Lorentz-HA: Quality Engineering (Step 4b)

QE (Opus), 2026-10-08. Project: H. A. Lorentz, The Theory of Electrons (2nd ed., Teubner 1916; Columbia lectures 1906; 1909 text with [1915] notes). One document, 361 PDF pages, OCR text.

Inputs read: _text/manifest.json and _textprep.log; all 13 digests (pp.1-361) in full; the deep read in full; facts.json; claims.md; sites.md; the research/ notes (by section); physicist.md, mathematician.md, contrarian.md, arbiter.md and primer.md in full; example.py, which I ran. Own checks: I rendered PDF pp.204, 206, 228 and 348 at 150 dpi and read them. I grepped the text layer for the Note 72* quotation, Poincaré, Larmor and Ehrenhaft. I fetched Brace's 1904 paper (Wikisource text) and the Michelson-Morley Wikipedia source to check two numbers the arbiter took from a model summary. Tags: [read] = the book (PDF page; printed page = PDF page minus 9); [read: page image p.N]; [web] with URL; [memory] with confidence.

Verdict: MINOR. No central claim or verdict changes. The defects are the following. The arbiter's corrections have not yet been applied to claims.md, facts.json and the deep read; the main one is the 10^-13 that should be 10^-12. Two numbers need tightening (the Michelson-Morley "one-fortieth" bound, and a digest error). Some pertinent material from the digests and from the Investigator is missing from the arbiter and the primer. One of the arbiter's open questions can be answered from the book itself.

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1. Coverage

Coverage: pass.

2. Shortcuts

• Chapter V, §§161-194 (PDF pp.196-239), plus Notes 72*, 75* and 86: deep read by Opus from page images, with SymPy checks. These pages carry claims 1-6, so this is the right place for the deep read. Acceptable.
• Chapters I-IV and Notes 1-61 (digest only): only claim 7 (background) rests on them, and every reviewer says so. Acceptable, with two exceptions where a number in a reader-facing table rests on a digest alone: 1. Note 69* (pp.328-329), Zeeman's 1914-15 repetition of Fizeau's experiment. The arbiter (claim 7) and the primer (evidence table, row 7) quote "0.826 +/- 0.007 at 4500 Å" from a table the digest calls "partly garbled". An experimental number in the evidence table should be read from the page image. This is a minor defect: deep read 1 below. 2. Chapter I, §§26-35 (pp.44-56), Lorentz's first account of Kaufmann. On p.51-52 Lorentz says Kaufmann's 1906 data agree with Abraham's formula. He adopts "Kaufmann's conclusion that negative electrons have no material mass at all" and calls it "one of the most important results of modern physics" [read: digest pp.51-52]. That is the background against which §179 calls the same data "decidedly unfavourable" to his own electron. It also bears on the arbiter's open question on the 1906-1909 change of mind. Claim 3 does not depend on it, but the history in the arbiter and the primer would be fuller with it: deep read 2.
• Chapter V, §§146-160 (pp.177-195), first-order theory, Stokes, Planck's condensed ether, Fresnel drag: digest only. These pages are not a central claim. They do hold the one "dragged ether" alternative Lorentz examines (Stokes's ether, with Planck's ether condensed around the earth, Note 67: sliding 0.011 w or 0.0056 w). Readers of alternative science care about that idea, and no review file weighs it. Deep read 3 is optional.

3. Missed material (from my reading of all the digests)

None of these changes a verdict. Each is pertinent and is missing from claims.md, the reviews, the arbiter or the primer, or only appears there in passing.

1. Ehrenhaft's sub-electron charges, Note 16* [1915] (pp.259-260). Lorentz reports Millikan's oil-drop charges as multiples of one elementary charge. He then writes: "Ehrenhaft, however, has been led to the conclusion that in some cases the charges are no multiples of the elementary one and may even be smaller than it. The question cannot be said to be wholly elucidated" [read: text layer p.260, grep-checked]. This is a contested anomalous experimental claim, and the author leaves it open in 1915. facts.json mentions only "falling charged bodies (Note 16*)". No review, the arbiter or the primer mentions it. Under SOURCE HONESTY it should be stated with its source. The later history of the Millikan-Ehrenhaft dispute is a [memory] matter for the Investigator, not for QE.
2. Who Lorentz credits, and who he leaves out (this answers the arbiter's open question 2). The arbiter says the book "was not searched" for Poincaré. I searched it. Poincaré appears only on pp.222-224, for the electron's stress and its stability (§§181-182, the Palermo 1906 paper), and in the index [read: grep of text layer; index p.351]. The book does not credit Poincaré with the transformation, its group property, or the principle of relativity. Those it attributes to Einstein (§§189-194), and the transformation to Voigt (p.207 fn.1). Larmor is named only in the 1909 preface, as one of the authors whose work "is not mentioned" [read: p.8]. This is a fact [read]. The reasons are not stated in the book, and any priority question is a separate matter.
3. Note 75* [1915]: "all forces are propagated with the velocity of light", gravitation included [read: deep read, pp.337-340]. The contrarian and facts.json carry it; the arbiter and the primer drop it. It is a testable consequence Lorentz draws from relativity, and the primer should state it in one line.
4. Lorentz's self-criticism on metals, §50 (pp.75-76). His more rigorous electron theory makes the Drude estimate of the ratio of thermal to electrical conductivity agree worse than the cruder one. He concludes the earlier agreement may be "a fortuitous coincidence". A [1915] footnote names Kamerlingh Onnes's low-temperature conductivity results as unexplained [read: digest pp.75-76]. This is peripheral, but it is a second example of the conduct the primer praises.
5. Lorentz against Jeans, Note 42 (pp.296-298). Silver reflects about 90% of yellow light, so by Kirchhoff's law it would have to glow visibly in the dark at 15 °C if Jeans's equipartition law held at all wavelengths [read: digest pp.296-297]. The reader can check this argument by hand (reader profile: prefer worked numbers). Claim 7 states the Jeans difficulty only in general terms. Deep read 5 is optional.
6. §120 and §145, absorption. Lorentz says the cause of optical absorption "remains yet to be discovered". He estimates the undisturbed vibration time from line breadth as τ ≈ 1-2×10^-8 s, and finds that only a small fraction of sodium atoms in a flame absorb [read: digest pp.151, 175-176]. This is a peripheral open question of 1909, now answered by quantum theory [memory, high].
7. §177, a residual ether effect Lorentz predicts. If the sun is at rest in the ether, sunlight D-lines and a terrestrial sodium flame differ in relative frequency by a factor of order w^2/c^2, which he calls "of a purely theoretical interest" [read: deep read p.218]. This is the one second-order effect his own theory leaves for celestial sources, and no review file mentions it. One line in facts.json is enough.
8. Investigator items dropped between the reviews and the arbiter or primer (see Retention): Trouton-Rankine 1908, Glitscher 1917, the Columbia lecture dates, and E. B. Wilson's 1917 review.

4. Accuracy spot checks

5. Retention check

Question: was pertinent material from the source or from the Investigator left out of the arbiter or the primer because a reviewer judged it negatively?

• The negatively weighed material is kept. Dayton Miller's non-null drift and Lorentz's correspondence and lectures on it are in the arbiter (absence-of-evidence item 4) and the primer (open question 5). The neo-Lorentzian literature and Bischoff van Heemskerck 2023 are in the arbiter claim 6 and the primer §§6, 9. The Zahn-Spees and Faragó-Jánossy critique of the early mass experiments is in the arbiter claim 3 and the primer §5b, beside Lorentz's reading. Kaufmann's 1906 result against Lorentz is kept and quoted. Lorentz's 1913 "dispute about words" and the 1927 Mount Wilson remark are kept and flagged as unverified. NHA archive 364 items are kept as unread records. The "Michelson proves contraction" sentence and the shell electron are kept with their verdicts. No retention defect of the kind the rule targets.
• Omissions that are not negative-judgement drops, but are gaps (minor completeness):
• Trouton-Rankine 1908: in the physicist and contrarian files, not in the arbiter or primer.
• Glitscher 1917: in sites.md and the contrarian file, not in the arbiter or primer.
• Wolz 1909 (an electron-mass measurement listed beside Bucherer's): in sites.md, not in the arbiter or primer. Bestelmeyer is kept.
• Columbia Spectator lecture dates (Chapter V given 26-27 April 1906) and the Delpher notices: dropped from both.
• E. B. Wilson's 1917 review (Bull. AMS 24): dropped.
• Schmelzer 2012, Arminjon and Clube 1980: in the arbiter, not in the primer's further reading. The primer lists the others.
• Note 75* on gravitation (item 3.3 above): dropped.
• Source honesty. Einstein's 1920 characterisation is labelled as an interested party's. Wikipedia's "unfounded" is labelled as its characterisation. Lorentz's Voigt footnote is treated as single-source evidence, stated and weighed, not labelled away. Good.

6. Process

• Source tags: present throughout and honest. "[calc]" is used as an extra tag for recomputation; every use is clear about what was computed. The [memory] items carry a confidence. The 1927 quotation and the 1913 translation are flagged as unread primaries in every file.
• Web checks: the physicist made about 2 searches, the mathematician 1 page, the contrarian a handful of Wikipedia pages, the arbiter 2 of 8. The medium/low-confidence [memory] items that touch verdicts are the Rogers 1940 reference (checked by the arbiter via Wikipedia) and the water dispersion values (magnitude check only, and stated as such). The remaining unchecked items (classical radius versus point-like electron, Poincaré and Larmor priority, Shankland 1955) are stated not to bear on any verdict. Acceptable. The arbiter's Brace figures came from a model summary. They are now confirmed in the primary (check 6).
• Verdict scale: used consistently, with split verdicts stated part by part. One stretch: "Tested, not supported" is applied to "Kaufmann 1906 as an exclusion of the formula", which is a reading of data rather than a claim. It is clearly explained, so this is acceptable.
• Primer: it follows the Step 4 order (sections 1-9, answers at the end). It is written for the reader profile: symbols are defined, no tensors are used, Heaviside-Lorentz units are explained, worked numbers are given, and a floating-point trap is explained. The related primers it names (Poincare-Henri, Ives) exist under review/.
• example.py: ran to "All checks passed". Its outputs match the primer: split β²/10, index difference 1.86e-11, margin 19, the Kaufmann table, 4/3, R = 1.879e-15 m, and the §190 checks.

7. Corrections to earlier documents

(For the orchestrator to apply. Corrections already listed by the arbiter are repeated where they are still unapplied.)

1. Still unapplied (arbiter correction 1): Brace's reach is 10^-12. Fix it in claims.md claim 4, in facts.json (Ch. V second part: the summary "1e-13 vs 2e-11" and key claim 5), and in deep/…d80e55.md §7 and reader summary item 3. Evidence: page image p.228, now rendered four times (physicist, contrarian, arbiter, QE).
2. Still unapplied: arbiter corrections 2-6 to claims.md and facts.json: "must" in claim 3; "null" in claim 2 to be given as bounds; the l = 1 and sources caveats in claim 1; the 1909 Note 87 date for the deformable-electron reversal; and "wholly electromagnetic" holding for momentum only.
3. Michelson-Morley 1887 bound (contrarian Correction 3, arbiter claim 2 and correction 4, primer §3.2 and evidence table row 2). Change "about 1/40 (0.02 fringe observed against 0.40 expected)" to "certainly below 1/20 (at most 0.02 of the 0.40 fringe expected), probably below 1/40". Evidence: arithmetic; [web: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment]; the 1887 paper's wording [memory, high].
4. Digest .08, line p.206: "u_x' = u_x" should read u′ₓ = k²uₓ (eq. 289) [read: page image p.206]. Add this to the digest-error list in claims.md.
5. facts.json, "Notes 1-61" entry: text_available "partial" should be "yes". The text layer is complete and only equations are garbled, as in every other chapter.
6. Arbiter open question 2: answer it from the book (see §3 item 2) [read: pp.8, 222-224, 351].

8. Remediation (MINOR: update facts, arbiter and primer; one round)

Deep reads (most important first):

1. Notes 69*-72, pp.327-330, Sonnet. Read the page images. Transcribe Zeeman's 1914-15 Fizeau-repetition table: wavelengths, observed shifts with errors, calculated shifts with and without the dispersion term, and the 4500/6870 ratio. Also give Lorentz's comparison with Michelson-Morley's 0.434 ± 0.02 in Note 69. This verifies the number quoted in the arbiter and the primer evidence table.
2. Chapter I §§26-35 and Notes 14-16*, pp.44-56 and 254-260, Sonnet. What did Lorentz say in Chapter I about Kaufmann's 1906 data, Abraham's masses (68)-(71) and "mass wholly electromagnetic"? Give his numbers for e/m, the electron mass and the electron radius (R ≈ 1.5e-13 cm) from the page images. How does this sit beside §179's "decidedly unfavourable"? In Note 16*, what exactly does he say about Millikan and Ehrenhaft?
3. Chapter V §§147-160 and Notes 65-68, pp.178-195 and 324-327, Sonnet. Stokes's dragged ether, Planck's condensed-ether rescue, the sliding velocities in Note 67 (0.011 w, 0.0056 w) and the density ratios; why Lorentz calls it "not very satisfactory"; the electron-theory derivation of Fresnel's coefficient (1 - 1/μ²).
4. Chapter II §§59-76 and Notes 38, 42, 42*, pp.87-106 and 293-299, Sonnet. Lorentz's long-wave radiation formula (148) and its relation to Planck's; his three ways out of Jeans's difficulty; the silver-in-the-dark argument (Note 42) with its numbers. Do this one only if the primer adds the background worked number.

facts.json: apply corrections 1, 2, 4 and 5. Add Note 16* (Ehrenhaft and Millikan, Lorentz's "not wholly elucidated") to the Notes 1-61 entry. Add the §177 sunlight/sodium-flame residual effect and the Note 75* propagation of all forces at c to the Chapter V entries. Add the Poincaré and Larmor citation facts to the Chapter V second-part entry. Fold in the results of deep reads 1-3.

claims.md: apply arbiter corrections 1-6 and QE correction 3 (bound wording). Add the digest .08 error to the correction list.

arbiter.md: add a "QE revision" section. - (a) Michelson-Morley bound wording (correction 3). No verdict change. - (b) Open question 2 answered from the book. Poincaré is credited only for the electron stress; the transformation is credited to Voigt and the interpretation to Einstein; Larmor is named only in the preface. - (c) Note the Ehrenhaft item as a 1915 open question Lorentz records. No verdict is needed, since it is outside the claims. - (d) Restore Trouton-Rankine and Glitscher 1917 to claim 2 and claim 3 respectively, as the reviewers had them. - (e) Record that Brace's 7.8e-13 and "1600 times" are confirmed in the primary text (QE check 6), and that Brace's light path is "30 metres" of water in his own words. - (f) Fold in deep read 1 (Note 69* numbers) under claim 7, and deep read 2 under the absence-of-evidence item 1 (the 1906-1909 change of mind).

primer.md: - Fix the 1/40 wording in §3.2 and in evidence table row 2. - Add one line on Note 75* (all forces, gravitation included, must propagate at c) to §4, "Where they fall short", point 1. - Add a short note under "What is genuinely open" or "Further reading" on Ehrenhaft's sub-electron claim as Lorentz left it in 1915. - Add to §4 or §7 who the book credits: Voigt for the transformation, Einstein for the interpretation, Poincaré only for the electron stress, Larmor only as unmentioned. - Add Trouton-Rankine to §3.3, and the Columbia lecture dates to the source note. - If deep read 4 is done, add the silver-in-the-dark argument as a check-yourself item. - Update the evidence table row 7 figure from deep read 1.

No redo of Steps 2-4 is needed.

Recheck

QE recheck (STEP 4b), 2026-10-08. I re-read claims.md, facts.json, arbiter.md and primer.md and grepped the deep read, contrarian.md, physicist.md and mathematician.md. Write scope: this file only.

Remaining defects are stale copies of corrections that are already made and recorded elsewhere. Neither changes a verdict or the primer. To clear them: replace 10⁻¹³ by 10⁻¹² at deep read lines 122, 126 and 170, and "about 1/40" by "certainly below 1/20, probably below 1/40" at contrarian.md lines 19 and 45.

Final: OPEN (2 issues)

Orchestrator fix (2026-10-08)

• deep/The-theory-of-electrons-and-its-applicat-HA-LORENTZ-d80e55.md lines 122, 126, 170: 10⁻¹³ -> 10⁻¹² (each with inline correction note).
• contrarian.md lines 19 (two places) and 45: "about one-fortieth" / "about 1/40" -> "certainly below 1/20, probably below 1/40" (with notes).

Final: PASS