Compton: arbiter (Step 3)

Document under review: A. H. Compton, "A Quantum Theory of the Scattering of X-Rays by Light Elements", Phys. Rev. 21(5), 483-502 (May 1923). Source: source folder: Compton/Compton_1923.pdf. Reviews arbitrated: physicist.md, mathematician.md, contrarian.md.

Source gap (repeated)

The PDF is an image-only scan with no text layer (Step 1: text_available none). Between them the three reviewers viewed essentially all pages as images, so the paper's own content is now well covered [read: page image]. The arbiter re-read pp. 4, 11 and 19 myself. What was never obtained: Compton's follow-up papers (Phys. Rev. 22, 409, 1923; Bull. Natl. Research Council 20, 1922), the 1925 Compton-Simon and Bothe-Geiger papers, Ishino (1917), Hewlett (1921), Barkla-Ayers, and the Klein-Nishina paper. Everything below about later tests, replications and the Klein-Nishina formula therefore rests on secondary web summaries or on [memory], tagged each time. Where a conclusion rests on [memory] alone, it is said.

A note on notation used throughout. alpha = h/(m c lambda_0) is a dimensionless number: the Compton wavelength h/(mc) = 0.024263 A (Angstrom = 10^-10 m) divided by the incident wavelength. sigma_0 is the classical (Thomson) scattering coefficient. sigma is the energy removed from the beam, sigma_s the energy truly re-radiated, sigma_a the energy handed to recoil electrons. "KN" is the Klein-Nishina formula (1928-29), the correct quantum-electrodynamic result for a free electron.

Corrections to Step 1 and to claims.md (confirmed by me)

1. Energy removed from the beam is sigma_0/(1+2 alpha) (Eq. 28, [read: page image p.493]). The factor (1+alpha)/(1+2 alpha)^2 is the truly scattered part (Eq. 29). Thus claim 4's "(1+2 alpha)^2/(1+alpha)" is correct for true scattering only, and Thomson over-predicts total energy removal by (1+2 alpha). All three reviewers agree; facts.json's "1/(1+2 alpha)^2" is wrong.
2. The RaC gamma-ray wavelengths (0.022 to 0.068 A) are inferred from absorption in lead with an assumed lambda^3 law; the primary 0.022 A is the output of the same method that feeds the prediction. Not a spectroscopic measurement (all three agree). Only the Mo K-alpha line is a direct spectrum.
3. Eq. 1 (p.486) is printed with "+ 2 (h nu_0/c)(h nu_theta/c) cos theta" [read: page image p.4]. Round 2 page-image read (see QE revision, Round 2): Fig. 1B marks theta as the interior angle between the incident and scattered momenta, i.e. the true scattering angle, so the law of cosines needs a MINUS. The plus sign is a real print error (paper typo, not a researcher fault). It does not propagate: Eq. 3 is correct. (An earlier version of this note read it as a Fig. 1B labelling inconsistency; the zoomed image shows that was wrong.)
4. Eq. 23 (p.10): the first two lines print 2 pi R^2, but the final numbered line prints 16 pi R with no square [read: page image p.10]. Real print slip (paper typo, not a researcher fault, not an OCR artefact); dimensionally intensity must fall as 1/R^2, and the rest of Eq. 23 checks out symbolically (Round 2 [calc]). Not load-bearing.

Recomputed numbers where reviewers differed (numpy, arbiter [calc])

Eq. 27 as printed on p.493: I/I_0 = (1/2)[1 + cos^2 theta + 2 alpha (1+alpha)(1 - cos theta)^2] / [1 + alpha(1 - cos theta)]^5. Integrating it over the sphere reproduces Eq. 29 exactly (0.90486 at 0.7 A, 0.74526 at 0.22 A, 0.20462 at 0.022 A). So Eqs. 27-30 are mutually consistent; all reviewers agree.

Disagreements settled:

• The physicist says KN would give "about twice Compton's number" for the Eq. 29 scattering part. That is wrong: it is 0.265 versus 0.205, a factor 1.3. The mathematician (about 25%) and contrarian (0.265 vs 0.205) are right.
• Eq. 27 vs the 40/140 deg ratio: Compton prints "about 1.10"; his own Eq. 27 gives 1.134 (physicist 1.136, mathematician 1.136, contrarian 1.134: agree). The KN ratio depends on what is measured: 1.105 for photon number, 1.162 for energy. So the physicist's "KN is 1.106, closer to Compton's rounded number" and the mathematician's "KN is 1.164, farther from observation" are both right, for different quantities. The observed 1.04 disagrees with both Eq. 27 and KN, so it does not discriminate between them; it points to the measurement (ionisation response, excess scattering) rather than to Eq. 27 specifically.
• Fig. 7 / p.501 [read: page image p.19]: the text says the 90 deg datum is 0.074 of the classical value, i.e. 0.037 I_0 (classical at 90 deg is 0.5 I_0, consistent). Eq. 27 gives 0.0697 I_0, so the datum is about half the formula (mathematician and contrarian agree; the physicist did not examine it). "Beautiful agreement ... not a single adjustable constant" is therefore a qualitative statement. Also, the "no adjustable constant" is true of the intensity scale but the 0.022 A input comes from the same absorption method (above). Reviewers disagree on whether the plotted points sit above or below the curve at 60 deg; I did not resolve the plot and do not rely on it.
• Wavelength constants: 2h/mc is 0.04853 A today; Compton's 0.0484 is 1923 constants, a 0.3% difference. No dispute.

Web checks (budget 8; 3 used before the search budget ran out)

• Klein-Nishina total cross-section reduces to Thomson (8 pi r_e^2/3) at low energy and "further scattering experiments agreed" with KN: [web] https://en.wikipedia.org/wiki/Klein%E2%80%93Nishina_formula. Wikipedia flags that experimental claim as uncited, so the experimental verification of KN stays at [memory: high] for me. The reviewers' NIST XCOM cross-check (Al mass energy-absorption 0.0287 cm^2/g at 0.5-0.6 MeV vs KN-derived 0.0286 and Compton/Ishino 0.021) is the contrarian's [web] https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z13.html; I accept it, since my own KN integral reproduces the 0.265/0.148 fractions the contrarian used.
• Both a shifted and an unshifted component appear when X-rays scatter; the unshifted part is coherent scattering off the whole atom: [web] https://en.wikipedia.org/wiki/Compton_scattering. This retags the contrarian's [memory: medium] to [web], and means the paper's "only a small part, if any" at the primary wavelength (p.3) is too strong as a statement about data.
• The 1925 Bothe-Geiger and Compton-Simon experiments and the end of Bohr-Kramers-Slater: [web] https://en.wikipedia.org/wiki/Bothe%E2%80%93Geiger_coincidence_experiment (cited by the mathematician and contrarian), and arXiv 1106.1365 (cited by the physicist). 1927 Nobel: stays [memory: high] (nobelprize.org returned HTTP 403 for the contrarian); the Wikipedia Compton scattering page also states it.
• The search tool was exhausted (200 of 200 calls). Not checked and remaining [memory: medium or low]: Duane's experimental challenge and later concession, Debye's independent 1923 derivation, the quality of Ishino (1917) and Hewlett data, Compton's Phys. Rev. 22, 409 follow-up numbers, replications by Ross and others. No verdict below depends on these; they affect only history colour. They are not stated as fact here.

Verdict scale applied consistently

Rule used: a claim's verdict says what a controlled test or accepted theory says about the claim as stated. Where the 1923 paper's own evidence is weak but the claim was later confirmed by independent work, the verdict is Established and the paper's evidence is described separately. Where a formula was right at leading order but replaced by a more exact theory, it gets Historically superseded but instructive.

Per-claim arbitration

Claim 1. A scattered quantum gives its energy and momentum (h nu/c) to one electron, which recoils.

• Agreement: all three say Established; the maths (energy plus momentum conservation) is exact special relativity and was re-derived by every reviewer.
• Disagreement: none on the verdict. The mathematician flags the Eq. 1 sign issue (resolved in Round 2 as a real print sign error that does not propagate) and that the unshifted line is a bound-electron effect outside the paper's scope.
• Tested vs never-tested vs dismissed (contrarian's distinction): this was tested, not dismissed. The 1923 evidence was indirect (a shifted line plus beta-ray speeds, roughly 0.5 c average, paper's own admission that recoil electrons from ordinary X-rays were not observed). Direct event-by-event evidence came in 1925 (Compton-Simon cloud chamber, Bothe-Geiger coincidence counters) [web: Wikipedia Bothe-Geiger page], by independent groups in Chicago and Berlin, and it counted against Bohr-Kramers-Slater. The claim met resistance (Duane, BKS) [memory: medium for Duane], but it was resolved by experiment.
• Stronger argument: all agree; contrarian is most careful in separating the 1923 paper's support (Plausible-level, indirect) from the later decisive tests.
• Settling experiment: already done (1925 coincidence/cloud-chamber).
• Final verdict: Established. (The 1923 paper alone supported it at roughly Plausible-to-supported level.)

Claim 2. Shift = (2h/mc) sin^2(theta/2) = 0.0484 sin^2(theta/2) A, independent of lambda_0.

• Agreement: all three Established. Maths consistent: Eq. 5 follows from Eq. 3, alpha times lambda_0 cancels the incident wavelength.
• The paper's own test: a single line (Mo K-alpha, 0.708 A, graphite, 90 deg): observed 0.022 A against 0.024 A predicted, about 9-10% off, no stated uncertainty, with the promised experimental paper unpublished (footnote). Independence of wavelength rests on an earlier unpublished "roughly 0.03 A" over 0.7-0.025 A, 25% from 0.024 A. The contrarian and mathematician are right to call this a rough test.
• Tested/replicated: yes widely, by modern Compton spectrometers [memory: high; no web source retrieved]. Specific 1920s replications [memory: medium, unverified].
• Settling experiment: already done (angle series at several wavelengths, high precision).
• Final verdict: Established, with the caveat that the 1923 paper itself shows it at about 10% precision at one angle.

Claim 3. Mo K-alpha 0.708 to 0.730 A; RaC gamma 0.022 to 0.068 A at 135 deg.

• Agreement: the three agree on the facts (Table I: 45 deg 0.030 vs 0.029; 90 deg 0.043 vs 0.047; 135 deg 0.068 vs 0.063; scatter 5-9% in both directions; absorption-based, partly circular wavelengths). They differ in labelling: the physicist gives "Plausible, untested in this form" for the gamma data; the mathematician and contrarian say Established for the formula and crude/indirect for the data.
• Which is stronger: the physicist's label is awkward, because "untested" misdescribes data that exist but are weakly probative. The verdict scale applies to the claim; the claim "experiment agrees" is a statement about the evidence. Split fairly:
• Mo K-alpha shift, 0.730 vs 0.708: Established (a direct spectroscopic result, consistent with all later work), at about 10% precision.
• RaC gamma-ray numbers as evidence for the formula: not independently probative (indirect inference, circular calibration, no error bars). The formula is Established by later work, so the item is a weak 1923 test of a claim that is true, not a failed test. On the scale: described in words rather than forced onto the scale (QE revision): a weak, indirect 1923 test; the formula itself is Established by later work.
• One further 1923 weakness: the paper's statement (p.3) that "only a small part, if any" of the secondary radiation has the primary wavelength is too strong (QE: the words "little or none" are not in the paper). The unshifted component is real [web: Wikipedia Compton scattering].
• Settling experiment: direct crystal-spectrometer measurement of the gamma-ray scattered wavelength, which modern gamma spectroscopy does routinely [memory: high].
• Final verdict: Split. Mo K-alpha shift: Established. RaC gamma Table I as evidence: weak indirect 1923 test (inferred wavelengths, circular calibration); formula Established by later work.

Claim 4. Thomson scattering fails for hard X-rays/gamma-rays; true scattering over-predicted by (1+2 alpha)^2/(1+alpha); quantum coefficients match Ishino and Hewlett.

• Agreement: all three split it: qualitative failure of Thomson, Established; Eqs. 28-30, Historically superseded but instructive.
• Disagreement: how badly the agreement with Ishino was misleading. The physicist's claim that KN would give "twice" Compton is wrong (1.3x, see recomputation). The contrarian's NIST comparison is the strongest evidence: KN gives 0.0286 cm^2/g for Al absorption at 0.56 MeV, matching NIST, while Compton and Ishino both give about 0.021, 27% low. Agreement between a low formula and a low measurement. This holds at [web] for NIST and [calc] for KN; Ishino's quality itself is [memory: low].
• Hewlett: Compton concedes the agreement below 0.5 A is "perhaps within the experimental error" [read: page image p.16]; the data cannot discriminate Compton from KN there (contrarian). Above about 0.5 A Hewlett's points lie above the curve (excess scattering, unexplained in the paper).
• Tested vs never tested: the qualitative failure was tested and settled before and after the paper. Compton's coefficients were compared post hoc with existing data, not with a pre-planned test. They were refined, not suppressed.
• Settling calculation: integrate KN over angle and compare to NIST XCOM (done above: 0.413 vs Compton's 0.312 at alpha = 1.10; 0.936 vs 0.935 at alpha = 0.035).
• Final verdict: Split. Thomson fails at high photon energy: Established. Eqs. 28-30: Historically superseded but instructive (correct to first order in alpha; 25% low at alpha about 1).

Claim 5. Forward-concentrated intensity (Eq. 27), via moving radiator with beta = alpha/(1+alpha); Barkla-Ayers fits imperfectly.

• Agreement: all call it Historically superseded but instructive; all note the author's own admission "I have not, however, succeeded in showing rigidly ..." (p.491) and that the algebra downstream is correct (Eqs. 22, 25, 27 reproduce numerically).
• Disagreement: (i) the mathematician adds "Tested, not supported" for the Barkla-Ayers comparison; the physicist and contrarian do not. (ii) Whether Eq. 27 is "refuted by calculation". The physicist argues no, because the refutation needed the 1929 Dirac-based theory.
• Arbitration: (i) Barkla-Ayers 1.04 vs 1.10-1.16 disagrees with Eq. 27 and with KN alike (see recomputation), so it is not a test of Eq. 27 versus an alternative; it indicates measurement problems (ionisation response, excess scattering; Compton's rescue is plausible but unquantified, as the contrarian says). I do not adopt "Tested, not supported" for Eq. 27 on that dataset alone; it was a single 1910s-era dataset, not a controlled test of the claim. (ii) The physicist is right: "Refuted by calculation" requires accepted laws applied correctly. KN is the accepted law and shows Eq. 27 is wrong at large alpha (forward/backward 32 vs 5.8; at 90 deg and alpha = 1.09 Eq. 27 gives 0.0697 I_0 and KN gives 0.0859, so KN is 1.23 times larger, i.e. Eq. 27 is about 19% low). That is a replacement by a better theory, which fits the superseded label; the premise was never a contradiction of its own equations, so not Internally inconsistent either.
• Qualitative forward concentration: Established (experiment predates the paper and KN agrees). The black-body check (Eq. 20) tests the Doppler intensity transformation only, not the hypothesised equivalence; the contrarian is correct that it does not support the key assumption.
• Fig. 7 caution: the single quoted datum is about half Eq. 27 at 90 deg; "beautiful agreement" is overstated; the ionisation chamber's wavelength response is admitted unknown (p.501).
• Settling calculation: KN versus Eq. 27 (done above); settling experiment: a calibrated energy-resolving detector for gamma-ray scattering angular distributions (done by later experiments [memory: high; not web-verified]).
• Final verdict: Split. Forward concentration (qualitative): Established. Eq. 27 as the quantitative law and its heuristic derivation: Historically superseded but instructive. Barkla-Ayers comparison: inconclusive (disagrees with both Eq. 27 and KN, so measurement-limited), not scored separately.

Claim 6. The theory holds only for loosely bound electrons in light elements.

• Agreement: all Established for the stated limitation (recoil energy must exceed binding energy). The mathematician's estimate: recoil kinetic energy about 0.57 keV for Mo K-alpha at 90 deg, far above carbon valence binding (about 10 eV) and above the carbon K-shell 0.28 keV [memory: medium for the binding energy]. I did not re-derive; it is plausible arithmetic (17.5 keV times 0.0333).
• Disagreement: only on the "quantum spreads over many electrons" speculation. Physicist: Not testable as stated. Contrarian: Plausible, untested in 1923, later replaced by coherent scattering. I side with the contrarian's historical reading but the physicist's scale reading: the remark is a vague guess with no equation, so by the scale it is Not testable as stated; the later coherent-scattering account (whole atom scatters with negligible recoil; unshifted line) [web: Wikipedia Compton scattering] is the accepted replacement.
• Final verdict: Established (as a stated limitation). The "spread over many electrons" speculation: Not testable as stated (superseded by atomic coherent scattering).

Contrarian lens, kept visible

For this project the three categories come out as follows.

• Tested and held: photon momentum and single-electron recoil (Claim 1), the shift formula (Claim 2), qualitative failure of Thomson scattering (Claim 4), forward concentration. Tested by independent groups in 1925, which beat the prevailing wave-theory and Bohr-Kramers-Slater consensus. A heterodox claim that won on experiment.
• Tested, partly or approximately: Compton's quantitative formulas (Eqs. 27-30) were compared with existing data, did not hold up at alpha about 1, and were replaced by KN.
• Never properly tested in the paper: wavelength-independence of the shift across 0.7-0.025 A (rests on an earlier unpublished report); the gamma-ray wavelengths (never measured directly in this paper); the ionisation-response assumptions behind Fig. 7 and Barkla-Ayers.
• Dismissed without testing: nothing in this project. The claim was contested (Duane, BKS [memory/web, as stated above]) and then tested. No funding or publication block is documented in what was read.
• Researcher-side faults (the contrarian's, accepted): cites unpublished experiments; overstates "beautiful agreement" (Fig. 7 datum a factor of about 2 off; no error bars); absolute scale fixed by the same method as the gamma wavelength; admitted-unproven step in Eq. 27; "only a small part, if any" unshifted. No fabricated data or unit errors found; the Eq. 1 sign and the Eq. 23 R vs R^2 slips are confirmed by page image as printed errors (see QE revision, Round 2); they are paper typos, not researcher faults.

Corrected claim list

1. A scattered X-ray or gamma-ray quantum transfers energy and momentum (h nu/c) to a single, essentially free electron, which recoils (relativistic kinematics). Direct event-by-event confirmation came in 1925 (Compton-Simon, Bothe-Geiger).
2. The wavelength shift is (h/mc)(1 - cos theta) = (2h/mc) sin^2(theta/2) with 2h/mc = 0.04853 A (Compton used 0.0484), independent of the incident wavelength. (Paper typos, not researcher faults: Eq. 1 prints + where the law of cosines needs -; Eq. 23's final line prints R where R^2 is needed. Neither propagates.) The paper's own test: Mo K-alpha off graphite at 90 deg, 0.022 A observed vs 0.024 A predicted (about 10%, no error bar, one angle).
3. The gamma-ray "shift" 0.022 to 0.068 A at 135 deg is inferred from lead absorption with an assumed lambda^3 law (the 0.022 A primary comes from the same method), and gives 0.068 observed against 0.063 calculated at 135 deg (Table I, headings and values confirmed from the page image: 0.030/0.029 at 45 deg, 0.043/0.047 at 90 deg; Eq. 31 gives 0.046 at 90 deg). It is a weak, indirect test; the formula is Established by later work.
4. Thomson scattering fails at short wavelengths. The energy removed from the beam is sigma_0/(1+2 alpha) (Eq. 28); the truly scattered part is sigma_0 (1+alpha)/(1+2 alpha)^2 (Eq. 29), the absorbed part sigma_0 alpha/(1+2 alpha)^2 (Eq. 30). These are right to first order in alpha but about 25% low at alpha near 1 compared with Klein-Nishina; the agreement with Ishino reflects a low formula meeting low data.
5. The angular law (Eq. 27) rests on an admittedly unproven assumption; it reproduces the qualitative forward concentration but not the correct distribution (forward/backward 32 vs 5.8 at alpha = 1.09; Eq. 27 is about 20% low at 90 deg and 33% low at 135 deg against KN). Barkla-Ayers (1.04 observed) does not match Eq. 27 (1.13 by recomputation, not Compton's rounded 1.10) nor KN (1.105 by number, 1.16 by energy).
6. The treatment holds when the photon energy far exceeds the binding energy (loosely bound electrons, light elements). For tightly bound electrons the atom scatters coherently with no wavelength shift, which the paper's "only a small part, if any" at the primary wavelength (p.3) understates. Fig. 4 does not resolve an unshifted peak at 0.708 A but cannot exclude one (poor resolution, normalised heights).

What would settle it

• Claim 1: already settled by the 1925 coincidence and cloud-chamber experiments.
• Claim 2: a modern angle-and-wavelength series with a Bragg spectrometer (reader-accessible via published data); already done.
• Claim 3 (gamma data): a direct crystal or germanium-detector measurement of scattered RaC/Cs-137 gamma-ray energy against angle.
• Claim 4: integrate KN and compare with NIST XCOM for light elements at 0.02-0.7 A (a calculation the reader can run; the arbiter's numbers above do this for three wavelengths).
• Claim 5: compare Eq. 27 with the KN differential cross-section at several angles (done above) and with a measured gamma-ray angular distribution from a calibrated energy-resolving detector.
• Claim 6: compare shifted-to-unshifted intensity versus momentum transfer for light vs heavy targets (the standard Compton profile / form-factor measurements).

Open questions

• Fig. 7: resolved by the QE deep read (see QE revision): points are on or above the curve only at about 44-60 deg and below it at 75-150 deg.
• What exactly Barkla-Ayers and Ishino measured, and why Barkla-Ayers got 1.04. Source documents not obtained.
• The content and outcome of Duane's challenge, the numbers in Compton's Phys. Rev. 22, 409 follow-up, and the replications by Ross and others (all [memory: medium or low], unverified).
• Whether Compton knew his Eq. 27 forward normalisation (Eq. 26, classical forward intensity) was an assumption, or how sensitive Table I is to the choice of 0.022 A.
• Eq. 23's R vs R^2 and the Eq. 1 sign: resolved in Round 2 (both are real print errors, not researcher faults; neither affects a verdict).

Verdict summary

Files: review/Compton/arbiter.md (output); scratch images in /tmp/compton_arb (pp. 4, 11, 19).

QE revision

QE verdict was MINOR. No final verdict changes (also after Round 2); one label is reworded (Claim 3b). Source for the new evidence below: deep/Compton-1923-fb4d86.md, a Sonnet read of PDF pp.18-19 at 200 and 400 dpi [read: page image p.18]; read-offs are good to about +/-0.01 in I/I_0 and +/-3 deg.

New evidence: Fig. 7 (resolves the open question)

• The 8 filled dots (the text says "circles"), no error bars, at about 28, 44, 60, 75, 90, 120, 135, 150 deg, all lie far below the classical curve (about 0.04 vs 0.50 at 90 deg, 12 times lower). The classical law is decisively rejected.
• Against Eq. 27: on or slightly above at about 44 and 60 deg (60 deg about 20% above); below at about 28 and 75 deg (75 deg 15-20% below); systematically below at 90-150 deg (about 0.55-0.75 of the computed Eq. 27 value). This settles the disagreement: the mathematician was closer (a one-sided deficit at large angles), and the contrarian's "above near 60 deg" is also right but only at one point.
• The 90 deg datum read from the plot is about 0.041; the text says 0.037 I_0 (0.074 x classical 0.5), against Eq. 27 about 0.069-0.070. Confirmed: the curve is nearly twice the measured value.
• The drawn solid curve at large angles sits above the printed Eq. 27 evaluated at alpha = 1.10 (about 0.046 vs 0.034 at 150 deg; 0.040 vs 0.030 at 180 deg). Cause unidentified (drawing, smoothing or a different alpha). Against the drawn curve the large-angle dots are 40-45% low; against the formula about 25% low. Treat as the deep reader's own read-off and numpy check, not as a confirmed error in the paper.
• Details: the scatterer is iron, not a light element; the plotted "intensity" is an ionization reading under the admitted assumption that ionization varies little with wavelength ("not clear ... appears probable", p.19); ordinary X-ray data agree only "if correction is made for the excess scattering ... at small angles" (p.18). The "no adjustable constant" claim holds for the curve, but the scale is tied to the 90 deg calibration and to the assumed 0.022 A.
• Verdict effect: "beautiful agreement" is fair as shape (steep fall, low plateau) and overstated as numbers. Claim 5 verdicts are unchanged: Eq. 27 stays Historically superseded but instructive.

Corrections adopted from QE

• Quotation: the paper (p.3) says "only a small part, if any, of the secondary X-radiation is of the same wave-length as the primary". "Little or none" is not in the paper. Corrected in Claim 3, Claim 6 and the Corrected claim list.
• Claim 5 sentence about the 90 deg intensity rewritten (Eq. 27 0.0697 vs KN 0.0859; KN 1.23 times larger).
• Claim 3b label: the Table I gamma data are not a claim about physics but about the strength of 1923 evidence, so they are described in words (weak indirect 1923 test; formula Established by later work) rather than "Plausible, untested in this form". No scale verdict changes.
• Table I values (observed/calculated, p.14, QE-checked against the OCR text): 45 deg 0.030/0.029, 90 deg 0.043/0.047, 135 deg 0.068/0.063. The digest swapped observed and calculated for two rows; no review used the wrong values.
• Source gap statement: the PDF now has a full OCR text (Step 0) and the arbiter's "no text layer" wording at the top is out of date. Equations still need page images.

Added to the contrarian lens

• Compton reversed his own published position. In a footnote on p.3 he says that in 1921 (Phil. Mag. 41, 749; Phys. Rev. 18, 96) he had defended an admixture of fluorescent radiation as the cause of the softening of secondary X-rays, that J. A. Gray (1913, 1920) and Florance (1914) had argued for true scattering, and that "the latter view is the correct one" [read: OCR text p.3, via QE]. He also drops his own earlier "large electron" hypothesis as "superfluous" (p.19). Lesson for this collection: the researcher followed the data against his own earlier theory, and Gray and Florance were partly right before him.
• Compton admits that recoil electrons from ordinary X-rays had not been observed (p.14).
• The 0.022 A primary is anchored by two partly independent cross-checks: his own 0.025 A from small-angle scattering by lead (Phil. Mag. 41, 777, 1921) and Ellis's beta-ray lines (0.045, 0.025, 0.021, 0.020 A) [read: OCR text p.14, via QE]. The self-calibration criticism stands but is softened.

Round 2 (deep reads 2 and 3 completed)

Source: deep/Compton-1923-fb4d86.md, the sections "Deep read: p.10", "Second QE round: Fig. 4 and Table I, pp. 13-14" and "QE round 2: page 4 and page 10". All read from rendered page images (200-500 dpi) [read: page image p.4, p.10, p.13, p.14]. The deep read of p.10 and the later p.4/p.10 read agree.

• Fig. 1B and Eq. 1 sign (p.4). Fig. 1A marks theta between the scattered quantum and the extension of the incident direction (the true scattering angle). In Fig. 1B the arc theta sits INSIDE the momentum triangle at the vertex between the incident momentum (h nu_0/c) and the scattered momentum (h nu_theta/c). It is theta itself, not 180 deg minus theta. Eq. 1 is printed with a PLUS before the cross term; the law of cosines for that interior angle gives a MINUS, and Eq. 3 follows only with the minus. Outcome: a real print error, recorded as a paper typo (not a researcher fault). It does not propagate (Eq. 3 and later equations are correct). This replaces my earlier "labelling inconsistency" reading. [read: page image p.4; law of cosines standard]
• Eq. 23 (p.10). Printed denominators: line 1 is 2 pi R^2 sin(theta) d(theta); line 2 is 2 pi R^2; the final numbered line is 3 n h nu_0 / (16 pi R), with NO square on R, and (1 + alpha - alpha cos theta)^5. So Eq. 23 does not print R^2 in its final line: the missing square is a real printed slip, NOT an OCR artefact (the OCR text "167R" matches the image; the earlier "OCR shows R^2" note referred only to line 1). Dimensionally the denominator needs R^2. With beta = alpha/(1+alpha) the final line equals line 2 exactly in SymPy [calc, deep reader]. Paper typo, not a researcher fault; not load-bearing.
• Fig. 4 (p.13), Mo K-alpha off graphite at 90 deg. No separate unshifted peak at 0.708 A is resolved. The scattered curve is one broadened peak displaced a few tenths of a degree to larger angle (0.730 vs 0.708 A), with a fatter right flank; any unshifted component would be buried in the overlap (shift about 0.2 deg, comparable to peak width). The only extra bump (about 6.0-6.2 deg) appears in the primary curve too and is a primary-spectrum feature, not an unshifted K-alpha. Heights are normalised, no counts or error bars, so a minor unshifted line is neither seen nor ruled out. Wording to use: "not resolved in Fig. 4", not "absent". [read: page image p.13] Also read there: experiment 0.022 A vs theory 0.024 A (0.0484 x sin^2 45 deg = 0.0242), about 8-9%, no uncertainty.
• Table I (p.14): headings and values confirmed from the page image. Headings: Angle | mu/rho | tau/rho | lambda obs. | lambda calc. Rows (obs/calc): 45 deg .030/.029; 90 deg .043/.047; 135 deg .068/.063; primary .076 and .017, 0.022 A. The OCR is garbled; the image fixes it. [read: page image p.14]
• New detail from Table I (deep reader's arithmetic): "observed" wavelengths follow lambda = 0.022 (tau/rho / 0.017)^(1/3) (gives .0298, .0425, .0680), so they are absorption inferences scaled to the primary 0.022 A, which itself comes from the same extrapolation, cross-checked against the author's own 0.025 A and Ellis's beta-ray lines (0.020-0.025 A and 0.045 A). Eq. 31 gives 0.0291, 0.0462, 0.0633, so the printed 0.047 at 90 deg should round to 0.046 (0.001 A, trivial). Observed minus calculated is +0.001, -0.004, +0.005 A at 45, 90, 135 deg (the sign changes, so no systematic trend). The gamma beam is a mixture of lines (Ellis), not monochromatic.
• Other pp.13-14 notes: scattered background above the primary at small angles in Fig. 4 (extra diffuse radiation); recoil-electron maximum speed beta_max c = 2 c alpha(1+alpha)/(1+2 alpha+2 alpha^2), zero forward; ordinary X-ray recoil electrons "have not been observed"; the claim that most secondary beta-rays are recoil electrons rests on Compton's own 1922 report.

Verdicts changed by Round 2: none. Claim 2 and Claim 3 stay as before (Mo K-alpha shift Established at about 10% precision; RaC Table I a weak, indirect, partly circular 1923 test). Claim 6 stays: the unshifted line is a later, web-sourced result, and Fig. 4 neither shows nor excludes it. What does change is the error record: the Eq. 1 sign and Eq. 23 R slips are now confirmed printed errors (paper typos, not researcher faults), and the Table I 90 deg "calc" entry is 0.001 A off a straight evaluation of Eq. 31 (rounding, trivial). Verdict table and Corrected claim list are annotated accordingly below.

Not done

• None of the QE deep reads remain outstanding. Web verification of the unshifted line still rests on [web] Wikipedia Compton scattering; the Fig. 4 reading adds no new [web] source.