Ampere: Quality Engineering (Step 4b)

QE agent: Opus. Date: 2026-10-03. Inputs checked: _text/manifest.json, all 32 files in digest/, facts.json, claims.md, physicist.md, mathematician.md, contrarian.md, arbiter.md, primer.md, example.py. Spot checks were made against _text/Amperes-Electrodynamics-28a544.txt and _text/chunks/...31.txt. There is no deep/ folder.

Page numbers: "PDF p.N" means the === page N === marker in the extracted text. The book's printed page numbers run about 3 lower, so PDF p.271 = printed p.268. The reviewers cite printed pages, the digests cite PDF pages.

Verdict: MINOR. The five central verdicts hold up. There are four defects. A digest is missing. The key document was sampled, with no deep reads. One factual error appears in three files: they say Ampere ran his "law of similarity" experiment, but he did not. And several pieces of important material were missed. All four can be fixed by updating facts.json, claims.md, arbiter.md (a "QE revision" section) and primer.md. Steps 2-4 do not need to be redone.

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1. Coverage

Defect C1: the chunk 31 digest is missing. I read the chunk's page markers and the conclusion text myself [read]. The chunk contains: - PDF pp.481-490: the end of Ampere's Notes to the Theorie. These are Sec. 31.2-31.4: the force formula in derivative form, the direction of the directrix (Ampere's term for the axis along which a closed circuit acts on a current element, the forerunner of the field direction), and the force of an indefinite angular conductor on a magnet pole. They are dense mathematics, and some of it is garbled in the text layer. - PDF p.494: Part IX, the Conclusion. It is one page of quotations: Maxwell ("undoubtedly the best", "Newton of electricity"), Whittaker, Williams and Tricker. The authors say "We subscribe to them" [read, PDF p.494]. - PDF pp.496-517: Appendix A, the redrawn Theorie figures. These are figures only. - PDF pp.518-519: the start of the bibliography.

None of this changes a verdict. Still, the chunk was never digested, and the Notes are part of Ampere's own derivation. Remediation: write the missing digest (Haiku), and have deep read 4 below cover pp.481-490.

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2. Shortcuts

Defect S1: the key document was sampled, and there were no deep reads. facts.json how_read says "text layer sampled". That wording is not one of the allowed values. It also hides the fact that Part VI (Ampere's 1820 paper, PDF pp.290-323) and Parts VII-VIII (the full Theorie translation, PDF pp.324-490) were read by no one. The arbiter (open question 5) and the primer's source note admit this. STEP 4b treats "sampling only part of a key document" as a defect. This is the only document, so it is the key document.

Now that the digests exist, they cover the Theorie well enough to show what was missed (section 3). Three load-bearing points still rest only on the book's commentary or on a digest: - Ampere's own deduction of n and k (Sec. 29.3-29.11, PDF pp.359-383, and Note 31.1, PDF pp.479-490); - the bridge and magnet-rotation explanations (Ch. 21, PDF pp.266-281). Sec. 21.3 was never read: the arbiter lists it as "Not rated; nobody read it in depth"; - the Biot-Savart "three errors" claim (Ch. 17, PDF pp.240-243). facts.json lists it as key claim 7, but claims.md dropped it without saying why.

Each reviewer's own reading was targeted and stated honestly. The shortcut is acceptable for claims 4 and 5. It is not acceptable for the part of claim 2 about which experiments fixed k and n, or for the unrated magnet-rotation controversy.

S2: the bridge-force verdict rests on one abstract. Moyssides 2014 was seen only as an abstract, and every reviewer says so. The QE accepts this because the book itself concedes the point (see spot check 3). The arbiter should cite that concession.

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

The items below are not in facts.json, claims.md, the reviews, the arbiter or the primer, or they appear there in an inaccurate form.

1. Ampere never performed the "law of similarity" equilibrium. This is one of the four "cases of equilibrium" from which the Theorie claims to deduce the law "uniquely from experience". Verified [read, PDF p.191]: "it was not apparently performed at that time, as he himself admitted. Probably he never performed it in its final format." Ampere's own words at the end of the Theorie [read, PDF p.191 and digest p.463]: "I have not had time to build the instruments shown in figure 4 ... the experiments for which they are intended have not yet been done." Ettingshausen (1878) and Felici (1882) later ran variants, and Tricker used solenoids. All found n = 2 [read, PDF p.191-192]. - Accuracy defect. mathematician.md ("the 'law of similarity' equilibrium of 1825, repeated by Ettingshausen, Felici and Tricker"), arbiter.md D4 ("repeated by") and primer.md Sec. 4 ("the 1825 'similarity' equilibrium, repeated by Ettingshausen, Felici and Tricker") all imply that Ampere did the experiment. He did not. - This also matters for the reader: the title's "uniquely deduced from experience" is partly a rhetorical reconstruction (the book quotes Maxwell on this at digest p.54).
2. An earlier, independent route to k = -1/2 (the Ampere-Despretz experiment, 20 January 1821). Ampere predicted, with k = 0, that a magnet would turn under a horizontal and a vertical wire. It did not move. This was a refuted prediction, and it halted his research for about two years [read, PDF p.119-120]. The book shows that his full law gives a torque proportional to [(1-k) + (1+2k) sin^2 b]/c, so a zero net torque implies k = -1/2. He could have found the right value a year earlier [read, PDF p.120, eq. 6.7]. This is a refuted prediction followed by a reinterpretation. It is exactly the kind of evidence claim 2 needs, and it would make a good primer exercise.
3. Savary's independent determination (1823). Savary combined Ampere's relation n - 1 + 2k = 0 with the Gay-Lussac-Welter finding that a ring-shaped magnet exerts no external force (kn + 1 = 0). That gives two solutions, (k, n) = (1, -1) or (-1/2, 2). The bridge (k < 0) and the n > 1 experiment select the second [digest p.155-156]. So by 1823, n = 2 no longer rested on analogy. The reviewers mention Savary only in passing, and the primer's "n = 2 was an assumption" needs that date attached.
4. The Biot-Savart "two errors that cancelled" story [digest p.165-167, p.240-243; Ampere's own calculation at digest p.475]. Biot and Savart's first measurement gave a torque proportional to the bend angle rho. Integrating sin(omega)/r^2 actually gives tan(rho/2). Their later, careful experiment (1824) confirmed tan(rho/2), so the law came out right through two errors that cancelled. The claim is in facts.json but in no later file. It is a clean calculation the reader could do, and it shows why an element law cannot be deduced from one integrated measurement.
5. Magnet rotation about its own axis (Ampere's motor, Sec. 21.3, PDF pp.272-281) [digest p.272-280]. The book argues that the modern field explanation uses a self-torque of the magnet on itself, which violates Newton's third law. Ampere instead predicted a reaction torque on the external circuit or the mercury, and claimed that experiments confirm it. This is a testable, distinct claim with a modern literature (homopolar motors, which the book's bibliography cites). No one rated it. It should become claim 6, or at least an arbiter note.
6. Ampere's energy argument [digest p.248-251, p.425-426, p.459-460]. Forces that depend only on distance cannot keep a body rotating against friction. Continuous rotation therefore shows that the source is moving electricity, which takes its energy from the battery, and not static poles. This is an early use of energy conservation (vis viva, "living force", = mv^2). It is a central argument of the book against Biot and Faraday, and none of the files mention it.
7. Ampere did not regard his force as truly elementary [digest p.424-428]. In the Theorie he suggests it may come from the motion of the electric fluids or from an ether. The book's framing (and claim 5's) of Ampere as a pure action-at-a-distance theorist should note this. The digest of PDF p.461 says Ampere's summary includes "(1) ether theories unnecessary". That seems to contradict PDF p.424-425 and should be checked in deep read 4.
8. Smaller items worth a line in facts.json: - the 1914 Nature note calling Kamerlingh Onnes's persistent superconducting current "an Ampere molecular current" [digest p.111]. This is good support for claim 4; - Fresnel's role in the molecular-current idea, and Ampere's suggestion to Fresnel that light waves are transverse [digest p.106-107]; - Grassmann (1845) and Clausius found the same element force independently [digest p.218]; - the Gay-Lussac/Thenard spark-gap observation, which Ampere used to keep k = 0 until 1822 [digest p.91]; - Ettingshausen's bifilar improvement of the tangential-force experiment [digest p.329].

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4. Accuracy spot checks (against the extracted text)

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5. Process

• Source tags: present throughout and honest. The reviewers consistently state when they saw only an abstract. Two weak points:
• The physicist cites researchopinion.in, a low-quality outlet, for the bridge behaviour. Replace it with the book [read] or drop it.
• The [computed] tag used by the mathematician, the arbiter and the primer is not in the prompt's tag set. It is clearly defined in the primer, so this is acceptable, but aaa-index-to-artifacts.md or prompt.txt should record it.
• Web checks: done for the verdict-relevant medium-confidence items (Weber, the Ampere force law, Moyssides). The Bohr-van Leeuwen, Hertz and Einstein-de Haas items are [memory, high] and are not verdict-critical. That is acceptable.
• Verdict scale: applied consistently, and split verdicts are well explained. Two issues: 1. Claim 3, "quantitative bridge agreement: Plausible, untested". The primer's Part B argument shows that for any closed, steady circuit the force on each element from the whole circuit is identical under both laws. The book concedes the quantitative agreement (spot check 3). Together these make the claim that the field law fails quantitatively "Refuted by calculation" (with the primer's calculation shown), or at least a point both sides agree on. The arbiter should revise this. 2. "Refuted by calculation" for the self-force framing: the scale says "Show the calculation". The arbiter gives only an argument, but the primer's Part B supplies the calculation. The arbiter should point to it.
• facts.json: how_read uses a non-allowed value ("text layer sampled"). The mainstream_conflict field's "for the cases tested in the book" understates the general theorem (the contrarian's correction 3), and facts.json was never updated. The facts.json phrase "one-parameter family indexed by k that all give the same force on closed circuits" is wrong at a fixed prefactor (mathematician and primer Part C: the force scales as (2/3)(2+k)) and should be corrected.
• Primer: follows all nine STEP 4 sections in order. It defines every symbol, includes a three-tier worked example with real numbers, and gives an evidence table that matches the arbiter, check-yourself questions with answers, and further reading. It fits the reader profile: only vectors, line integrals and the Lorentz force are needed, and each is introduced. One small error: the statement in section 2 that field momentum "balances the books" is irrelevant for steady closed circuits, where net forces already balance under both laws. The primer should say this so the reader is not left thinking that steady-current momentum needs fixing.
• example.py: runs cleanly with .venv/bin/python. Its output matches every number in primer Part A, Part B and Part C (checked: 1e-7 N pairs; the along-element force is 0 at k = -1/2 and -2.148e-8 N at k = 0; the coaxial loops give -2.742e-4 N, which agrees with the elliptic-integral result to 2.5e-7; the (2/3)(2+k) ratios hold, including in the skew check).

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6. Remediation actions

Deep reads (most important first)

1. Ch. 21, PDF pp.266-281 (Opus). What exactly does the book claim about (a) the quantitative bridge analysis (which of Bueno and Assis's calculations, what measured values, and the size of the self-term), and (b) the magnet rotating about its own axis: what the field explanation is said to violate, what reaction torque Ampere predicted on the mercury or external circuit, and what experiment, if any, is cited as confirming it? Rate claim 6 (magnet self-rotation) with all four Step 2 questions.
2. Sec. 29.2-29.11 and Note 31.1, PDF pp.350-383 (Opus). In Ampere's own Theorie, which of the four equilibrium cases fixes which constant (n, k)? Which cases were actually performed, and which (Fig. 4, Fig. 20) were not? How does the Theorie justify n = 2 (similarity case vs Laplace/Biot)?
3. Sec. 6.x-7.5, PDF pp.117-142 (Sonnet). The Ampere-Despretz orthogonal-currents experiment (January 1821) and eq. 6.7: confirm the torque formula, the date, and that a zero net torque implies k = -1/2. Confirm the full context of the "no proof deduced directly from experiment" quote and of the null-rotation experiment of March 1822.
4. PDF pp.420-428, 459-465 and 481-494 (Sonnet). (a) Does Ampere call ether theories unnecessary, or does he propose an ether or fluid origin for his force (resolve the digest contradiction between PDF p.424-425 and p.461)? (b) Summarise Notes 31.2-31.4 and the Part IX conclusion (the missing digest region).
5. Ch. 17 and Sec. 9.6-9.7, PDF pp.164-167 and 240-243, plus PDF p.475 (Sonnet). The Biot-Savart bent-wire errors: the measured result vs tan(rho/2), Biot's 1824 correction, and Ampere's integration. Give the formula chain for a primer exercise.
6. Ch. 22, PDF pp.282-289 (Sonnet). Exactly what the book claims for Weber's law (equations given, any claimed tests, and the regime of validity), so that claim 5 does not rest on a two-page summary seen by one reviewer.

Other actions

• digest/: write Amperes-Electrodynamics-28a544.31.md (Haiku, chunk 31).
• facts.json:
• set how_read to "digest + deep read (pp. ...)" after the deep reads;
• correct the "one-parameter family indexed by k" sentence;
• state the closed-circuit equivalence as a general theorem at k = -1/2;
• add the Despretz 1821 experiment, Savary's 1823 determination, the never-performed similarity experiment, Ampere's energy argument, the magnet self-rotation claim, the Onnes 1914 note and Grassmann/Clausius;
• drop or keep key claim 7 (Biot-Savart errors) consistently with claims.md.
• claims.md:
• claim 2: k = -1/2 follows from three null results (Despretz 1821 in hindsight, null rotation 1822, Savary 1823 with the ring magnet). n = 2 was asserted in 1822, derived by Savary in 1823, and checked experimentally only in 1878-1882. The similarity experiment was never performed by Ampere;
• add claim 6, magnet self-rotation and Newton's third law (Sec. 21.3);
• either restore the Biot-Savart-errors claim as a historical sub-claim or note why it was dropped.
• arbiter.md, add a "QE revision" section:
• correct D4 (Ampere did not perform the similarity experiment; Despretz and Savary routes);
• claim 3, quantitative bridge agreement: cite the book's own concession at PDF p.271 and primer Part B, and change it from "Plausible, untested neutrally" to "Refuted by calculation" for the strong claim that the field law fails quantitatively, or justify keeping it;
• rate claim 6 after deep read 1;
• close open question 6 (prefactor confirmed: eq. 2.16 with ii' <-> (mu0/2pi)II').
• primer.md:
• Sec. 4: fix "repeated by" (Ampere never built the similarity apparatus) and add the Despretz route to k = -1/2. It is a short calculation: (1-k)/c from the horizontal wire against (2+k)/c from the vertical wire, net (1+2k)/c = 0;
• Sec. 2: qualify "field momentum balances the books" (not needed for steady closed circuits);
• Sec. 6: add a row for claim 6;
• optional: add the Biot-Savart tan(rho/2) exercise to Check yourself;
• attribute the "elongate the current" quotation to the contemporary journal report.
• physicist.md: no rewrite needed. The arbiter's QE revision should note that the researchopinion.in citation is weak.
• prompt.txt / aaa-index-to-artifacts.md: consider adding [computed] to the allowed tag set.

Recheck

Recheck agent: Sonnet. Date: 2026-10-03. Checked the current claims.md, facts.json, arbiter.md, primer.md, example.py and the digest/ and deep/ folders against this QE. Source tag for every item: [read] of the current review files unless stated.

Defects

Missed material (QE section 3)

Remediation actions

Checks that still pass

• example.py runs cleanly in .venv; Parts 4 and 5 reproduce the Despretz and Biot-Savart numbers cited in the primer.
• The verdict scale is applied consistently in the arbiter's final table.

Open issues

1. Chunk 31 digest (PDF pp.481-519) still missing.
2. Deep reads 2-6 not run, so Part VI-VIII (Ampere's own text) and Ch. 22 (Weber) remain digest-level, and the ether question is unresolved.
3. [computed] tag not recorded in prompt.txt or aaa-index-to-artifacts.md.

Final: OPEN (3 issues)

Recheck 2

Recheck agent: Opus. Date: 2026-10-03. Checked the current facts.json, claims.md, arbiter.md, primer.md and deep/ against the three issues the first recheck left open. [read] of the current files.

1. Chunk 31 digest missing: REMAINS. digest/ has 35 entries and still no Amperes-Electrodynamics-28a544.31.md. The facts.json entry for PDF pp.491-519 still says "Not digested because the chunk 31 digest was never written", and claims.md and primer.md still say 32 of 33 digests. The deep/ file has no section on PDF pp.475-494 either, although facts.json lists it under how_read.
2. Deep reads 2-6 not run: PARTLY FIXED, REMAINS. deep/ now holds the Ch. 21, Ch. 22, Ch. 6.3-7.5, Part VI, Parts VII-VIII opening (to Sec. 29.1) and PDF pp.420-465 reads. The ether question is resolved (arbiter Round 2). Still not deep-read, and the arbiter and primer say so: Sec. 29.2-29.11 and Note 31.1 (Ampere's own statement of the four equilibrium cases, PDF pp.350-383 and 475-490), Notes 31.2-31.4, and Ch. 17 and Sec. 9.6-9.7 (the Biot-Savart bent wire, digest level). facts.json how_read claims "deep read" for pp.350-383, 475-494 and 240-243, which the deep/ file does not support, so it overstates coverage.
3. [computed] tag not recorded: REMAINS. grep computed finds nothing in prompt.txt or review/aaa-index-to-artifacts.md. The tag is defined only in primer.md.

Final: OPEN (3 issues)