Heaviside: Arbiter (Step 3)

Inputs: facts.json, claims.md, physicist.md, mathematician.md, contrarian.md; updated 2026-10-05 with sites.md, research/ and the three reviewers' "Investigator findings (2026-10-05)" sections (see the section of that name below). I re-read the page images (Electromagnetic Waves pp. 139, 142, 143) myself and recomputed the numbers where reviewers differed. Tags: [read], [web] URL, [memory] with confidence.

Source gap (repeated from Step 1)

The folder holds only three saved Google Books viewer pages with nine page images: contents of Electrical Papers Vol. 1, contents of Electromagnetic Theory Vol. 1, and pp. 139, 142, 143 of a Phil. Mag. paper reprinted in Electromagnetic Waves. No full text of any work was read. Only claim 4 rests on pages actually read. Claims 1, 2, 3, 5, 6, 7 rest on contents headings plus [web] (Wikipedia) and [memory]. To review properly obtain: Electromagnetic Theory Vols. 1-3 (1893, 1899, 1912), Electrical Papers Vols. 1-2 (1892), and the 1888-89 Phil. Mag. papers (public domain; Internet Archive / Wikisource).

Update 2026-10-05. The Investigator has now read parts of Electrical Papers Vol. 2, Electromagnetic Theory Vols. 1-3 and the 1902 Britannica "Telegraphy" article on archive.org (nothing was saved to research/files/, so every quotation is the Investigator's transcription of OCR text, [web]). The gap is partly closed: claims 3, 5, 6, 7a, 7b and 7c now have primary text, but no formulas for 7a or 7b, and none of eqs. (47)-(48), have been read from a page image, and claims 1, 2 and 4 gain nothing. I fetched the Electromagnetic Theory Vol. 1 OCR text myself for one check (see "Investigator findings"). Claim 4 is still the only claim whose mathematics was read from page images.

Reconciled disputes

1. The "3/2 H1" glyph on p.143 (physicist: unresolved; mathematician: unresolved; contrarian: read as 3/2). I enlarged the image. It prints "The H disturbance is made 3/2 H1, the E reduced to 1/2 E1 on the transmission side" [read: page image p.143]. The contrarian's reading is correct. The sentence admits two readings: from eqs. (60)-(62) with E2/E1 = 1/2, the transmitted fields are H2 = H1/2 and E2 = E1/2. The 3/2 is the total H on the incident side (H1 + H3 = H1 + H1/2), where E is also 1/2 E1 by continuity. Check: jump in H across the sheet = 4 pi k1 z E2 = H1, and with 2 pi mu k1 z v = 1 this equals 2 H2 = H1. Consistent. So: no error in the equations. If "on the transmission side" governs both clauses, the H clause names the wrong side; if it governs only the E clause (E is 1/2 E1 on both sides by continuity, H is 3/2 H1 at the incident face), the sentence is exact. The printed text does not decide between the two readings, so I record it as ambiguous phrasing, not as an error by Heaviside (revised 2026-10-05). The "persistence of H, dissipation of E" remark refers to this incident-side build-up.
2. Eq. (63) number. Recomputed: 2 pi x 3e10 / 1600 = 1.178e8 per cm, z = 8.488e-9 cm = (8/3 pi) x 1e-8 exactly. SI cross-check z = 2/(sigma Z0) = 9.15e-9 cm with sigma = 5.8e7 S/m (resistivity 1.724e-8 ohm m), Z0 = 376.7 ohm; the ~7% gap is Heaviside's rounded k1 = 1/1600 against the modern 1/1724 (8% difference in k1). All three reviewers agree. All also agree z ~ 0.085 nm is below an atomic spacing (~0.25 nm [memory, high]), so (63) is a valid thought-experiment formula, not a prediction for a real foil. Energy audit (mathematician): for E2/E1 = 1/2, power transmitted 1/4, reflected 1/4, absorbed 1/2. Confirmed.
3. Physicist vs mathematician on claim 5 (Established vs Historically superseded). Not a factual dispute; they judged different things. Outputs: correct and verified by later theory (Bromwich; Laplace transform). Method as Heaviside practised it: unrigorous, superseded. I give a split verdict.
4. Claim 2 (Established vs split). The mathematician is right: the integral statement is tested constantly; E x H as a local flow is fixed only up to adding the curl of a vector field (div curl A = 0), so point-by-point static flow is a convention no measurement fixes. Split verdict.
5. Claim 6 date (1923 vs 1924). Checked [web] https://en.wikipedia.org/wiki/Kennelly%E2%80%93Heaviside_layer : Appleton showed existence in 1924 (Nobel 1947); Breit and Tuve mapped altitude 1925; Appleton and Barnett published direct evidence December 1925. The Heaviside article says "confirmed in 1923" [web] https://en.wikipedia.org/wiki/Oliver_Heaviside. The two Wikipedia pages disagree; I use 1924 and treat 1923-25 as the window. Does not affect the verdict. (Updated 2026-10-05: Bruton 2018 gives Appleton's experiments as begun in late 1924 and the IET archives blog says he demonstrated the layer in 1924 [web, via Investigator: https://royalsocietypublishing.org/rsta/article/376/2134/20170454/115714/From-theory-to-engineering-practice-shared ; https://ietarchivesblog.org/2023/04/05/from-under-the-sea-to-the-edge-of-space-the-work-of-oliver-heaviside/]. Two further sources favour 1924; the "1923" remains unexplained.)
6. Gravity Probe B and "confirmed" gravitoelectromagnetism. The Heaviside article says his 1893 extension "was confirmed by Gravity Probe B in 2005" [web, same URL]. The GEM article says only that Heaviside published the analogy "differing only by some small factors" from the later GR form, and that GP-B gave "direct evidence of frame-dragging consistent with ... general relativity" [web] https://en.wikipedia.org/wiki/Gravitoelectromagnetism. GP-B final results: frame dragging -37.2 +/- 7.2 mas/yr against GR -39.2 (about 19% uncertainty); geodetic -6601.8 +/- 18.3 against -6606.1 [web] https://en.wikipedia.org/wiki/Gravity_Probe_B. So GP-B tested GR's gravitomagnetism, not Heaviside's 1893 equations; "confirmed" is overstated. Physicist and mathematician flagged this [memory, medium]; now [web]-checked. (The "about 19%" is my reading of 7.2/37.2; the 15% figure on that page is an earlier-stage statement.)
7. Heaviside condition minimum. Contrarian says alpha = R/(2 Z0) + G Z0/2 is minimised at Z0 = sqrt(R/G), i.e. R/L = G/C. I computed with R = 0.1 ohm/km, G = 1e-6 S/km, C = 5e-8 F/km (L = RC/G = 5 mH/km): alpha = 3.95e-4 (L/4), 3.35e-4 (L/2), 3.162e-4 = sqrt(RG) (L), 3.35e-4 (2L), 3.95e-4 (4L) nepers/km. Confirmed: minimum at the condition. This also vindicates the mathematician's caveat that "inductance reduces attenuation" holds only up to the balance point. (This formula is the low-loss approximation.)
8. Claim 3 testing record. Contrarian's [web] items checked: Preece blocked the 1887 paper that proposed loading coils [web] https://en.wikipedia.org/wiki/Oliver_Heaviside ; Campbell's first demonstration on a 46-mile cable 6 Sept 1899; Pupin filed Dec 1899; Pupin paid $200,000 by Jan 1901 and $455,000 in total (Wikipedia; the Investigator found two other figures, "over $400 000" (IET blog) and $500,000 (Hunt 2012, who calls the circumstances "somewhat shady"); no primary AT&T/Pupin contract seen, so the total is not settled); Krarup's continuous loading 1902; Heaviside proposed discrete inductors in 1893 [web] https://en.wikipedia.org/wiki/Loading_coil. On Preece's motive, the Heaviside article states: "Preece's motivations in suppressing Heaviside's work were more to do with protecting Preece's own reputation and avoiding having to admit error than any perceived faults in Heaviside's work" [web, same URL, re-checked 2026-10-05]. That is a published secondary account; its primary basis is not cited in what I read, so I report it as that article's characterization and weigh it beside the documented facts that Preece had publicly committed to the opposite view and held the power to block (see claim 3).
9. Count of equations. "Twenty replaced by four" is loose. [web] Wikipedia: twelve of the original twenty equations in twenty unknowns reduced to four in two unknowns (1884). Corrected below.
10. Eqs. (58)-(59) sign. H = -e/2 mu v printed [read: p.142]. The mathematician finds +e/2 mu v under his sign convention; this depends on orientation and impressed-force conventions, not an error. Magnitudes and the left/right emission agree.
11. Eqs. (47)-(48). All three agree: Bessel-J0 form, structurally consistent with the damped (telegraph) wave equation; no reviewer verified prefactors (s, q, a defined on pp. 136-138, absent). Heaviside himself writes he leaves the "proof of (42) to (48)" to the reader, though "very laboriously worked out", and thinks the solutions "more likely to have been given before ... than to be new" [read: p.139]. Left at "Plausible, untested" (scale name; the check not yet done is a calculation).
12. Minor: the p.142 running head is "Forced Vibrations of Electromagnetic Systems" while pp.139/143 read "on Electromagnetic Waves, and the ...": one long Phil. Mag. paper whose bibliographic details were not verified here [memory, medium: 1888-89].

Per-claim arbitration

Where the reviewers agree on a claim I say so and give the single check that would settle any residue.

Claim 1: Maxwell's theory in four vector equations

• Agree: all three, Established. Disagree: none.
• Four questions: (a) consistent; (b) matches all classical EM; (c) tested daily and by Hertz 1887-88 [memory, high]; (d) nothing changes.
• Contrarian's tested/untested split: tested continuously. It is a reformulation with identical predictions. Priority/credit shared with Gibbs for vector analysis [memory, medium, not needed].
• Caveat (mathematician): dropping the potentials is a classical convenience; the Aharonov-Bohm effect shows potentials matter in quantum mechanics [memory, high].
• Verdict: Established.

Claim 2: field energy flows as E x H

• Agree on Established; mathematician adds the curl ambiguity and the contrarian notes Heaviside himself flagged sec. 73 ("Uncertainty regarding ... Electromagnetic Stress"), sec. 79 and the "gravitational difficulty" sec. 68 [read: contents]. Independent derivation with Poynting: [web] https://en.wikipedia.org/wiki/Oliver_Heaviside.
• Stronger argument: the mathematician's split, because it is a mathematical fact (div curl = 0) that no reviewer disputes.
• Verdict: Established for the integral/conservation statement (tested); Not testable as stated for the local flow direction in static configurations.

Claim 3: added inductance helps; Heaviside condition; Preece wrong

• Agree: Established. All three cite the same record.
• Contrarian's category: dismissed without testing (1887, blocked by Preece), then tested and confirmed (1899 onward) by an industrial lab, with replication across companies and countries. Credit and money went to others.
• Interested parties, each reported as that party's position with its stake (added 2026-10-05; all [web] https://en.wikipedia.org/wiki/Oliver_Heaviside and https://en.wikipedia.org/wiki/Loading_coil , re-checked 2026-10-05):
• Preece (Post Office; senior official who had publicly committed to the opposite view, and superior of Heaviside's co-author Arthur). His stated position: "Preece had recently declared self-inductance to be the great enemy of clear transmission." He blocked the paper "because part of the proposal was that loading coils (inductors) should be added". The Heaviside article attributes the block to reputation-protection (quoted in dispute 8) and quotes an unnamed author calling Preece "a powerful government official, enormously ambitious, and in some remarkable ways, an utter blockhead": a hostile characterization, kept as such. Heaviside "never succeeded in persuading the British GPO to take up the idea" (Loading coil page): the Post Office record here is non-adoption, not a failed test.
• AT&T (stood to profit from the technique; later owner of the patents). "In 1897, AT&T employed one of its own scientists, George A. Campbell, and an external investigator Michael I. Pupin to find some respect in which Heaviside's work was incomplete or incorrect." AT&T's engineers "estimated that they stood to save $700,000 in new installation costs in New York and New Jersey alone"; it is estimated AT&T "saved $100 million in the first quarter of the 20th century." AT&T bought an option on Pupin's patent "Fearing that there was a risk that the battle would end with the invention being declared unpatentable due to Heaviside's prior publication": a commercial party's own reasoning that recognises Heaviside's priority.
• Pupin (patentee, paid $455,000 in total). "Pupin himself claims that he first thought of the idea of loading coils while climbing a mountain in 1894, although there is nothing from him published at that time." This is Pupin's own account, with a direct financial stake; the page records no 1894 publication, and Heaviside's 1887 and 1893 proposals precede it.
• Heaviside (no patent, no payment). "Heaviside never patented his idea"; AT&T "offered Heaviside money in exchange for his rights", and he refused, "declining to accept any money unless the company were to give him full recognition"; "Heaviside was chronically poor". This verifies the physicist's [memory, medium] note that Pupin was paid and Heaviside was not.
• Investigator update (2026-10-05; weighed in the section below): Heaviside's own 1887 text is now on record. All three reviewers re-derived it independently and agree: V = e^(-Rt/L) f(x - vt) solves the telegrapher equation exactly when R/L = G/C; energy is half electric, half magnetic and dissipation half in the wire, half in the leak; and attenuation is minimal at that same balance (mathematician, numerically: minimum at L = 4.9996 mH/km against RC/G = 5 mH/km at three frequencies). Three points change the story: (i) the condition was in print, in Heaviside's name, in The Electrician in 1887, twelve years before Campbell's 1899 test, so \"dismissed without testing\" describes the gatekeeping of the joint paper with Arthur and of the Electrician series, not an absence of publication; (ii) the date of the coil proposal is not fixed by any primary text read (Hunt: coils at intervals in the 1886-87 work; Wikipedia and Grace's Guide: 1893; the 1887 section shows raised inductance by wire spacing and iron, not coils); (iii) the mechanism of the block is reported two ways (below).
• Link to claim 5: the Loading coil page says Heaviside found the condition "By applying his operational calculus" to the line network (1887) [web]. The engineering success of claim 3 is therefore also a use of the method whose rigour was disputed.
• The block, as the new sources describe it (all [web, via Investigator]; each is reported as that source's account):
• Before submission: Hunt 2012 (Physics Today, historian) and Bruton 2018 (Science Museum curator, citing IET archives): the April 1887 joint paper for the Journal of the Society of Telegraph Engineers needed clearance from Arthur's superior Preece, who "promptly declared the paper worthless and blocked it".
• Rejected by the Society: the 1925 IEE obituary (Grace's Guide; written by an admirer): Preece's circle "caused his papers and those of his brother ... to be rejected by the Society of Telegraph Engineers".
• Heaviside's belief: Grace's chronology says he "suspected" Preece; EMT1 sec. 1 says the Electrician series stopped for "pressure on space and the want of readers ... Perhaps there were other reasons ... We do not dwell in the Palace of Truth"; EP2 Art. 38 ("Mr. W. H. Preece on the Self-Induction of Wires", dated 24 Sept 1887 but "now first published" in 1892): "Mr. Preece is wrong, not merely in some points of detail, but radically wrong".
• Editor: Hunt (citing Mahon 2009, p. 79): the editor Biggs, a supporter, declined Heaviside's anti-Preece letters for fear of libel and was "abruptly removed" in October 1887, "a move he later hinted was prompted by his support for Heaviside". This is Biggs's own hint in one secondary source; no second source seen.
• A second blocked item: Bruton, from IET notebook SC MSS 005/I/1/12: Parts VIII and IX(?) of "On the Self Induction of Wires" "declined by the Philosophical Magazine and blocked by Preece, and partly published in The Electrician".
• Preece's own position (party with a stake: a public position, a costly iron-to-copper change justified by it, seniority over Arthur): IET SC MSS 022/VII/526, a pencil draft reply to Kelvin (catalogue description only; the letter was not read): "Heaviside and his dreadful twaddle", "calculating Kelvin's formula to show that he is correct and Heaviside is wrong", and "drawing room philosophers like Oliver Heaviside and Sylvanus Thompson".
• Complications: Kelvin to Preece, 12 July 1887 (SC MSS 022/VII/535): a Heaviside Phil. Mag. footnote "should not have appeared as it was so ill natured" (cataloguer's wording), though Kelvin praised the propagation theory in his 1889 IEE address and helped it into the Phil. Mag. (Hunt). 1873: Preece to Culley on Heaviside's duplex paper, "most pretentious and impudent ... He must be met somehow"; Culley: "We will try to pot Oliver somehow" (Bruton, citing an archive; letters not seen). Heaviside's paper had not cited Preece's 1855 duplex patent. Arthur later sided with Preece on loading; Heaviside in 1922 (his characterization): "AWH was very afraid of P ... The greatest mistake AWH ever made was to throw me overboard" (SC MSS 068).
• Heaviside's own pre-1899 evidence and caveat (added after QE, 2026-10-05; EP2 Sec. XL, p. 122, [web, via Investigator: https://archive.org/details/electricalpapers02heavrich]): for: he cites reports of good long-distance telephony on copper-covered steel wires, where current entering the steel "lowers the resistance and increases the inductance", offered cautiously ("I do not wish to magnify its importance"); this is his report of others' practice, not an independent controlled test (mathematician, contrarian), and it is raised inductance by iron, not coils. Against, or at least a limit he flagged himself: carried to an impracticable extent the method "could make the amplitude of sinusoidal currents received at the distant end of an Atlantic cable greater than the greatest possible steady current from the same impressed force -- an unbelievable result", which he blames on to-and-fro reflections ("This is to be avoided"). Reviewers' reading: physicist, plausible as a resonance effect, not verified; mathematician, a standing-wave resonance on a mismatched finite line, "mathematically ordinary, not a paradox", his specific case not computed; contrarian, "a candid caveat, not an error I can find". I agree: a resonance can raise one frequency's received amplitude above the DC steady value, so the statement is not self-contradictory, and it is a warning against over-loading, consistent with the "critical value of the inductance" in the same section. Unchecked numerically for his case.
• Arthur's observations and experiment (added after QE, 2026-10-05; EP2, reported by Oliver, [web, via Investigator, research/2026-10-05-archive-org.md section B]): A. W. Heaviside's observations of oscillations on telegraph lines that made ABC indicator pointers jump prompted part of the induction work (EP2 pp. ~120s), and his tube-return experiment found no inductive action outside the tube (EP2 pp. ~185-186). A witness account and an experiment by Arthur, known only through Oliver's text; no reviewer weighed them. They document the brothers' collaboration on line induction before the 1887 block; the tube result (no field outside a closed coaxial return) is what textbook electromagnetism predicts for equal and opposite currents [memory, high], and it may bear on the 1880 coaxial patent no. 1407 (below; my inference, no source links them).
• Weighing: the reviewers agree that Preece obstructed publication; the sources differ on the mechanism and I do not choose between them (deciding records: STE council minutes 1887; notebook 005/I/1/12). On why, I keep two readings open. Reputation and stake (the Heaviside article's characterization; the 1873 exchange; Preece's public position) are documented as stakes. A model difference is also consistent with the one primary glimpse we have: Kelvin's 1855 formula is the L = 0, G = 0 (KR law) limit of the telegrapher equation, correct for slow cable signalling and wrong for voice frequencies, where omega L exceeds R (physicist's numbers: about 12.6 against about 5 ohm/km at 1 kHz for a 2 mm copper wire [memory, medium]). Heaviside's 1887 text itself says the Kelvin theory "wholly ignores inertia". That inference rests on a catalogue description of the draft; both readings may be true at once, and neither is a settled fact.
• Corrected statement: R/L = G/C gives alpha = sqrt(RG), frequency-independent, and distortionless; added inductance lowers attenuation only up to that balance, and constant R, L, G, C fails at high frequency (skin effect).
• Verdict: Established.

Claim 4: wave-plus-diffusion, repeated reflection, perfect reflector (the only claim read)

• Agree on mathematics of eqs. (58)-(62); I rederived (60)-(62): E2 = E1 + E3 and H1 + H3 = H2 + 4 pi k1 z E2 with E = +/- mu v H give E2/E1 = 1/(1 + 2 pi mu k1 z v). A perfect conductor: E2 = 0, E3 = -E1, incident-side H doubled, nothing transmitted [read: p.143; derived].
• Disagreement resolved: the 3/2 glyph (see above); the 7% SI discrepancy (conductivity rounding).
• Tested vs not: the physics (skin effect, thin-film transmission, metal reflectivity) is tested continuously [memory, high]. No source names a replication of Heaviside's specific numerical case; none is claimed. His "repeated internal reflexion" picture is an equivalent reformulation, used in transmission-line analogues of multilayer films [memory, medium].
• Contrarian's rigour point on Heaviside: eqs. (47)-(48) asserted without proof (Heaviside says so himself and calls the working "very laborious"); the "transmission side" sentence is ambiguous (two readings, one exact; see dispute 1); eq. (63) is below atomic scale, which Heaviside presents as a calculation for a sheet, not as a claim about real foil.
• Verdict: Established for eqs. (60)-(62), the diffusion limit and the perfect-reflector statement; eq. (63) Established as a formula, not as a physical prediction at 0.085 nm; eqs. (47)-(48) Plausible, untested (form checked only; the full check is a calculation no reviewer has done).

Claim 5: operational calculus

• Disagree on label only (see dispute 3). Heaviside's expansion theorem is a special case of the inverse Laplace transform for rational functions [memory, high]; Bromwich contour-integral justification [web] https://en.wikipedia.org/wiki/Oliver_Heaviside ; distribution theory (Schwartz, 1940s) [memory, medium].
• Contrarian's category: resisted over rigour and validated later by theory and use.
• How it was resisted (added 2026-10-05): Heaviside sent "On Operators in Physical Mathematics" to the Royal Society in 1892-93; Parts I and II were printed (Part II: [web] https://archive.org/details/philtrans01936980 ; Part I: [web] https://gwern.net/doc/math/1892-heaviside.pdf), and the third part was refereed and rejected. Secondary accounts give the referee's ground as his use of divergent series, "dismissing their apparent tendencies to infinity while producing accurate results", and report Heaviside's reply that, handled properly, his methods "gave demonstrably right answers, and that ought to be justification enough" [web, search summary of https://physicstoday.aip.org/features/oliver-heaviside-a-first-rate-oddity and https://deadreckonings.com/2007/12/07/heavisides-operator-calculus/ ; wording not checked verbatim against either page]. The rejection is the stated position of an institution's referee, reported as such; the referee report itself was not seen. My earlier line "Heaviside's own divergent-series use was not always safe [memory, medium]" named no failing case and is withdrawn: no source read here shows a wrong result from his method. Whether any of his divergent-series results needed correction is left open (see Open questions).
• Investigator update (2026-10-05): Hunt 2012 (verbatim, Physics Today https://physicstoday.aip.org/features/oliver-heaviside-a-first-rate-oddity): "pure mathematicians objected to the cavalier way he handled divergent series, and when he submitted a third installment, it was sent to a referee and rejected"; this checks the earlier search-summary version against the page. A Google snippet of Hunt's 1991 chapter names the referee as William Burnside (Royal Naval College, Greenwich); the chapter and the referee's report (Royal Society RR series) have not been opened. Heaviside's answer in print is now his own: EMT2 sec. 425 (p. ~434), "if investigations of this matter are not good enough for Another Place, how can they be good enough for Electromagnetic Theory? ... the wet blankets of rigorists", and EMT2 p. 9, "Shall I refuse my dinner because I do not fully understand the process of digestion? No, not if I am satisfied with the result." [web, via Investigator: https://archive.org/details/electromagnetict02heavrich]. A secondary source (deadreckonings.com, snippet) says Vol. 2 contains a modified Part III. Weighing: the physicist (Established) and mathematician (Historically superseded but instructive) are again judging different things, the outputs and the justification. The referee's objection was to the argument, not to wrong results; Heaviside's reply is a test by outcome, which the mathematician rightly notes works until it does not, but no source read here shows a failure. A refusal by a referee with the content later in print is a milder case of resistance than a blocked outlet; the report itself is the missing record.
• Verdict: Established (outputs correct, confirmed by Laplace-transform theory and routine engineering use); Historically superseded but instructive (the unrigorous method itself). Source gap: the folder shows only one use of the operator, "let p = ni" (p.142, tying p = d/dt to phasors) [read: page image p.142]; the expansion theorem itself is not in the folder.

Claim 6: reflecting ionised layer

• Agree: Established. Mathematician's check: f_p = 8.98 sqrt(n) Hz; n = 1e11 m^-3 gives 2.84 MHz [memory, high for formula; recomputed: 8.98 x 316228 = 2.84e6].
• Contrarian's earlier category: predicted 1902 (Kennelly and Heaviside, independently); not tested until Appleton 1924 (Nobel 1947), with Breit and Tuve 1925; a prediction vindicated, not suppressed. Not discussed on any saved page. Revised 2026-10-05 on the primary text (below).
• Investigator update (2026-10-05). The 1902 text: Encyclopaedia Britannica 10th ed., vol. XXXIII, "Telegraphy", I. Theory (pp. ~213-215): "There may possibly be a sufficiently conducting layer in the upper air. If so, the waves will, so to speak, catch on to it more or less. Then the guidance will be by the sea on one side and the upper layer on the other." [web, via Investigator: https://archive.org/details/in.ernet.dli.2015.209824]. The author's initials are OCR-garbled (likely Heaviside, not confirmed); the 1925 IEE obituary says he put "sarcasms, in a veiled form" into the concluding part of this article (obituarist's claim, not checked). Kennelly, "On the Elevation of the Electrically-Conducting Strata of the Earth's Atmosphere", Electrical World and Engineer 39(11): 473, 15 March 1902, is cited by search results and by Bruton (Kennelly March 1902, Heaviside December 1902); no reviewer, the Investigator or I have read Kennelly's text.
• Weighing. All three reviewers agree on the facts: the sentence is tentative ("may possibly"), it describes guidance between two conductors, not reflection, and on the citation dates it follows Kennelly by about nine months. They differ on the label for Heaviside's part: physicist, a correct early qualitative proposal (guidance between sea and conducting layer is physically sound for very-low-frequency waves, the Earth-ionosphere cavity, Schumann resonances [memory, high]; long-range short-wave propagation is refraction and reflection from electron-density gradients [memory, high]); mathematician, a parallel-plate waveguide analogue whose mechanism differs from the plasma-frequency reflection his earlier check concerned, "Plausible but not shown" for the credit claim; contrarian, "Plausible, untested in the form stated" with "the reflection form is Kennelly's and later Appleton's". I take the physicist's and mathematician's facts and set the contrarian's last clause aside: it assumes a content for Kennelly's paper that nobody has read, so it is not yet a finding. On the verdict scale the layer's existence is Established; Heaviside's 1902 sentence is a priority question rather than a separate testable claim, so I do not give it a scale verdict and record it as stated: tentative, qualitatively right for guidance, silent on reflection, second by publication date on citation data, credit shared (as the name Kennelly-Heaviside layer already does). claims.md's "explains long-distance radio" is stronger than the 1902 text.
• Whether Heaviside wrote earlier or later on the layer (the Wikipedia Heaviside article's "confirmed in 1923" sentence assumes a prediction) is not known from what has been read.
• Verdict: Established for the layer (Appleton 1924-25, Nobel 1947); Heaviside's own 1902 text: tentative guidance proposal, published after Kennelly (per citations), credit shared.

Claim 7: minor positions

• 7a, force on magnetised matter "probably wrong" (sec. 83): only a heading was read. Three reviewers: not assessable. Modern note: different force-density expressions (Kelvin, Helmholtz, Maxwell stress) give the same total force on a body [memory, medium; unverified], so "Maxwell wrong" may partly be a choice of model. Category: never assessed here; no source on testing. Verdict (revised 2026-10-05): Never properly tested (on this record; argument unread). (Updated later the same day: the argument has now been read in transcription; see "Investigator update" below, verdict kept with a narrower statement.) Earlier verdict was "Not testable as stated (from these sources)". That misapplied the scale: the heading states a definite physical claim (that Maxwell's force expression for intrinsically magnetised matter is wrong), and force on a magnetised body is measurable, so the claim is testable in principle. What was missing was our reading of it, not testability. No test of Heaviside's alternative is on record in any source seen; that is silence in a thin record, not evidence of a failed test, and his own sec. 79 heading suggests the total force may agree with Maxwell's while the internal distribution differs (in which case only an internal-stress measurement could separate them).
• 7a Investigator update (2026-10-05). His argument (EMT1 sec. 83, pp. 103-104; heading "Difficulty. Maxwell's Solution probably wrong"), as transcribed [web, via Investigator: https://archive.org/details/electromagnetict01heavuoft]: the resultant force on a magnet may be had from the surface stress outside, but "it is impossible that the real forcive can be represented merely by the surface traction"; to get it "we must go inside the magnet. This can only be done hypothetically, and with precarious validity"; Maxwell's way "I believe to be quite erroneous for many reasons, the principal being that it does not harmonise with his scheme generally, and that it lumps together intrinsic and induced magnetisation, which have essential differences and are physically distinct." All three reviewers read this the same way: the total force on a body is not in dispute; his objection is to the internal force distribution and to merging permanent and induced magnetisation (mathematician: M = M0 + chi H, with force densities differing in the M0 part). This makes the earlier worry that "Maxwell wrong" might be partly a choice of model a sourced reading rather than my memory. Reviewers' labels: physicist and mathematician keep "Not testable as stated" (total-force measurements cannot separate the formulations, and his own text calls the internal route hypothetical); contrarian "Never properly tested". I keep Never properly tested: the physicists' reasoning shows that the measurements usually made (total force) cannot decide it, not that none could (an internal-stress or strain measurement in a permanent magnet is possible in principle, confounded in real materials by magnetostriction, physicist), and no such measurement is on record. It was not dismissed after a test; no test exists. The narrowed claim is: Maxwell's treatment of the internal force on intrinsically magnetised matter is wrong because it conflates intrinsic and induced magnetisation. His formulas are still unread (OCR garbled; EMT1 pp. 103-107 need page images), so his alternative is unchecked.
• 7b, gravity-EM analogy (1893): The Heaviside article states it "was confirmed by Gravity Probe B in 2005" [web, re-checked 2026-10-05]; the GEM article says Heaviside's form differs from the later GR form "only by some small factors" [web]. Weighed: GP-B's published comparison is with GR's prediction (frame dragging -37.2 +/- 7.2 mas/yr against -39.2), and no source seen compares it with Heaviside's 1893 factors, so "confirmed" is stronger than the sources show; but neither does any source show GP-B disagreeing with his form. Whether his factors fall inside GP-B's ~19% band is an open calculation (see What would settle it). Verdict: Historically superseded but instructive.
• Investigator update (2026-10-05). Sec. 68 (EMT1 p. ~75): "we are entirely ignorant of its distribution in the ether, and of its mode of transference": the "gravitational difficulty" is that gravitational energy has no known flux, unlike E x H for electromagnetism; it is not a flaw in the Poynting flux. Appendix B (The Electrician, 1893, pp. 455-466 in EMT1): gravity propagated at finite speed v through the ether; "no aberrational effect, but only a slight alteration in the intensity of force", weaker along the line of motion, stronger equatorially, "the direction is still radial".
• The power of ten (all three reviewers flagged it). The Investigator's notes give u = 3 x 10^6 cm/s and (u/v)^2 = 10^-6; with v = 3 x 10^10 cm/s that is 10^-8, not 10^-6. I fetched the archive.org OCR of EMT1 myself [web: https://archive.org/download/electromagnetict01heavuoft/electromagnetict01heavuoft_djvu.txt, App. B, near p. 464]. The line for u reads "u = 3 x 10^ centim. per sec." with the exponent missing in the OCR, so the Investigator's "3 x 10^6" was not read from the text. The text then says the value of u "is not very different from the speed attributed to fast stars", that v is the speed of light, that the ratio squared is "one-millionth", and that Sun-Earth attraction rises by "one two-millionth part". Those three printed statements are consistent with u = 3 x 10^7 cm/s (300 km/s), not with 3 x 10^6. So the likely reading is that the exponent is 7 and that the Investigator's note (and the "30 km/s" in sites.md) slipped; a page image of App. B would settle the printed exponent. Internal consistency of Heaviside's own text is not in doubt on what I read.
• Reviewers' reading "no frame-dragging prediction seen" is incomplete. Part I of the same article (my reading of the same OCR, pp. 457-459) does build the magnetic side of the analogy: matter in motion, pu, is "analogous to a convective current of electrification"; a circuital flux C = rho u - c e is formed; a field h follows the lines of latitude around a moving particle; and the energy flux E x H becomes "Veh", with "a reversal of direction ... since the radial e is directed to instead of from the centre ... This reversal arises from all matter being alike and attractive, whereas like electrifications repel one another." So the structure the claims.md phrase "giving gravitoelectromagnetism" names is in the primary text. What I did not find, in the passages I read, is a gyroscope or rotating-body (frame-dragging) calculation, and the equations are garbled in OCR, so I have not checked coefficients. The physicist and contrarian's "true in structure only" is therefore supported; the mathematician's "general analogy Plausible, untested in his form" is fair.
• Weighing the verdict. Mathematician: moved to Historically superseded but instructive for the 1893 model, general analogy Plausible, untested; physicist and contrarian: unchanged. My verdict was already Historically superseded but instructive; I keep it, and keep the mathematician's second part as a note. "Confirmed by Gravity Probe B" (Wikipedia's wording) remains stronger than any source shows: GP-B compared GR frame dragging and geodetic effects with measurements, nobody has compared Heaviside's coefficients with them, and what Heaviside wrote about (u/v)^2 intensity changes is not frame dragging. Nothing seen shows GP-B disagreeing with his form either.
• 7c, opposition to relativity: "Heaviside was an opponent of Albert Einstein's theory of relativity" [web] https://en.wikipedia.org/wiki/Oliver_Heaviside . The page quotes the historian of mathematics Howard Eves that he "was the only first-rate physicist at the time to impugn Einstein, and his invectives against relativity theory often bordered on the absurd": Eves's characterization, kept as his (it also records Eves ranking Heaviside "first-rate"). His arguments are not in the folder, so their content is unknown. Relativity's own test record is extensive (time dilation, GPS timing, light bending) [memory, high]. Reviewers differed and all three views stay on record: physicist "Not assessable from the folder" (with Tested, not supported for relativity-opposition generally); mathematician "Historically superseded but instructive"; contrarian "Not testable as stated" with "Tested, not supported" as far as the record shows. Verdict: Not testable as stated (his specific argument unread). Unlike 7a, here even the content of the claim is unknown ("opposition" is not a proposition one can test), so the scale fits. (Investigator update 2026-10-05: EMT vol. 3 (1912), OCR keyword counts [web, via Investigator: https://archive.org/details/electromagnetict03heavuoft]: "Einstein" 0, "Minkowski" 0, "relativ" 21 (including "the principle of relativity of motion" for a moving ether; page not identified), "Lorentz" 30, "FitzGerald" 15; sec. 473 is "Lorentz's Equations of a Moving Dielectric" (5 Oct 1900). So the Wikipedia/Eves invective is not in a published volume read; it may be in the unpublished fourth-volume notes (2003 AMS Chelsea edition, lending-only, not opened), Nature letters 1903-1905 (listed, not read) or letters. The physicist keeps "Not assessable", the mathematician and contrarian "Historically superseded" and "unchanged"; I do not infer a view from a keyword count (OCR can hide a name, and vol. 3 largely collects earlier work). Hunt adds that Foeppl's 1894 textbook carried Heaviside's form of the equations, "from which Albert Einstein, among others, would learn electromagnetic theory", and Russell (Nature 1925, an admirer) says he "was one of the first to predict the increase of mass of a moving charge": records of his relation to relativity's ancestry, kept without weighing.) Later relativity tests bear on whatever physical prediction he may have made, but which tests are relevant cannot be said until his Vol. 3 remarks are read.

Tested / never tested / dismissed (contrarian's distinction, kept visible)

The contrarian's honest limit stands: this is a vindication story, so it is no evidence that outsiders are generally right. His confirmed claims were conventional-physics extensions with clear tests. His anti-relativity position is recorded as opposition whose arguments have not been read; relativity has since passed many tests [memory, high], but what Heaviside actually argued, and so which tests answer it, is not yet known. The record of resistance is also documented here: the 1887 block (claim 3), AT&T's 1897 commission to find fault with his work (claim 3), and the Royal Society referee's rejection of Operators Part III (claim 5); in the first two the resisting party had a stake, and in all three the work was later borne out in use. Added 2026-10-05, applying the same rigour to the inventor: the new records also show provocation on Heaviside's side (the 1873 duplex paper that ridiculed Culley's and Preece's work and omitted Preece's 1855 patent; Kelvin's 1887 remark that a footnote was "ill natured"), a non-uniform resistance (Kelvin later praised his theory), and an editor who stated libel and space reasons; and in claim 6 the primary text is more modest than the claim as worded. None of this removes the documented blocks; it makes the story less one-sided than the vindication version.

Corrected claim list

1. Heaviside (1884) reduced twelve of Maxwell's twenty equations (twenty unknowns) to four vector equations in two unknowns (E, H, with D, B via constitutive relations), by eliminating the potentials. Established.
2. Field energy obeys div S + d(u)/dt = -J.E with S = E x H (Poynting 1884, Heaviside independently); the closed-surface flux is tested, the local S is defined only up to adding a curl. Established / local form not testable.
3. For R/L = G/C a line is distortionless with alpha = sqrt(RG); added inductance helps up to that balance (Heaviside's own 1887 Electrician text states the condition, the exact solution, the half-and-half energy split and the optimum inductance; all re-derived by reviewers); tested from 1899 (Campbell), after Preece blocked the April 1887 joint paper with Arthur before submission (Hunt, Bruton) or caused its rejection (1925 IEE obituary); the coil proposal is dated 1887 (Hunt) or 1893 (Wikipedia, Grace's), not fixed by a primary text read. Established.
4. A thin sheet of conductivity k1 and thickness z transmits E2/E1 = H2/H1 = 1/(1 + 2 pi mu k1 z v) (his units, mu v = 3e10 cm/s); half transmission needs z = 8.5e-9 cm (formula valid, thickness unphysical for bulk copper); at half transmission, the incident side has E = 1/2 E1 and total H = 3/2 H1, and the transmitted H2 = H1/2 (Heaviside's sentence is exact if "on the transmission side" qualifies only E; ambiguous otherwise); a perfect conductor doubles incident-side H and destroys E. Eqs. (47)-(48) plausible, untested (calculation not yet done).
5. Operational calculus gave correct results ahead of proof (including, per the Loading coil page, the 1887 Heaviside condition); the Royal Society refused Part III of "On Operators" over divergent series (referee William Burnside per a snippet of Hunt 1991; report not seen; Heaviside's reply in EMT2 sec. 425 and p. 9); later justified (Bromwich, Laplace). Established outputs; method superseded. The folder shows only the operator substitution p = ni (p.142) [read], not the expansion theorem.
6. Kennelly (Electrical World and Engineer, 15 March 1902; text unread) and Heaviside (Britannica vol. XXXIII, Dec 1902: "There may possibly be a sufficiently conducting layer in the upper air ... guidance by the sea on one side and the upper layer on the other") proposed a conducting layer in 1902; Heaviside's text is tentative, about guidance rather than reflection, and later by citation dates; Appleton showed the layer in 1924 (Breit and Tuve 1925). Established (layer); credit shared. (Not 1923 as claims.md said; Bruton and the IET blog give 1924.)
7. 7a: Heaviside disputes Maxwell's internal force on magnetised matter (conflation of intrinsic and induced magnetisation), not the total force on a body; measurable in principle, never properly tested on this record, formulas unread; 7b Wikipedia's "confirmed by Gravity Probe B" is stronger than the sources show: GP-B was compared with GR frame dragging (about 19% precision), not with the 1893 analogy, and no source compares the two (his App. B does build a moving-mass "h" field and a reversed energy flux, and a (u/v)^2 radial intensity change, with the printed exponent of u probably 7 not 6; no frame-dragging calculation seen); 7c reasons unread (not in vol. 3 by keyword).

What would settle it

• Claim 4 residue (eqs. 47-48): obtain pp. 136-138 for definitions of s, q, a, then check with SymPy that the J0 expressions solve the telegraph equation with the stated initial data and the persistence-of-momentum integral. A calculation, no experiment.
• Claim 2 local flow: no experiment distinguishes S from S + curl A in electrodynamics; settling it would need a gravitational measurement sensitive to local energy flux, none available. A theoretical question.
• Claim 7a: page images of Electromagnetic Theory Vol. 1 secs. 79-85 (pp. 103-107), where the formulas are; then compare his force on a magnet with F = grad(m.B) and the Kelvin/Maxwell force densities for a magnetised body.
• Claim 7b: take page images of EMT1 App. B (pp. 455-466; settles the printed exponent of u and the equations) and compare factors and signs with the linearised GR gravitomagnetic equations; then compute the gyroscope frame-dragging rate his form would predict for GP-B's orbit and set it against -37.2 +/- 7.2 mas/yr.
• Claim 5 resistance: the Royal Society referee report on "On Operators" Part III (RR series; Burnside named by a snippet only) and whether EMT2's modified Part III matches it.
• Claim 3 block: the 1887 Heaviside-Arthur "Bridge System of Telephony" manuscript; Society of Telegraph Engineers council minutes 1887 and IET notebook SC MSS 005/I/1/12 (to decide whether the paper was blocked before submission or rejected); BT Archives (TCB 274/1, POST 30 files); The Electrician 1887 volumes (Biggs's removal); the AT&T/Pupin contracts (the payment total); and the Preece draft SC MSS 022/VII/526 itself (to see whether his objection was a model or a motive).
• Claim 6: Kennelly's 15 March 1902 article (text), to compare mechanism and date with the Britannica passage; the author's initials on that passage; then whether Heaviside wrote on the layer earlier or later.
• Claim 7c: read his relativity remarks (not in the published Vol. 3 by keyword; look in the 2003 Chelsea edition's Vol. 4 notes and the 1903-1905 Nature letters) to find the actual argument, then match it against GPS timing, time-dilation and light-bending tests.
• Priority claims (Poynting, Gibbs, Kennelly): original 1884-1902 papers.

Open questions

• Did Heaviside's energy-flow thinking really anticipate gravitomagnetism, or only resemble it? (Answered in part: the "gravitational difficulty" of sec. 68 is that gravitational energy has no known flux, and App. B builds a moving-mass h field and a reversed energy flux. Whether the coefficients match linearised GR is still open.)
• Did Heaviside's operational calculus give any wrong result in the divergent-series cases the Royal Society referee objected to, and which of his results (if any) needed Bromwich's correction? No source read here names one.
• Was the Preece block an engineering judgement that went wrong, or reputation defence, and was it before submission or a rejection by the Society? The block and Preece's prior public position are documented; the Heaviside article attributes it to reputation-protection; the first primary glimpse (the SC MSS 022/VII/526 catalogue description: "dreadful twaddle", Kelvin's formula) fits both a stake and a model that omitted inductance. The 1873 exchange and Kelvin's 1887 remark are documented complications. The draft itself and the STE minutes have not been seen.
• Is the Wikipedia 1923 ionosphere date a sourced alternative (for example an earlier experiment) or an error? (Bruton and the IET blog give 1924.)
• What did Kennelly's March 1902 paper say, and did either man propose reflection rather than guidance? Nobody here has read Kennelly.
• What is Heaviside's printed formula in sec. 83, and does his intrinsic/induced split give a different internal stress that any measurement could reach?
• Did Heaviside's App. B gravitomagnetic field h yield a rotating-body (frame-dragging) result, and with what coefficients against GR?
• Where did the anti-relativity remarks appear, if not in Vol. 3?
• What is the true total of Pupin's payment ($455,000, over $400,000 or $500,000)?
• Do the 1893 and 1912 volumes contain results in other areas (cable theory, waveguides) that were also ahead of their time? Not covered by the saved pages.

Web-check log (8 budget, 5 calls used)

(Superseded heading: 5 calls at the first Step 3 pass; 8 of 8 after the evidence-rule revision, which made 3 more; then 3 over-budget fetches of the EMT1 OCR in the Investigator update, disclosed below. Total 11.)

Kennelly-Heaviside layer page (dates); Heaviside page (Preece, GEM/GP-B wording, relativity); Gravitoelectromagnetism page; Gravity Probe B page (results); Loading coil page (1899 test, Pupin payments). Update 2026-10-05: the budget was already exhausted, and I made three further fetches of the archive.org OCR of EMT1 (a direct download of the page text the Investigator cites) for two checks only, the exponent of u in App. B and the content of the gravitational analogy; this exceeds the budget and is disclosed. The Investigator's quotations from archive.org, Grace's Guide, IET Archives, Physics Today and Bruton are otherwise [web, via Investigator], not rechecked by me. Not web-checked, left [memory]: Hertz dates, Aharonov-Bohm, copper lattice spacing, Kelvin vs Maxwell force densities, Schwartz distributions, the Phil. Mag. publication year of the Waves paper.

Final verdicts

QE revision (after qe.md, verdict MINOR)

No deep reads were requested, and no web checks were needed (all new evidence is [read] from page images already in the folder, as cited by qe.md). No verdict changed. Wording changes only:

1. Claim 5 (correction of a statement). I wrote "no document in the folder contains the calculus". That is slightly wrong. Electromagnetic Waves p.142, sec. 10 "Effect of Impressed Force", says "In equations (23), (24), let p = ni, where n/2 pi = frequency of alternations" [read: page image p.142]. This is Heaviside's operator p (= d/dt) set to i times the angular frequency for sinusoidal driving, the bridge from operational calculus to phasors. It is a direct but small use of the operator. The expansion theorem and the divergent-series cases are still absent, so the source gap and the split verdict (outputs Established; method Historically superseded but instructive) stand. The claim 5 text, the corrected claim list and the final table are updated.
2. Claim 4 (new supporting detail). p.142 also states the high-frequency limit: as n grows, k and g act only as small attenuation exponents and E and H come into phase [read: p.142], i.e. the low-loss limit. p.143 states the duality: "To produce dissipation of H with persistence of E requires the plate to be a magnetic, not an electric conductor", and that the vorticity of e produces magnetic induction while that of h produces electric displacement [read: p.143]. This supports the reading that the fictitious magnetic conductivity g (balanced against k, as on p.139) is what removes the tail in the distortionless case. Eqs. (58)-(63) and the verdict are unchanged. (Quote taken from qe.md, which verified it against the image; the printed "n2pi" is old typesetting of n/2 pi.)
3. Claim 7a (support, not a change). The Electromagnetic Theory contents (p. xv) list sec. 79, "Resultant Action on Solid Body independent of the Internal Stress, which is statically indeterminate" [read: contents p. xv]. This is Heaviside's own heading for the point I made from [memory, medium] in 7a: different force-density expressions can give the same total force on a body. It also sits beside sec. 73 ("Uncertainty regarding the General Application of the Electromagnetic Stress") and sec. 63 ("The Cardinal Feature of Maxwell's System. Advice to anti-Maxwellians"). Still only headings, so 7a remains Not testable as stated (from these sources) (superseded: changed to Never properly tested in the evidence-rule revision 2026-10-05, item 1), now with the total-force point sourced to a heading rather than memory alone. Sec. 83 ("Maxwell's Solution probably wrong", p.103) may concern a different question, which is unread.
4. Minor housekeeping. facts.json's "sections 20-85, pp. 20-131" for Electromagnetic Theory Chapter II is unverified; the page seen puts sec. 85 at p. 107. No claim depends on it. Step 0 did not OCR the extensionless _files/content(1)-(3) images; this is a tooling gap for the batch owner, not a content gap, since all nine images were read directly.

Records that go quiet (absence of evidence, added 2026-10-05)

(Updated 2026-10-05.) The first Investigator run (sites.md, six research/ notes; 6.5 minutes of searching) has now touched items 1 to 4; its additions are marked "Investigator" below. No deep/ reads exist and nothing was saved to research/files/. Items 5 and 6 are new.

1. The 1887 Heaviside-Arthur paper "Bridge System of Telephony". The record says it was blocked [web] https://en.wikipedia.org/wiki/Oliver_Heaviside and then goes silent: no source seen says whether the manuscript survives or was later printed. Competing explanations: it was never published and is lost; its content was absorbed into Heaviside's later Electrician articles and Electrical Papers (he kept publishing on loading, 1887 and 1893, per the Loading coil page); it survives in Post Office or Arthur family papers. For: Heaviside's later published proposals show the ideas were not lost. Against: no source names the manuscript's fate. Deciding records: BT Archives (Post Office engineering files), IET Archives (Heaviside papers), and Electrical Papers Vol. 2 notes. Investigator update: the manuscript's location is still not stated anywhere seen, but the silence is partly answered. Bruton says its theory went into EMT1 (1893) and the Electrician sections; Heaviside's 1887 Electrician text (EP2 Sec. XL) already states the distortionless condition; Arthur published his part only in his 1900 IEE Newcastle address (Bruton); and notebook SC MSS 005/I/1/12 holds a manuscript copy of "Self Induction of Wires" with notes on the blocked Parts VIII-IX. The explanation "absorbed into later publications" is now supported; "lost" is not excluded for the joint paper as written. Whether the paper was blocked before submission (Hunt, Bruton) or rejected (IEE 1925) would be decided by the STE council minutes: a paper never submitted leaves no council record, which is itself a prediction that can be tested. A separate silence, the Electrician series, has three explanations on the table: space and readership (stated contemporaneously by the editor, per Hunt, and by Heaviside); libel caution (Biggs's stated fear); and pressure from Preece's circle (Biggs's later hint, one secondary source, and the timing with his October 1887 removal). The first two are better documented than the third; none is proved. Deciding records: Electrician proprietors' and editorial papers, the 1887 volumes (HathiTrust, not reached).
2. The fourth volume of Electromagnetic Theory. Vol. 3 appeared in 1912; Heaviside lived to 1925. The Heaviside article lists a 1971 Chelsea edition "Including an account of Heaviside's unpublished notes for a fourth volume" [web, same URL], so work continued but was not published in his lifetime. Competing explanations: poverty, ill health and isolation in his last years (the article calls him "chronically poor") made publication impractical; publishers or journals declined it; the material was incomplete; part of it was lost after his death [memory, low: I recall accounts of papers lost from his house after his death; not found on the page checked, unverified]. Deciding records: the 1971 Chelsea account itself, the IET Archives Heaviside collection, and the biographies (Nahin; Mahon) [memory, medium for the biographers' names]. Investigator update: Russell (Nature 1925, an admirer) says Heaviside planned Vol. 3 for 1904 and a concluding volume for 1910 but "found [this] impossible" and issued the 1912 volume as the "concluding" one, which supports ill health and poverty as the stated reason. Bruton: papers were "discovered under the floorboards of OH's former home in Paignton around 1957" (used by H. J. Josephs of the GPO), so some papers were hidden or left in place rather than lost, and nothing seen shows an effort to preserve them before 1957. The 2003 AMS Chelsea edition with the Vol. 4 notes is on archive.org as a lending item (not opened). I find no evidence of suppression in these records, and none of a preservation effort; the GPO's formal engagement with his work came only after Appleton (1924-25, per Bruton). My earlier [memory, low] recollection of papers lost after his death is replaced by the floorboard find (Bruton), which is a different account.
3. Royal Society "On Operators" Part III. Rejected after refereeing (claim 5); no source seen says whether the text survives or appeared elsewhere. Competing explanations: absorbed into Electromagnetic Theory Vol. 2 (1899), which treats operational methods [memory, medium]; lost; held in the Royal Society archive. Deciding record: Royal Society referee reports and Heaviside correspondence. Investigator update: the referee is named as Burnside (snippet only); Heaviside's reply is in EMT2; a secondary snippet says EMT2 holds a modified Part III. "Absorbed into EMT2" now has some support; the referee report has not been found.
4. Claim 7a, Heaviside's magnetised-matter force. No later discussion found of his "probably wrong" verdict on Maxwell's force. Silence here is expected to be partly explained by the narrowness of the question and by our not having read sec. 83 at all; it is not evidence of a failed test. Deciding record: Electromagnetic Theory Vol. 1, secs. 79-85, and later literature on Kelvin vs Maxwell magnetic force densities. Investigator update: the sec. 83 argument has now been read in transcription, so the silence is narrower (the formulas are unread, and no later discussion of the intrinsic/induced split in his terms has been found).
5. The 1932 GPO report (new). Bruton: "The Application of the Heaviside Analysis to Electrical Engineering Problems", "no copies of which survive". Competing explanations: ordinary loss of an internal report never widely circulated; withdrawal; retention in a GPO or BT file not yet searched. For: its title is known, so it existed. Against: no source says why it vanished. Deciding records: BT Archives and GPO engineering files.
6. Heaviside's Nature letters 1892-1905 and unread own works (new). Listed by the Investigator (for example "The Undistorted Cylindrical Wave", 1903; "The Waste of Energy from a Moving Electron"; "Electromagnetics in a Moving Dielectric", 1905), unread; they are where his relativity remarks may be, so the silence in Vol. 3 is not yet an absence. Deciding records: the Nature volumes and the Vol. 4 notes.

Evidence-rule revision (2026-10-05)

Audit of every claim against the four SOURCE HONESTY rules (no suppression, interested parties, absence of evidence, keep pertinent information). Three new web checks (Heaviside and Loading coil Wikipedia pages fetched; one search on the Royal Society Operators rejection), making 8 of 8 budget used. One verdict changed.

1. Claim 7a verdict changed: Not testable as stated -> Never properly tested (on this record; argument unread). Reason: the earlier label described our failure to read sec. 83, not the claim, which is a definite and in-principle measurable statement about force on magnetised matter. Using "Not testable" read as dismissal by label. Final table, tested/never-tested table and corrected claim list updated.
2. Claim 3, interested parties added. Preece's own stated position ("the great enemy of clear transmission"), his stake and power to block; AT&T's 1897 commission of Campbell and Pupin "to find some respect in which Heaviside's work was incomplete or incorrect", its savings estimates ($700,000; $100 million) and its stated reason for buying Pupin's option (risk of unpatentability "due to Heaviside's prior publication"); Pupin's own 1894 mountain account, reported as his, with nothing published at the time; Heaviside's lack of patent, refusal of payment without "full recognition", and poverty. Previously these were dropped or reduced to "credit and money went to others" [all web, re-checked].
3. Preece's motive: dismissal-by-label removed. "Preece's motive is interpretation, not sourced fact" replaced by a quotation of the published account (Heaviside article) attributed as that article's characterization and weighed against the documented facts; the open question reworded to name the primary records that would decide it. The hostile "utter blockhead" quotation is kept and marked as a characterization.
4. Claim 5, resistance record added and an unsourced negative removed. Royal Society refusal of "On Operators" Part III after refereeing, with the referee's stated ground (divergent series) and Heaviside's reply, reported as each party's position (sourced to a search summary; verbatim not checked). Withdrawn: "Heaviside's own divergent-series use was not always safe [memory, medium]", which named no failing case. Added the Loading coil page's statement that the Heaviside condition was found with operational calculus. Verdict unchanged.
5. Claim 4, "prose slip / mislabel" softened to "ambiguous phrasing". The p.143 sentence is exact if "on the transmission side" qualifies only the E clause; the earlier text asserted an error where the printed text supports a correct reading. Dispute 1, claim 4 and corrected claim list updated. Eq. (63) note now says Heaviside presents it as a sheet calculation. Verdict unchanged.
6. Claim 4, scale wording. "Plausible, unverified" / "Plausible, untested by us" normalised to the scale name "Plausible, untested". Verdict unchanged.
7. Claim 7b, "overstated" reworded. Wikipedia's "confirmed by Gravity Probe B" is quoted as that page's statement and weighed: no source compares GP-B with his 1893 factors either way. Added the calculation that would decide it. Verdict unchanged.
8. Claim 7c, characterizations attributed and an unread position no longer called defeated. The Eves quotation is given in full as Eves's characterization; all three reviewers' differing verdicts are kept on record; the contrarian-limit paragraph's "his anti-relativity stand lost" replaced by a statement that his arguments are unread. Explained why "Not testable as stated" fits 7c but not 7a. Verdict unchanged.
9. Contrarian-limit paragraph now also records the documented resistance episodes (1887 block, AT&T's 1897 commission, Royal Society Part III), noting where the resisting party had a stake.
10. New section "Records that go quiet" analyses four silences (the 1887 blocked paper; the unpublished fourth volume; Operators Part III; the 7a argument) with competing explanations and deciding records, and notes that no Investigator run exists for this project. (Superseded: the Investigator ran on 2026-10-05; see "Investigator findings (2026-10-05)" and the updates in "Records that go quiet".)
11. What would settle it gains three items: GP-B calculation for 7b, Royal Society referee report, and the 1887 manuscript / Post Office file.

Investigator findings (2026-10-05)

Weighed: sites.md "Leads for review", the six research/ notes of 2026-10-05, and each reviewer's "Investigator findings (2026-10-05)" section. The Investigator reports leads, not verdicts, and saved no files, so every primary quotation is its transcription of OCR text; no reviewer opened a source themselves. I fetched the EMT1 OCR text once (see below). Tags: [web, via Investigator] is the Investigator's reading; [web] with my own URL is something I fetched.

Where the reviewers agree. (1) Claim 3: Heaviside's 1887 text is exact and re-derived by all three, and no verdict changes. (2) Claim 6: split. (3) The (u/v)^2 arithmetic in the 7b transcription is wrong as written. (4) 7a: the argument is about the internal force distribution. (5) Claims 1, 2 and 4 gain nothing. (6) The 1887 block is documented in two versions and the deciding records are unseen.

Where they differ, and how I weigh it. - Claim 6, label for Heaviside's role. Physicist: correct, early, qualitative; mathematician: credit claim "Plausible but not shown"; contrarian: "Plausible, untested in the form stated", reflection "is Kennelly's". Facts agree. I take the physicist's and mathematician's description and drop the contrarian's attribution of reflection to Kennelly, because nobody has read Kennelly's paper. The scale does not fit a priority question well, so the claim list states it plainly instead of forcing a label. - Claim 7a. Physicist and mathematician "Not testable as stated"; contrarian "Never properly tested". I keep Never properly tested: what the argument shows is that total-force measurements cannot separate the formulations, not that no measurement could, and no test exists on record. The earlier arbiter revision turned on the same point. - Claim 7b. Mathematician moves it (superseded for the 1893 model, general analogy plausible and untested); the other two leave it. I keep it, and add something none of them reported: Part I of the same article builds the magnetic side of the analogy (see claim 7b above). - Claim 5. Physicist "Established"; mathematician "Historically superseded but instructive": the split verdict stands (outputs against method). - Preece's motive. Reviewers all say the one primary glimpse is consistent with conviction plus stake and with a model that omitted inductance, and they reject neither. I keep both open; the physical statement that Kelvin's formula omits inductance is firm (it is the L = 0, G = 0 limit), the statement that this was Preece's reasoning rests on a catalogue summary.

My own checks. (a) The 10^-6 versus 10^-8 discrepancy is a transcription issue: the OCR has no exponent for u; the printed "one-millionth" and "one two-millionth" fit u = 3 x 10^7 cm/s. (b) Part I of EMT1 App. B has a moving-mass current analogue, an h field and a reversed energy flux (same OCR, pp. 457-459). (c) For claim 3, the algebra is easy to check: V = e^(-at) f(x - vt) with a = R/L removes both the V_t and V terms of V_xx = LC V_tt + (RC + GL) V_t + RG V exactly when GL = RC, as the three reviewers found.

Verdict changes (table).

Material kept in the record whatever it weighs. British patent 1880 no. 1407, "Improvements in Electrical Conductors", to Oliver alone, called by Bruton "essentially the patent for ... a 'coaxial cable'" (recognised by C. S. Bright, Submarine Telegraphs, 1898), specification unread. IET notebook SC MSS 005/I/1/12; Preece's "America Revisited - 1907" proof with Heaviside's MS notes (SC MSS 005/I/2/057); Stevenson correspondence 1897-1921 on "Heaviside's brother's career and being blocked by Preece" (SC MSS 005/I/6/43); other IET records seen only in search results. FitzGerald's notebook, 9 Sept 1888: "Very important ... Must be all in O. Heaviside" (Trinity College Dublin, per Hunt), a contemporary endorsement with no physics content stated. Kelvin's 1889 IEE address praising his propagation theory (Hunt; Grace's Guide). 1925 obituaries (IEE; Russell in Nature) naming Silvanus Thompson and Pupin as early adopters, both by admirers. Wiener's denunciation of AT&T and Pupin "as thieves" (Hunt, citing The Tempter, 1959): Wiener's characterization, and Hunt's "somewhat shady". Heaviside's Nature letters and the unopened Electromagnetic Waves (1889), the full text with eqs. (47)-(48) now located on archive.org (electromagnetic01heavgoog). Added after QE (2026-10-05), bearing on poverty, institutional relations and the outsider story: Hunt 2012 reports that Heaviside refused a Royal Society Relief Fund grant in 1894 and received a civil-list pension from 1896, GBP 120 a year, later GBP 220 [web, via Investigator: https://physicstoday.aip.org/features/oliver-heaviside-a-first-rate-oddity]; the IET archives blog says he had been "expelled previously for not paying his membership fees" before the IEE made him an honorary member in 1908, and Bruton dates the striking-off 1881 [web, via Investigator: https://ietarchivesblog.org/2023/04/05/from-under-the-sea-to-the-edge-of-space-the-work-of-oliver-heaviside/ ; Bruton 2018]; a Google snippet of Mahon 2009 (IET Digital Library) mentions a letter to Bethenod on why he refused the Hughes medal (snippet only; letter and its reason unread) [web, via Investigator, research/2026-10-05-google.md]; Föppl's 1894 textbook carried his form of the equations, from which Einstein among others learned electromagnetism (Hunt; also under 7c above).

Not reached and still needed. Royal Society referee report (RR series); BT Archives TCB 274/1, TCK 89/23, POST 30; HathiTrust The Electrician 1887 (Preece's British Association paper, 16 Sept 1887, p. 400); STE 1887 council minutes; Kennelly 1902 text (ETHW); De Gruyter Hunt 1991 chapter; AIM25 (blocked); the 2003 Chelsea edition with Vol. 4 notes; Yavetz 2011 (snippet only); six more IET records. Source gap: no formulas for 7a, 7b or eqs. (47)-(48) have been read from images.

QE fixes (after qe.md "Investigator update check", 2026-10-05). Text added only; no verdict changed. - QE defect 1 (retention, claim 3): added to claim 3 Heaviside's own cited evidence (copper-covered steel wire, "lowers the resistance and increases the inductance", "I do not wish to magnify its importance") and his self-flagged "unbelievable result" (Atlantic-cable sinusoidal amplitude above the steady current, blamed on reflections), with all three reviewers' readings and mine (resonance, not a contradiction; his case not computed). - QE defect 2 (retention, Arthur's work): added to claim 3 Arthur's ABC-pointer observations and tube-return experiment (EP2 pp. ~120s, ~185-186), reported by Oliver, as a witness account and an experiment; noted that no reviewer weighed them. - QE defect 4 (retention, peripheral): added to "Material kept in the record" the 1894 Relief Fund refusal and the 1896 civil-list pension (GBP 120, later 220; Hunt), the earlier expulsion for unpaid fees (IET blog; Bruton: 1881) before the 1908 honorary membership, and the Bethenod/Hughes-medal snippet; Föppl 1894 was already in 7c and is now also listed there. - QE defect 5a (stale lines): evidence-rule item 10 ("no Investigator run exists") and the "Web-check log (8 budget, 5 calls used)" heading now carry "superseded" notes giving the current state (5 at Step 3, 8 of 8 after the evidence-rule revision, 3 disclosed over-budget fetches; 11 in all). - QE defect 5b (sites.md exponent): sites.md is the Investigator's file and is not edited here. Arithmetic re-done for the record, with v = 3 x 10^10 cm/s: u = 3 x 10^6 cm/s (30 km/s) gives (u/v)^2 = (10^-4)^2 = 10^-8, and half of it 5 x 10^-9; u = 3 x 10^7 cm/s (300 km/s) gives (10^-3)^2 = 10^-6 ("one-millionth") and half of it 5 x 10^-7 ("one two-millionth"). Only the exponent 7 fits Heaviside's printed words, as in claim 7b above; the page image is still the deciding record. - QE defect 3 (primer's kept-material paragraph): primer only; the arbiter's list already carries the Stevenson correspondence, the "America Revisited" proof and Yavetz 2011 (the last under "Not reached").