Ampere: central claims

Coverage note (no source gap): the folder holds one text-layer PDF (548 pages), so all text is available. It was read through 32 of 33 digests (chunk 31, PDF pp.481-519, has no digest) plus one Opus deep read of Ch. 21 (PDF pp.266-281). Ampère's own 1820 papers (Part VI) and the 1826 Théorie translation (Parts VII-VIII) were digest-only, and Ch. 22 (Weber) and the Biot-Savart chapters (Ch. 17, Sec. 9.6-9.7) are digest-level. Claims about those parts rest on the book's commentary and digests [read], not on a deep read. Page numbers are PDF pages (printed = PDF minus 3).

1. The force between two current elements is central (along the line joining them), varies as 1/r^2, and depends on the angles through (sin(alpha) sin(beta) cos(gamma) + k cos(alpha) cos(beta)) with k = -1/2, so that Newton's third law holds in its strong form.
2. The constants were fixed by null results, not by one decisive measurement: k = -1/2 follows from the 1821 Ampère-Despretz non-rotation (in hindsight, torque proportional to (1+2k)), the 1822 null rotation, and Savary's 1823 combination with the Gay-Lussac-Welter ring-magnet null. The exponent n = 2 was asserted by Ampère in 1822 as not directly proved, derived by Savary in 1823, and tested directly only by Ettingshausen (1878), Felici (1882) and Tricker. Ampère never performed his own "law of similarity" equilibrium, so the title's "uniquely deduced from experience" is partly a rhetorical reconstruction.
3. Ampère's law predicts that collinear current elements with currents in the same sense repel, confirmed by the 1822 mercury-bridge experiment (Ampère and de la Rive). The field law (Grassmann/Biot-Savart-Lorentz) gives zero force between collinear elements, so it matches the measured bridge force only after adding the bridge's force on itself. The book concedes this match (PDF p.271), and the Ch. 21 deep read showed the two accounts give identical net forces for any closed source circuit. So the bridge cannot tell the laws apart; what differs is the interpretation of where the force comes from, and the strong third law fails for Grassmann at the level of single elements.
4. The standard field description violates the strong form of Newton's third law for elements. The authors extend this to the magnet that spins about its own axis (Ampère, 1821-22): they say the field explanation needs a self-torque and that the true torque comes from the external circuit or mercury, which feels an equal and opposite reaction (Davy 1823 and modern counter-rotation demonstrations are cited; no numbers are given in the book). The deep read judged the self-torque charge to be a bookkeeping point for steady closed circuits, and counter-rotation does not discriminate between the laws.
5. All of magnetism reduces to electric currents: magnets and the Earth contain molecular currents, so magnetic poles and fluids are unnecessary. Supporting items include the solenoid-magnet equivalence and a 1914 Nature note calling Onnes's persistent superconducting current an "Ampère molecular current" (digest only). Ampère argued energetically that continuous rotation cannot come from distance-only (static pole) forces because they cannot sustain rotation against friction.
6. Weber's later force law between charges (depending on relative distance, velocity and acceleration) unifies Ampère's electrodynamics with electrostatics and Faraday induction while keeping Newtonian mechanics, and is thus a better foundation than the field concept (rests on a short summary; Ch. 22 not deep-read).

Historical sub-claim, not counted among the central six: Biot and Savart's 1820s bent-wire "deduction" had errors (the first result, a torque proportional to the bend angle, is wrong; the integral gives tan(rho/2), confirmed by their 1824 experiment). The book says three errors; only this one is itemised in the digests.

Items unresolved by reading: whether Ampère held that ether theories are "unnecessary" (digest p.461) or proposed an ether/fluid origin for his force (digest p.424-428); whether Davy's 1823 mercury experiment tests the reaction-torque prediction; what the Notes (PDF pp.481-490) add.