomson does not say this himself.

What this changes. My claim 3 text says the strong form "lost to crystal diffraction" (Laue 1912). Read 8 shows that this reason is too quick. Thomson had already turned one diffraction result into a pulse thickness, and nothing in principle stops the same move for crystal diffraction. An irregular train of thin pulses is, by Fourier analysis, a continuous spread of wavelengths. A crystal picks out the wavelengths that fit its spacing from such a spread [memory, high: the Gouy-Schuster-Rayleigh treatment of white light as irregular pulses]. Diffraction of the continuous spectrum therefore does not by itself decide between "waves" and "pulses". The evidence that does decide against "not waves, no periodicity" is: - sharp characteristic lines, which are periodic, monochromatic radiation (Barkla's homogeneous radiations; the Bragg spectrometer lines and Moseley, 1913); - the sharp short-wavelength cutoff (Duane-Hunt 1915), which no classical pulse spectrum has [memory, high; not web-checked, as already flagged above]. Laue 1912 is the experiment that made those wavelength measurements possible. That is why it still belongs in the record.

Verdict. The verdict of the strong form does not change: Tested, not supported. Controlled tests were run, and they showed periodic line radiation and a quantum cutoff, which the exclusive pulse picture cannot produce. What changes is the reason given. It is the line spectra and the cutoff, which crystal diffraction made measurable. It is not diffraction as such. The contrarian's point gains weight: Thomson's position in 1906 was more careful than "not waves" ("if we regard" the rays as pulses), and his pulse picture is still the classical account of the continuous component (verdict 3b, Established, unchanged). The other claim 3 verdicts (3a, 3b, 3d) are unchanged.

Read 7 (Electricity and Matter 1909, PDF pp.167-179). This read does not bear on the pulse-or-wave question. Two points go into the record: 1. The 50,000-year radium life. The arithmetic is correct: (1/2)(1 g)(2 x 10^9 cm/s)^2 / (4.2 x 10^9 erg/h) = 4.8 x 10^8 h, about 54,000 years, and 5 x 10^10 cal in all. Thomson states it as an upper limit ("superior limit"). The modern mean life of radium-226, about 2,300 years [memory, high], is below it, as an upper limit allows. No verdict is needed. 2. Penetrating Röntgen rays in place of Le Sage's corpuscles. Thomson proposes this as a cause of inverse-square gravity, using the momentum of electromagnetic waves. He states the costs himself: gravity would travel at light speed, which astronomers then denied, and the re-emitted rays must be more penetrating than the incoming ones. He says the needed "simple calculation" of energy turnover per gram but does not perform it. He uses the proposal only to show that the size of radium's output does not rule out an external energy source. He decides for an internal source on another ground: radioactivity is "a transient property" of each active product [read: deep, pp.174-179]. Note that in this 1909 passage he calls Röntgen rays "waves of electric and magnetic force", while the pulse picture in the same book's chapter III is of a single thin pulse [read: deep, 1909 section E]. No reviewer assessed the gravity proposal, and it is not one of the six central claims. I give it no verdict here. It stays in the record, with Thomson's own objections and the unperformed calculation, for the reader to weigh. A verdict would need a reviewer to do the energy and drag budget for radiation-pressure gravity.

Corrections to earlier documents (QE revision, for the orchestrator)

1. This file, "Kaufmann table" paragraph and Corrections item 2: do not say the 1907 book's headings are interchanged or that the labelling is resolved. Say the three printings disagree (E&M 1904/1907/1909 and Corpuscular label 3.09... as Kaufmann's; Conduction labels 3.1...), and that Kaufmann's 1901-03 table decides it. Same for claims.md claim 2, the Corpuscular deep read item 3, the primer §4 table, §7 bullet and answer 2, and example.py Part D (print the 1904 labelling and the (e/m)0 assumption).
2. Equation (1) is correct in Electricity and Matter p.61 and misprinted in Conduction p.664. Fix the Conduction deep read ("the printed closed form is not right"), the mathematician's slow-limit statement and arbiter claim 2 agreement paragraph to say "Conduction's printing". Conduction deep read's "2.55, 2.01, 1.70, 1.54, 1.44": 2.55 is at v = 2.83 (2.71 at 2.85).
3. Barkla: add the .0002 / .00025 inconsistency and the 11-14 range to claims.md claim 4, the primer §5 steps and point 4, and facts.json (QE C2). Conclusion (about Z, not A) unchanged.
4. Primer §3.1: replace "agrees" for Thomson's 1897 measurement with section 3 above (QE C6). Digest corrections: Conduction digest part 04 p.135 (7.7 x 10^6, not 10^7), part 21 p.668 (labels), Corpuscular digest p.30 (3.1, not 8.1 x 10^-10 esu), digest p.89 (contact potential V = (2/3)(a theta/e) log(N1/N2); Peltier values 1/30 volt, log 1.33; n > 1.8 x 10^24; 6 cal against 0.6 cal).
5. facts.json: vortex entries (Part IV was deep read; kinetic result carries a wall term, pv a little below Boyle); E&M entry (QE C5 and C7: the Le Sage statement and a reader's margin annotations in the project's copy; the 1904 scan carries one page from the 1907 printing); add sections 3-5 and 6 above (the positive-carrier claim, the specific-heat paradox, pre-1913 null searches and Bumstead).
6. claims.md: claim 6 add Part IV predictions; claim 1 add Thomson's own first values; add the universal-carrier claim; apply earlier arbiter corrections 1-8 (still pending per QE).
7. sites.md "Leads": Wall 1924, Nelson's tritium, Tolman 1922, Trinity fonds THMJ/THMF (QE C8).
8. Open after this revision: Kaufmann's 1901-03 table; Barkla 1904; Thomson's 1922 paper; Reynolds 1879 and Knudsen as primary papers; deep reads 7 and 8 above; Part I of the vortex essay; whether Thomson ever withdrew the two-carrier claim. [corrected 2026-10-09: "deep reads 7 and 8 above" are no longer open; they are done and weighed in section 10. The cited Haga-Wind, Wind and Marx papers themselves remain unread.]