Heaviside: PhD physicist review

Role: PhD physicist, mainstream view. Inputs: facts.json and claims.md (Step 1). I re-read page images p.139, p.142, p.143 of the "Electromagnetic Waves" Google Books preview and the Electromagnetic Theory Vol. 1 contents page (p. xiv) myself. Image content is tagged [read: page image p.N].

Source gap (repeated from Step 1). The folder contains only three saved Google Books viewer pages with a handful of page images (contents pages for Electrical Papers Vol. 1 and Electromagnetic Theory Vol. 1; pp. 139, 142, 143 of Electromagnetic Waves). No full text of any work exists in the folder. Conclusions about claims 1, 2, 3, 5, 6, 7 below rest on [web]/[memory] and on section headings only, not on reading Heaviside's derivations. Claim 4 rests on pages actually read. To review properly, obtain Electromagnetic Theory Vols. 1-3, Electrical Papers Vols. 1-2, and the 1888-89 Philosophical Magazine papers (public domain).

Corrections to Step 1

1. Page 143 numbers verified (Step 1 said "not independently checked"). Eq. (62) is E2/E1 = H2/H1 = 1/(1 + 2πμk1 z v). With k1 = 1/1600 and μv = 3e10 (his CGS-electromagnetic units, centimetres): 2π x 3e10 / 1600 = 1.18e8 per cm, so z = 8.5e-9 cm, equal to his printed (8/3π) x 1e-8 = 8.49e-9 cm. [read: page image p.143; arithmetic done here]. The value is correct as printed.
2. Independent SI cross-check (not in Step 1). The modern thin-sheet formula is T = 1/(1 + σ d Z0/2), with Z0 = 377 ohm (impedance of free space) and copper conductivity σ = 5.8e7 S/m. Half transmission needs d = 1/(5.8e7 x 188.5) = 9.1e-11 m = 9.1e-9 cm. Agreement with Heaviside to about 7%, the difference being his rounded copper resistivity. [memory, high for the formula; arithmetic done here]
3. Physical caveat Step 1 omitted. z ~ 0.85e-8 cm is under 1 angstrom, smaller than a copper lattice spacing (~2.5 angstrom, [memory, high]). Heaviside's own remark is only that this is "a very small fraction of the wave-length of visible light". The formula is a valid thin-film idealisation, but a bulk conductivity does not apply at that thickness, so it is not a realistic prediction for a real film. This does not affect the algebra.
4. Unresolved reading on p.143. After eq. (63) the page says, as I read the image, that H is "made [a fraction] H1" while E is "reduced to 1/2 E1". Eq. (62) gives 1/2 for both at half transmission. The printed fraction on the H clause is hard to read at this resolution. I could not settle whether it is a printer's/scan artefact or a real inconsistency, so I do not rely on that sentence.
5. Source attribution. The page header on p.142 reads "Forced Vibrations of Electromagnetic Systems" while pp.139 and 143 read "on Electromagnetic Waves, and the ..." So the pages are from one long paper, titled as in the running header. Step 1 listed the reprint date as unknown. Not resolved here.
6. Step 1's description of the Electromagnetic Theory contents (Poynting flux, spherical sheet from a jerked charge, sec. 83 on magnetised matter) matches what I saw on p. xiv for secs. 33-61: circulation laws, curl (sec. 36), impressed force classes, motional forces (sec. 44), the sudden-jerk spherical sheet (secs. 54-55). [read: page image p. xiv] Sections 62-85 (including Poynting flux sec. 70, sec. 83) are on a page I did not re-read. No other Step 1 errors found.

Web checks (budget used: 1 call)

Source: https://en.wikipedia.org/wiki/Oliver_Heaviside - 1884 recasting of Maxwell into vector form, reducing twelve of the original twenty equations (in twenty unknowns) to four: confirmed [web]. Note the wording is "twelve of twenty", so Step 1's phrase "twenty component equations replaced by four" is loose. - Independent discovery of the Poynting vector: confirmed [web]. - Preece called self-inductance "the great enemy of clear transmission"; Heaviside showed uniform inductance reduces attenuation and distortion; AT&T hired Campbell and Pupin in 1897 and filed patents extending his work: confirmed [web]. - Layer proposed 1902; existence confirmed 1923 per Wikipedia, with Appleton's Nobel Prize in 1947 [web]. I recall Appleton and Barnett's experiment as 1924 [memory, medium], so the "1923" date is a Wikipedia statement I did not reconcile. Treat as "mid-1920s". - Operational calculus criticised for lack of rigour, later put on a rigorous footing (Bromwich integral, Laplace transform): confirmed [web]. - 1893 gravitational/electromagnetic analogy and Heaviside's later hostility to relativity: confirmed [web] (Howard Eves quote there).

Claim 1: Maxwell's theory fits into four vector equations (curl and divergence of E and H)

• a. Mathematics consistent? Yes. The four equations are the standard Maxwell equations used in every textbook, and the vector form is mathematically equivalent to the component forms. The contents page confirms Heaviside defines curl (sec. 36), divergence (sec. 51), the two laws of circulation (secs. 34-35). [read: page image p. xiv]
• b. Consistent with experiment? Yes. All of classical electrodynamics (radio, optics, circuits) is built on these equations. [memory, high]
• c. Tested? Constantly, over 130 years. Hertz's 1887-88 wave experiments were the key early confirmation [memory, high]; they overlap with Heaviside's work, not a test of his priority.
• d. If true, what changes? Nothing; it already is mainstream. One nuance: in modern notation the equations are "Heaviside's" in form, "Maxwell's" in content, with the displacement current and the Lorentz force law added by others.
• Verdict: Established.

Claim 2: Energy is localised in the field and flows at E x H

• a. Mathematics consistent? Yes. Poynting's theorem follows from the curl equations by a vector identity. I did not read Heaviside's derivation (only section headings on the contents pages, "Poynting flux" etc.), so I can say only that the result he states is the standard one.
• b. Consistent with experiment? The flux E x H is consistent with every energy-transport measurement (radiation pressure, antenna power, absorbed light), [memory, high]. Caveat: the Poynting vector is only fixed up to adding a curl, because only its divergence enters energy conservation. "Localisation" of energy at a point is therefore a convention that works, not something a measurement forces. Consistent in all uses so far; relevant to gravity (energy density sources curvature), where the local form matters. [memory, medium]
• c. Tested? Indirectly by every radiometric and radiation-pressure experiment. No experiment distinguishes the standard form from curl-added alternatives.
• d. If true, what changes? Nothing. Textbook.
• Verdict: Established (with the nuance above: the localisation is a convention). Priority: Poynting 1884 and Heaviside independently [web].

Claim 3: Added inductance reduces attenuation and distortion (Heaviside condition) against Preece

• a. Mathematics consistent? Yes. Telegrapher's equations with R, L, G, C per unit length give distortionless propagation when R/L = G/C. This is textbook transmission-line theory. I did not re-derive from Heaviside's own text; the Electrical Papers contents shows the relevant article headings (propagation of current in wires). [read: page image]
• b. Consistent with experiment? Yes. Loaded telephone lines (Pupin coils, Campbell) work, [web] per Wikipedia above.
• c. Tested? By AT&T engineers from 1897 on, with patents and commercial use [web]. The Pupin/Campbell result is a replication in practice. The dispute with Preece is historical and the engineering outcome favoured Heaviside.
• d. What changes? Nothing. The Preece view was wrong, the Heaviside view is now engineering standard.
• Verdict: Established. (Note: an important caveat on how the credit went: Pupin patented the coils and was paid; Heaviside was not. [memory, medium] Not needed for the verdict.)

Claim 4: Disturbances follow wave-plus-diffusion equations; magnetic diffusion is repeated internal reflection; a perfect conductor is a perfect reflector

This is the one claim I could read directly.

• a. Mathematics consistent?
• The thin-sheet boundary conditions are eq. (60) E1 + E3 = E2 and eq. (61) H1 + H3 = H2 + 4π k1 z E2. Tangential E is continuous across a thin sheet, and tangential H jumps by the sheet current (4π x current in his units). With E = ±μv H for forward/backward waves these give eq. (62). I checked the algebra: E2 = E1 + E3 and H1 + H3 = (E1 - E3)/μv, so (E1 - E3)/μv = E2/μv + 4π k1 z E2, hence E1 - E3 = E2 (1 + 4π k1 z μv). Adding E1 + E3 = E2: 2E1 = E2 (2 + 4π k1 z μv), E2/E1 = 1/(1 + 2π μ k1 z v). This matches (62). [read: page image p.143; algebra checked here]
• A perfect conductor (k1 z infinite) gives E2 = 0, E3 = -E1, H3 = H1 (so H doubled at the surface, E destroyed). Consistent with the standard boundary condition for a perfect conductor. [read: page image p.143]
• Eqs. (47)-(48) on p.139 are Bessel J0 solutions for a lossy line. He gives no derivation and tells the reader to verify them ("very laboriously worked out"). I did not verify them. The solutions have the right form: this is the telegraph equation, whose Green's function involves J0 (or I0) of the form s/v sqrt(z^2 - v^2 t^2). The head/tail description matches the known structure of the damped wave equation (a sharp attenuated front plus a wake). [read: page image p.139; recalled structure [memory, medium]; not re-derived]
• Eq. (58)-(59) (plane sheet of impressed force gives H = -e/2μv, E = ∓e/2 on either side): consistent with symmetric emission of two waves with E = ±μvH. Page 142 also says that in a good conductor the front is attenuated so strongly that pure diffusion applies, a standard conclusion (the diffusion equation is the low-frequency limit of the telegraph equation, where displacement current is negligible). [read: page image p.142]
• b. Consistent with experiment? Yes. Skin effect, shielding by thin metal films, and the behaviour of good conductors as near-perfect reflectors are all measured routinely. My SI cross-check above reproduces his thickness within about 7%.
• c. Tested? The thin-film transmission formula is used in shielding and thin-film optics. I do not have a source naming a specific replication of Heaviside's numerical case; do not claim one. [no source]
• d. If true, what changes? Nothing.
• Verdict: Established for the equations read (60)-(63) and the perfect-reflector statement; not independently verified for eqs. (47)-(48), which are consistent in form only.

Claim 5: Operational calculus (treat d/dt as an algebraic operator) solves differential equations

• a. Mathematics consistent? Heaviside's procedures were unrigorous but correct in practice, and later justified by the Laplace transform and the Bromwich contour integral [web]. As an informal method it is correct for the classes of problems he used.
• b. Consistent with experiment? The results it generated for line transients matched engineering practice [memory, medium]. I have not read any operational-calculus text from the folder.
• c. Tested? Justified mathematically (Bromwich, Carson and others) [web for Bromwich; names beyond that are [memory, medium]].
• d. What changes? Nothing.
• Verdict: Established (historically unrigorous, later rigorous). Source gap: no document in the folder contains the calculus itself.

Claim 6: A reflecting ionised layer in the upper atmosphere explains long-range radio

• a. Mathematics consistent? Not examined; no document in the folder contains it. It is qualitative.
• b. Consistent with experiment? Yes. The ionosphere reflects short waves; confirmed experimentally in the 1920s (Appleton, Barnett, Breit and Tuve) [web: Wikipedia gives 1923; I recall 1924, [memory, medium]].
• c. Tested? Yes, by Appleton, whose work earned the 1947 Nobel Prize [web].
• d. What changes? Nothing.
• Verdict: Established. Credit belongs jointly to Kennelly and Heaviside (proposed 1902 [web]); outside the saved pages.

Claim 7: Minor positions

Three separate items, each judged separately.

• 7a. Maxwell's force on intrinsically magnetised matter is "probably wrong." Only a section heading (sec. 83, from Step 1; I did not re-read that page). The physics of force on magnetised matter does have known ambiguities (Maxwell stress versus Kelvin force versus Abraham/Minkowski type disputes). [memory, medium] Without the argument I cannot judge. Verdict: Not testable as stated from this evidence.
• 7b. Gravitational analogy (1893). An analogy between gravity and electromagnetism with a gravitomagnetic field is a recognised idea; in general relativity a weak-field gravitoelectromagnetism exists with different factors and sign conventions, and its modern incarnation (Lense-Thirring/frame dragging, tested by Gravity Probe B, [memory, medium]) differs from Heaviside's. I did not read his text, so I cannot say what he predicted. Verdict: Historically superseded but instructive, with the caveat that the content is unread.
• 7c. Opposition to relativity. An opinion, not a physical claim with a derivation in the folder. Relativity is among the best-tested theories in physics [memory, high]. Heaviside's hostility is reported [web] but his reasons are not in the saved pages. Verdict: Tested, not supported applies to relativity-opposition positions generally (relativity has passed all tests), but I cannot tell what specific claim Heaviside made, so I register this as Not assessable from the folder.

Summary table

Overall: Heaviside is a case of mainstream vindication, not an anomaly. The only substantive unorthodox content is in 7a-7c, and the saved pages do not show his arguments.

Investigator findings (2026-10-05)

Inputs weighed: sites.md "Leads for review" (all entries) and the six research/ notes dated 2026-10-05 (archive.org, Google, Grace's Guide, IET Archives, Physics Today, Royal Society Publishing). research/files/ does not exist: the Investigator read the texts in the browser and saved none, so every quotation below is the Investigator's transcription [web], from fair-quality OCR with garbled equations. I did not open the archive.org pages myself, and I used no new web calls. Everything marked "checked here" is my own algebra or arithmetic on the transcribed text. The Investigator reports leads, not verdicts; the judgements are mine. Source gap partly closed: claims 3, 5, 6, 7a, 7b and 7c now have primary text (transcribed), but I still have not read Heaviside's formulas for 7a or 7b, because the OCR is garbled and no page images were taken.

Summary of effect on verdicts

No verdict changes category. Four are re-argued or narrowed: claim 3 (primary text added, verdict unchanged), claim 6 (split, because the 1902 text is weaker than the claim as worded), 7a (his argument is now known; verdict unchanged but better grounded), 7b (his argument is now known; one numerical inconsistency in the Investigator's transcription flagged). Claims 1, 2, 4 and 5 are unchanged.

Claim 3: Heaviside condition (inventor's own work; historical record)

**Primary text (EP2 Sec. XL, The Electrician 1887, pp. ~119-124) [web] https://archive.org/details/electricalpapers02heavrich.** The Investigator reports: "Increasing the inductance is another way of improving things"; "There is a critical value of the inductance for minimum attenuation-ratio"; leakage increases attenuation "but the distortion is reduced. This has led me to a theoretically perfect arrangement. Make R/L = K/S, and the distortion is annihilated"; solution f(x - vt) e^(-Rt/L); "The energy is half electric, half magnetic; the dissipation is half in the wire, half [in the leak]". (K is leakage conductance and S permittance per unit length, so K/S is the modern G/C; this is the Investigator's reconstruction of garbled OCR.)

Checked here. - Telegrapher's equation: V_xx = LC V_tt + (RC + GL) V_t + RG V. Substitute V = e^(-at) f(x - vt) with v = 1/sqrt(LC) and a = R/L. The f' terms cancel when RC + GL = 2LC a = 2RC, i.e. GL = RC, and the f terms cancel when RG = LC a^2 = C R^2 / L, i.e. G = CR/L. Both are the same condition, R/L = G/C. So the transcribed solution and condition are mutually consistent. [algebra checked here] - Energy statement: magnetic energy per unit length (1/2) L I^2 equals electric energy (1/2) C V^2 because V = I sqrt(L/C). Dissipation V^2 G = I^2 (L/C) G = I^2 R, using G L / C = R. So "half in the wire, half in the leak" is correct. [checked here] - Orders of magnitude (typical values, [memory, medium]): a 2 mm copper wire has R about 5 ohm/km and an open-wire L about 2 mH/km. At 1 kHz, omega L is about 12.6 ohm/km, which exceeds R. So inductance is not negligible at voice frequencies, which is why Kelvin's cable theory (which ignores inductance and gives the delay-grows-as-length-squared "KR law") fails for telephony, as Heaviside says. With C about 6 nF/km, the condition needs G = C R / L, about 16 microsiemens/km, far above natural leakage. Hence the practical route is to raise L (coils), not to add leakage. That is the Pupin/Campbell loading of 1897-1900 [web: Wikipedia, in the original review]. - His thought-result that the far-end sinusoidal current could exceed the steady current from the same impressed force (p. 122), attributed by him to to-and-fro reflections, is plausible as a resonance effect but I did not verify it.

What the primary text does not show. Coils at intervals (the 1893 proposal per Grace's Guide chronology) are not in this section; only raising inductance by spacing wires and by iron-cored wire. Heaviside's cited experimental support is cautious ("I do not wish to magnify its importance"): good long-distance telephony on copper-covered steel wires.

Historical record, with stakes marked. - Mechanism of the block, three accounts. Hunt (2012, Physics Today, a historian with no stake) and Bruton (2018, Science Museum curator): the April 1887 joint paper with Arthur was blocked by Preece as Arthur's superior before submission to the Journal of the Society of Telegraph Engineers. The 1925 IEE obituary (written by an admirer): papers "rejected by the Society of Telegraph Engineers". Grace's chronology: Heaviside "suspected" Preece blocked it. These disagree on mechanism, not on outcome. I do not choose between them. Deciding records: STE council minutes 1887 and IET notebook SC MSS 005/I/1/12 (not yet read). - Dated silence in his own text. EP2 Art. 38, "Mr. W. H. Preece on the Self-Induction of Wires", is headed "[Sept. 24, 1887; but now first published.]" (published 1892): "Mr. Preece is wrong, not merely in some points of detail, but radically wrong." And EMT1 sec. 1: the Electrician series stopped in Sept 1887 for "pressure on space and the want of readers ... Perhaps there were other reasons ... We do not dwell in the Palace of Truth." This is Heaviside's own characterization. - Loss of the Electrician outlet. Hunt (citing Mahon 2009, p. 79): editor Biggs declined Heaviside's anti-Preece letters for fear of libel, was "abruptly removed" in October 1887, "a move he later hinted was prompted by his support for Heaviside"; the new editor cancelled the series. This rests on Biggs's own hint as reported in one secondary source; no second source has been found. It is evidence about motive, not a physics matter. - Preece's side, in his own papers (party with a stake: public position that self-induction harmed telephony, a costly iron-to-copper change justified by it, seniority). IET SC MSS 022/VII/526 (catalogue description only; contents not seen): pencil draft reply to Kelvin, "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". Physically, Kelvin's formula is the right low-frequency (diffusion) limit and the wrong tool for voice frequencies, per the numbers above. Bruton's characterization is that Preece reasoned "from inadequate experiments". Kelvin to Preece 12 July 1887 (SC MSS 022/VII/535): a Heaviside footnote "should not have appeared as it was so ill natured" (the cataloguer's bracket supplies "presumably anti-Preece"). Kelvin later praised Heaviside's propagation theory in his 1889 IEE address (Hunt; Grace's Guide). - Earlier stake (1873), Bruton citing an archival reference: 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." Heaviside had not cited Preece's 1855 duplex patent. This shows personal friction pre-dating the 1887 dispute; it does not bear on whether the physics is right. - Arthur Heaviside later sided with Preece on loading (Hunt; Bruton); Oliver in 1922: "AWH was very afraid of P ... The greatest mistake AWH ever made was to throw me overboard" (IET SC MSS 068; Heaviside's characterization, 35 years later). - Support by others: 1925 IEE obituary names Silvanus Thompson and Pupin as early adopters; Russell, Nature 1925: Pupin worked "on these lines some ten years later". Both are by admirers. Pupin payment is given as $455,000 (Wikipedia), "over $400 000" (IET blog), $500,000 (Hunt, who calls the circumstances "somewhat shady"). Three figures, no primary contract seen. - Own-work addition: British patent 1880 no. 1407, "Improvements in Electrical Conductors", to Oliver alone, which Bruton calls "essentially the patent for ... a 'coaxial cable'" [web] Bruton 2018. I have not seen the specification, so I cannot judge it.

Question c (tested?). Unchanged: tested in practice by AT&T from 1897. The new material shows that the 1887 dispute was fought by argument and authority, not by a controlled comparison at the time; the loaded-line engineering result came later. Verdict: Established (unchanged). The new records document that Heaviside's priority and the opposition to him are real; they do not alter the physics.

Claim 6: reflecting ionised layer

**1902 text, EB 10th ed. vol. XXXIII, "Telegraphy", I. Theory (pp. ~213-215) [web] https://archive.org/details/in.ernet.dli.2015.209824:** "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." 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 (obituary writer's claim; I have not seen that part).

Weighing. - The text is tentative ("may possibly") and describes guidance between two conductors (sea and layer), not reflection. That description is physically sound for very-low-frequency waves: the Earth-ionosphere cavity guides ELF/VLF waves (Schumann resonances) [memory, high]. Short-wave long-range propagation is refraction and reflection from electron-density gradients, not from a metallic conductor [memory, high]. So the 1902 sentence is a correct, early, qualitative proposal, but the claim as worded in claims.md ("explains long-distance radio") is stronger than the text. - Priority: Kennelly, Electrical World and Engineer 39(11):473, 15 March 1902, proposed an ionised conducting layer independently, some nine months before the Britannica volume (Dec 1902, per Bruton) [web per Investigator's search-result citations]. I have not read Kennelly's text. On publication date alone, Kennelly is first; the name "Kennelly-Heaviside layer" already shares credit. - Dating: Bruton gives Appleton's experiments as "begun in late 1924"; the IET blog says Appleton demonstrated it in 1924. This agrees with my earlier [memory, medium] and supersedes the Wikipedia "1923" I noted. Retag [web] Bruton 2018.

Verdict: Established, now split. (i) Existence of a conducting upper-atmosphere layer that guides and reflects radio: Established (Appleton 1924-25, Nobel 1947). (ii) Heaviside's own 1902 statement: a tentative, correct, qualitative proposal for guidance, made after Kennelly's publication; credit is shared.

Claim 7a: Maxwell's force on magnetised matter

**His argument (EMT1 sec. 83, pp. 103-104) [web] https://archive.org/details/electromagnetict01heavuoft.** Heading: "Difficulty. Maxwell's Solution probably wrong." For the resultant force one may use the surface stress outside the magnet, but "it is impossible that the real forcive can be represented merely by the surface traction"; to get the real force "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." The Investigator did not read his formulas.

Weighing. - He does not dispute the total force on a body (fixed by the outside stress, which fits the claims.md note on sec. 79). His objection is about the internal force distribution, and he says himself the internal route is hypothetical. - Physically, this matches the known situation: different force densities (Maxwell stress, Kelvin force, others) give the same total force on an isolated body but different internal distributions, and the differences are tied to the treatment of intrinsic (permanent) versus induced magnetisation [memory, medium]. This is a recognised ambiguity, not a refuted claim. - His "intrinsic vs induced" distinction is physically meaningful (permanent magnet versus soft iron respond differently), so the objection is not trivial. Only a measurement of internal stress could separate the formulations, and in real materials magnetostriction confounds it. I have not seen a neutral test.

Verdict: Not testable as stated (unchanged), now with his reason on record: the total force is not in dispute; the internal distribution is, and only an internal-stress measurement could decide it. Formulas still unread (page images of EMT1 pp. 103-107 needed).

Claim 7b: gravitational-electromagnetic analogy

His text (EMT1 App. B, "A Gravitational and Electromagnetic Analogy", The Electrician 1893, pp. 455-466; sec. 68, "gravitational difficulty") [web per Investigator]. - Sec. 68: gravitational energy has no known flux; "we are entirely ignorant of its distribution in the ether, and of its mode of transference." This is the "difficulty": unlike E x H, no energy flux is known for gravity. - App. B: the static theory "implies that the speed of propagation of the gravitative influence is infinitely great"; he assumes propagation at speed v. For gravitational aberration (the Lodge question): "no aberrational effect, but only a slight alteration in the intensity of force in different directions round a moving body", weaker along the line of motion, stronger equatorially, "the direction is still radial". Magnitude as transcribed: u = 3 x 10^6 cm/s ("fast stars") and v = speed of light, "(u/v)^2 = 10^-6".

Arithmetic flag (checked here). u = 3 x 10^6 cm/s is 30 km/s and v = 3 x 10^10 cm/s, so u/v = 10^-4 and (u/v)^2 = 10^-8, not 10^-6. For 10^-6, u would need to be 3 x 10^7 cm/s (300 km/s). So the transcription has a dropped power of ten, either in the OCR/reading or in the text. Heaviside's printed number needs checking against a page image before anyone relies on it. The sentence "an increase of Sun-Earth attraction of one two-millionth part" fits the 10^-6 scale, which suggests the speed is the printed 3 x 10^7 and the Investigator's "3 x 10^6" is the slip. I cannot settle this.

Weighing against mainstream. - Sec. 68 anticipates a real issue. In general relativity (GR; the theory of gravity as spacetime curvature, not assumed known to the reader) gravitational energy cannot be assigned a unique local density, and gravitational waves do carry energy, shown indirectly by the orbital decay of the Hulse-Taylor binary pulsar [memory, high]. So "no known local flux for gravity" was a fair statement then and is still partly true now. - Finite-speed gravity with no aberration of the force direction: in a theory with a field that propagates at c, a uniformly moving source's field points at its present, not retarded, position. This is the standard result for electromagnetism and carries over to GR's weak field [memory, medium]. Heaviside's "no aberration, direction still radial" has that structure. His modern counterpart (gravitoelectromagnetism, with different factors and signs) differs in numbers [memory, medium]. I have not compared coefficients because his formulas are unread. - No frame-dragging (gyroscope/Lense-Thirring) prediction was seen in the passages read (Investigator). So the claims.md phrase "giving gravitoelectromagnetism" is true in structure only. Gravity Probe B measured frame dragging [memory, medium]. - Heaviside's ether-based mechanism is superseded; the finite-propagation-speed analogy is instructive.

Verdict: Historically superseded but instructive (unchanged). The coefficient comparison with linearised GR remains undone.

Claim 7c: opposition to relativity

EMT vol. 3 (1912): "Einstein" 0 hits, "Minkowski" 0, "relativ" 21 (including "the principle of relativity of motion" for a moving ether; page not identified), "Lorentz" 30, "FitzGerald" 15; sec. 473 "Lorentz's Equations of a Moving Dielectric" (dated 5 Oct 1900) [web per Investigator, OCR keyword counts]. So his published volumes do not name Einstein, and the anti-relativity remarks reported by Wikipedia (and attributed to Howard Eves in the earlier review) must lie in the unpublished fourth-volume notes (2003 AMS Chelsea edition; lending-only, not opened), in Nature letters of 1903-1905 (listed, not read), or in letters. Russell (Nature 1925) says Heaviside "was one of the first to predict the increase of mass of a moving charge" (obituarist, admirer). Absence of Einstein in vol. 3 is not evidence of his view, and 1912 predates general acceptance in Britain; I draw no conclusion. Verdict: Not assessable from the folder (unchanged); the deciding text is the vol. 4 notes.

Claim 5: operational calculus

• Hunt (2012), verbatim: in 1893 Heaviside sent two installments of "On operators in physical mathematics" to the Royal Society; "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." Referee: William Burnside, Royal Naval College Greenwich, per a Google snippet of Hunt's 1991 chapter (chapter not opened; referee report not located in the Royal Society RR series).
• His reply in his own volumes: 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." 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." A secondary source (deadreckonings.com, secondary) says vol. 2 contains a modified Part III.
• Physics judgement: his defence was pragmatic (the answers agree with experiment). That is a sound engineering position, but it is not a proof. The mathematical justification came later (Bromwich integral, Carson; the Laplace transform) [web, original review]. For the divergent series he used, rigour for particular cases came later; I did not check each case. The mathematician's file is the proper place for that.
• Rejection note: this is a case of a paper rejected for rigour, not for wrong results. That bears on the Contrarian's question of how a claim was rejected, not on my verdict. Verdict: Established (unchanged).

Claims 1, 2 and 4

• Claim 1: no new finding. Hunt: Foeppl's 1894 textbook carried Heaviside's form of the equations, "from which Albert Einstein, among others, would learn electromagnetic theory" (Hunt; the textbook link is the historian's statement). Fits "Heaviside's form, Maxwell's content". Established (unchanged).
• Claim 2: sec. 68 (above) shows he regarded E x H as a known flux for electromagnetism and noted gravity has none. Consistent with my earlier caveat that localisation is a convention that works. Established (unchanged).
• Claim 4: the distortionless-line solution above is a special case of the damped-wave (telegraph) equation in which the diffusion-like term is cancelled by the leakage condition. That gives a checked example of "wave plus diffusion" which I verified algebraically, and it supports the form of the Bessel solutions (47)-(48) without verifying them. The Electromagnetic Waves item (1889) is listed on archive.org (electromagnetic01heavgoog) but was not read, so the full text containing eqs. (47)-(48) is now located. Verdict unchanged: Established for eqs. (60)-(63); (47)-(48) unverified.
• Also of note: Fitzgerald's notebook, 9 Sept 1888: "Very important. ... Must be all in O. Heaviside" (Trinity College Dublin, per Hunt). Contemporary endorsement; no physics content stated.

Leads the Investigator did not reach (kept in the record)

Royal Society referee report on Part III (RR series); BT Archives TCB 274/1, POST 30 files; HathiTrust The Electrician 1887 (Biggs removal, Preece's BA paper 16 Sept 1887 p. 400); Kennelly 1902 text; De Gruyter Hunt 1991 chapter; AIM25 (blocked); the lending-only 2003 edition with vol. 4 notes; Yavetz (2011) on Arthur's bridge system (snippet only); the papers found under the floorboards at Paignton c.1957 (Josephs, per Bruton) and a 1932 GPO report on "the Heaviside Analysis", "no copies of which survive" (Bruton). That last group is a record that goes quiet: competing explanations (ordinary loss, a GPO internal report never retained, Heaviside's papers dispersed after his death) are not decided by anything found yet; the GPO and IET catalogues are the records to search. Russell (1925) says Heaviside planned vol. 3 for 1904 and a concluding volume for 1910 but "found [this] impossible"; vol. 4 notes survive in print only in the 2003 edition.

Updated summary table