QE (STEP 4b): Summerfield (Arnold Sommerfeld), Atomic Structure and Spectral Lines

Date: 2026-10-09. QE agent (Opus).

What I read: prompt.txt; _text/manifest.json; all 27 digests (in full); facts.json, claims.md, sites.md, arbiter.md and primer.md (in full); the three reviews and the deep-read file by section (grep, then the relevant ranges); the research notes as needed. I checked facts against the folder OCR (_text/...0c4636.txt), against the Investigator's cleaner single-page OCR of the same 1923 edition (research/files/Sommerfeld-1923-AtomicStructure-IA-atomicstructures0000somm_djvu.txt, cited below as "IA OCR" with line numbers), and against the saved Paschen 1916, Glitscher 1917 and Gehrcke-Lau 1921 texts and the 1924 letter transcription (research/pages/trans02183.html). I ran example.py.

Tags: [read] = from a document or saved file, with location; [computed] = my own arithmetic; [memory] = recalled, with confidence.

Verdict: MINOR

The central verdicts hold. The arbiter's and primer's main story stands: formula right, picture wrong; the 1921 shortfall is largely blending; Abraham is excluded; Weber is not excluded by the splittings. I found one retention defect that touches a sub-verdict (claim 6b, Weber versus relativity). The arbiter says the deciding measurement "was not measurable then", but the book itself (book p.488) and Paschen's 1916 paper report it, with a number. I also found two pertinent passages in the saved sources that nobody used, one citation error, one verdict outside the scale, and a set of digest-only experimental results that never reached the reviews. All of this can be fixed by updating facts.json, claims.md, a "QE revision" section in arbiter.md, and primer.md. No redo of Steps 2-4 is needed.

1. Coverage

• The manifest lists one document (the 324-page scanned book, all pages OCR'd). All 27 chunks were digested. None was skipped. No coverage defect.
• The project also has saved Investigator documents (research/files/: Sommerfeld 1915 and 1916, Paschen 1916, Glitscher 1917, Gehrcke-Lau 1921, Eckert, arXiv papers, the IA OCR of the same book). These are not manifest documents. The reviewers read parts of them. Section 3 lists what was missed in them.

2. Shortcuts

The IA OCR is clean enough for every remaining deep read to be done cheaply from text, with page images only for tables.

3. Missed material (from the digests and the saved sources)

Most important first.

1. The book and Paschen report a measurement of the "circular-orbit" (l-independent) relativity term. That is exactly the term that separates relativity from Weber's law. The book says: "Very slight deviations from the formula ... have already been occasionally observed earlier, and ... these deviations, according to a paper by Paschen ... are of the order of magnitude of our relativity correction R alpha^2/64 required by theory and bear the correct sign" [read: IA OCR lines 42967-42984, book p.488; also the deep read, line 924]. Paschen 1916, section "Das Relativitätsglied", gives a number. He compares He+ 4686 with the 4339 group and says that leaving the term out puts 4339 0.025 Å too low. He finds "beob. N_He - nu_He = 0.569 +/- 0.25" against "Nach Bohrs Relativitätsglied berechnet ... 0.590" [read: research/files/Paschen-1916-BohrsHeliumlinien-AnnPhys50-iss16_djvu.txt, lines 6173-6283]. - Why it matters [computed]. In atomic units, Sommerfeld's level shift is -alpha^2/(2N^3 n) + 3 alpha^2/(8N^4). Weber's is -alpha^2/(2N^3 l) + alpha^2/(2N^4). For a circular orbit (n = l = N), Sommerfeld gives -alpha^2/(8N^4) and Weber gives zero. For N = 2 the relativistic circle term is R alpha^2/64 = 0.091 cm^-1, the very number the book quotes. - What this changes. If Paschen's figure is taken at face value, it sits about 2.3 of its own error bars from Weber's prediction of zero and 0.1 from relativity's. - Caveats, which belong next to the figure: one source; Paschen worked with the theory's author (an interested party, see his "freundlicher Hilfe"); the error bar is 44 per cent; the result depends on how R_He was fitted; and Abraham's 4/5 would also fit within it. - Counter-evidence that also belongs in the record: Sommerfeld's draft of 29 Dec 1915 found the absolute values of Balmer differences off by more than a factor of two (0.102 against 0.24). The primer says that draft concerns the circular-orbit shift [read: primer section 7]. - Where it went missing. The physicist quotes the book's sentence but then says the absolute shift "was not measured at the needed accuracy then", with no source [read: physicist.md line 85]. The arbiter repeats this as "that was not measurable then" (arbiter section 3, claim 6, and section 5). The primer drops the book's statement and Paschen's number altogether (section 4, and answer 3). This is pertinent evidence, left out of the arbiter and primer and replaced by an unsourced negative.
2. Paschen himself (1916) said the measured H-alpha doublet was probably too small, because of blending. "Die Messung war aber schwierig, und es ist wegen der übergreifenden Ränder der unscharfen Komponenten wahrscheinlich, daß der Abstand der eingestellten schwärzesten Stellen zu klein ist" (the measurement was difficult, and because the edges of the blurred components overlap, the distance between the darkest points set on is probably too small) [read: Paschen 1916 txt, lines 6312-6318]. In 1916 the experimenter gave the same explanation that the contrarian and arbiter reach by simulation for the 1921 shortfall. It belongs in arbiter claim 2 and primer Step 5. The book also names Doppler and Stark broadening as the cause of the blurring [read: IA OCR lines 42402-42424].
3. Electron-impact tests of He+ as a hydrogen-like ion (Ch. VI section 3, digest only). Predicted second-order ionisation potential of He: I + 4 x 13.5 = 79.3 V. Observed: 79.5 +/- 0.3 V (Franck and Knipping) and 80 V (Horton). Predicted excitation of 4686 from neutral He: 25.3 + 50.1 = 75.4 V. Observed by Rau: absent at 75 V, full intensity at 80 V [read: IA OCR lines 31190-31236]. These are independent, non-spectroscopic checks of claim 1a (the Z^2 energy formula). No review or arbiter cites them. The modern total binding energy of He, 79.0 eV [memory, high], agrees. (Digest .16 p.182 prints 79.8 V; the correct reading is 79.3.)
4. Selection-rule breaks blamed on electric fields, beyond He+ 4686. Ch. VI lists anomalous series n -> n-2 (Stark, Liebert, Hardtke), d -> s (Foote, Meggers, Mohler), b-p combinations in Li, Na, K, Al, Tl, Ag, and the He 1S-2S line at 585 Å. All are attributed to intense fields in the discharge [read: digest .15 p.176; .16 p.185]. The same pattern appears for the Zeeman components at two and three times the normal splitting (digest .14 p.160) and for Paschen's forbidden lines in a magnetic field (digest .17 p.191). This is the context for the arbiter's verdict 2e ("stray-field explanation ... Never properly tested"): the field explanation was used repeatedly, and in each case no field was measured. Today most of these are known to be allowed or field-induced lines in the modern scheme [memory, medium]. They belong in the record beside 2e.
5. Barkla's J-radiation (1917). Barkla reported a radiation harder than K. "Repeated tests by other observers have, however, not been able to confirm" it, "Nor has the theory a place for such radiation" [read: IA OCR lines 10915-10919]. This is an anomalous experimental claim by a leading experimenter (Nobel 1917 [memory, high]), weighed by replication and by theory. It is pertinent to this project's reader and should be in facts.json with both reasons stated.
6. Nebulium, Coronium and Protofluor. The book uses the nuclear model to exclude claimed new elements lighter than helium that were based on nebular and coronal lines [read: digest .04 p.45; IA OCR line 5246]. These lines were later shown to be forbidden lines of ionised O, N and Fe [memory, high]. The episode ties directly to the book's selection principle and is instructive.
7. Sommerfeld and Debye's accumulation theory (Ann. Phys. 41, 873, 1913), digest .03 p.32. This was the author's own classical alternative to light quanta: the atom stores radiation until it holds h nu. It predicts accumulation times of years for X-rays, and experiment shows immediate emission. It is a tested-and-failed alternative that bears directly on claim 3 (wave versus quanta). Not in facts.json or the reviews.
8. Other retractions and disputes the book records. - The earlier "A-doublet" assumption is "refuted by Hoyt's measurements and falls to the ground" (digest .09 p.101). - The earlier identification of theta with x' is withdrawn (digest .08 p.89). - The author's "false interpretation" of one doublet is withdrawn (digest .08 p.95). - The arbiter and primer say "two retractions". The book has at least five. - Fues's half-integer quantum numbers are rejected by the author in favour of integers (digest .17 p.198). Half-integers later proved right [memory, high]. That is a counterpart to the "formula right, picture wrong" lesson.
9. Doublet-atom model numbers. The addendum written with Heisenberg gives Li Delta nu = 0.32 cm^-1 (p-term) and 0.035 (d-term), "in excellent agreement" with the data (digest .19 p.214). This model, with its half-Bohr-magneton trunk, is a forerunner of spin [memory, high]. It is currently listed in facts.json only as "digest only" without the numbers.

10. Records named in the book but not examined:

    • R. T. Birge's careful retest of the H-alpha components (Phys. Rev. 17, 589, 1921) [read: IA OCR line 42957];
    • Birge's alpha^2 = 5.308e-5 (digest .23 p.274);
    • E. Grossmann's 1921 criticism of Newcomb's Mercury numbers (digest .21 p.244).

    Birge belongs in the arbiter's "what would settle it" table for the 1921 dispute. 11. Small items for the misprint or translation list (claims.md): - The English text says of Doppler broadening "the higher the temperature the lower the velocities due to heat motion" [read: IA OCR lines 42415-42416]. That is a translation or print slip; it should read "higher". - In the e/h passage Sommerfeld writes "If, then, Paschen has not under-estimated the accuracy of his measurement ..." [read: IA OCR line 47880]. So the author himself flagged the error bar of the key datum. This is worth one line in the primer's error-bar lesson.

4. Accuracy spot checks

5. Retention check

Was pertinent material left out of the arbiter or primer because a reviewer judged it negatively, or replaced by an unsourced judgement?

• Defect (item 3.1). The book's and Paschen's report of the circular-orbit relativity term was turned into "not measured at the needed accuracy" (physicist) and then "not measurable then" (arbiter). The primer drops it. This is source material that bears on a verdict (6b). The reviewer's opinion about its accuracy replaced the source instead of standing beside it. Retention rule: state the source's claim and its number, then the reviewer's caveats.
• Defect (item 3.2). Paschen's own 1916 statement that the measured doublet is "probably too small" is in a saved source the reviewers quoted from, yet it is used nowhere. It supports the arbiter's verdict, so this is an omission rather than suppression. It is still pertinent material lost from the record.
• Kept correctly (no defect):
• the Gehrcke-Lau dissent (quoted, with their stake stated separately);
• Sommerfeld's private 1924 doubt;
• Lau's He+ analogues, as one documented source;
• McLennan's confirmation, together with Sommerfeld's private discount of it (contrarian, physicist);
• the Weber result;
• the Nobel silence, with competing explanations;
• the Glitscher test;
• the Houston-Williams-Pasternack gap;
• the misprint list;
• the magneton coincidence.

The primer keeps the Investigator's leads (letters, Eckert, Kragh, Vickers, Ishiwara) and names interested parties on both sides. - Not reaching the primer. The Investigator's "doublet riddle" lead (Millikan and Bowen's 1924 extension of the relativistic doublet formula to optical spectra, Landé's polemic) is in the three reviews and the arbiter (claim 5), but not in the primer. The 1924 letter calls it "eine ungeheure Erweiterung des Gültigkeitsbereiches" (an enormous extension of the formula's range of validity), "jedenfalls ebenso unverständlich" (in any case just as incomprehensible) [read: trans02183]. It is pertinent to the "formula right, picture wrong" lesson and should be one bullet in primer section 7.

6. Process

• Source tags. Present and honest throughout. The arbiter and primer separate [read], [web], [computed] and [memory] with confidence levels, and mark second-hand web items ("abstract only", "search summary").
• Web checks. The arbiter used 3 searches and 2 fetches of 8 and lists what it did not check. One medium-confidence [memory] input feeds the primer's central worked example: the 8/N^3 scaling of the Lamb shift, and the 2P1/2 value of -12.8 MHz, used for n = 3 levels in example.py Part E. The effect on the blend table is small (Lamb shifts of about 0.035 cm^-1 or less, against 0.1-0.3 cm^-1 effects), and the inputs agree with standard values [memory, high from QE]. Still, a one-call web check would retag them. Minor.
• Verdict scale.
• Arbiter claim 2 ("The 1920s direct hydrogen measurements as a challenge to 0.365: Tested") and primer table row 2d ("Tested; not a refutation") use a label that is not on the STEP 2 scale. Use a scale verdict for the claim as stated. "0.365 is too large by 25 per cent" is Tested, not supported (the shortfall is explained by blending; Paschen 1916 already said so). The descriptive note can stay.
• Rows 4e and 7b carry "(no separate verdict)" and a description. Acceptable as non-claims, but row 7b could carry Historically superseded but instructive.
• Primer form. It follows STEP 4 in order (sections 1-9, answers at the end), has a worked example with real numbers, and has an example.py that runs. Reader profile: a few terms are used without definition:
• "WKB" (acronym not expanded);
• "6j symbol" and "line strength" (Step 5c);
• "parity" (Laporte's rule);
• "hartree" is defined only in section 4, after earlier use in the reviews.

Add one plain sentence each. Minor. - Arbiter inputs. The arbiter says it did not re-read facts.json, the digests or the deep reads. That shortcut is stated, but it is how items 3.1 and 3.2 were missed: the deep read (line 924) recorded the p.488 statement. - Pending corrections not yet applied. Arbiter corrections 2 and 3 (claims.md claim 2 "only partly explained", and the source-gap note on Ch. V sections 6-7) are not yet in claims.md or facts.json (facts.json still says "partly explained" and lists Ch. V sections 6-7 as digest-only). The orchestrator applies them. - Folder spelling. The spelling (Summerfield/Sommerfeld) is handled correctly everywhere.

7. Corrections to earlier documents

1. arbiter.md, section 3 claim 6 ("only an absolute shift of each n-level could, and that was not measurable then") and section 5 row 2; physicist.md line 85 ("not measured at the needed accuracy then"). Wrong as a statement of the record. The book reports Paschen's observation of the circular-orbit term "of the order ... R alpha^2/64 ... and the correct sign" (IA OCR lines 42967-42984). Paschen 1916 gives 0.569 +/- 0.25 against a calculated 0.590 (Paschen txt, lines 6173-6283). Weber's law predicts zero for circular orbits [computed, section 3 item 1]. Corrected statement: "one interested-party measurement (Paschen 1916, He+) reports the l-independent term at about 2 sigma from zero and in agreement with relativity; its accuracy and its dependence on the R_He fit are unexamined." Verdict 6b ("Never properly tested") should become a split: a single test reported, by an interested party, at low significance; never repeated. Pending deep read 1.
2. contrarian.md (Step 1 correction 3), arbiter section 3 claim 6, primer section 4 (Glitscher figures "need checking"). Resolved; the figures are confirmed. Glitscher widened Paschen's range to 0.350-0.380 cm^-1 "without doubting these observations". He took alpha^2 = (5.32 +/- 0.22)e-5 (relativity) and (6.65 +/- 0.28)e-5 (Abraham) from it. He compared these with the e,h value Sommerfeld had shown to agree with relativity, alpha = 7.29e-3 and alpha^2 = 5.30e-5 (OCR "7,99" and "5,80"). Then he took e = 4.8e-10 (described as surely too large) with h = 6.3e-27 (surely too small) and got alpha = 7.65e-3, alpha^2 = 5.86e-5, still below the Abraham minimum of 6.37e-5 [read: Glitscher txt, lines 4355-4436; computed: 2 pi (4.8e-10)^2/(6.3e-27 x 3e10) = 7.66e-3]. The contrarian's "about 5.8e-5" for the independent value is the extreme bound, not the best value (5.30e-5).
3. arbiter.md section 3 claim 7 and contrarian.md (Step 1 correction 6). Two letters are merged. "Ein harter Schlag für Bohrs sonst so überzeugende Modellfolge" is in Sommerfeld to Paschen, 23 May 1924 (TransDat/02183). "Die arithmetischen Regelmässigkeiten [reichen] viel weiter ... als nach den Modellvorstellungen zu erwarten wäre" is in Sommerfeld to Landé, 20 April 1924 (SBPK Nachlass Landé, per research/2026-10-09-sommerfeld-projekt-lmu.md item 7). Cite each to its own letter.
4. primer.md section 6, row 6a. "Bucherer" is not cited in the book. Replace with "Schaefer and Neumann 1914; Guye and Lavanchy 1916 [read: book p.464 footnote]".
5. arbiter.md and primer.md: "retracts two positions of earlier German editions". The book records at least five withdrawals: the L1/L2 levels in different atoms; Kossel's defects; the A-doublets "refuted by Hoyt"; theta = x'; and one doublet's earlier "false interpretation" (digests .08 p.89, p.95; .09 p.101; .23 p.262, p.272). Say "several, including ...".
6. Digest .16 p.182. The second-order ionisation potential of He is printed 79.3 V (25.3 + 54), not 79.8 [read: IA OCR line 31197].
7. claims.md misprint list. Add the translation slip "the higher the temperature the lower the velocities" (book p.~485; IA OCR lines 42415-42416).

8. Remediation

Deep reads (most important first; at most 8)

1. Paschen 1916, "Bohrs Heliumlinien" (Opus). research/files/Paschen-1916-BohrsHeliumlinien-AnnPhys50-iss16_djvu.txt, lines about 4040-4400 and 6160-6500; page images from research/files/sim_annalen-der-physik_1916_50_16.pdf for the tables. This is not a manifest document; the slug is its file stem. - Q: What exactly did Paschen measure for the circular-orbit (l-independent) relativity term in He+ and in hydrogen (0.569 +/- 0.25 against 0.590), and how was R_He fitted? - Q: Does the measurement separate relativity (-alpha^2/(8N^4)), Weber (0) and Abraham (4/5 of relativity) at the stated error? - Q: Quote his statement that the measured H-alpha doublet spacing is probably too small, with his H-alpha numbers (6562.853, 6562.7xx; Meissner 6562.849).
2. Book, PDF pp.178-187 (Ch. VI section 3, electron impact; Kossel's diagram) (Sonnet; use the IA OCR, page images for Tables 36-38). - Q: List every predicted-versus-observed excitation and ionisation potential (H, H2, He, He+ double ionisation 79.3 against 79.5 +/- 0.3 and 80, the 4686 appearance between 75 and 80 V against 75.4, Hg, the alkalis), with observers. - Q: List the stated selection-rule exceptions (585 Å; Hg 2P0 and 2P2 in collisions).
3. Book, PDF pp.167-177 and 188-216 (Ch. VI sections 1-2 and 5-7, Addendum) (Sonnet; IA OCR). - Q: List every selection-rule break the author attributes to fields, with the evidence offered for a field. - Q: Give the inner-quantum-number rules and Landé formula as printed. - Q: What did the author say against Fues's half-integers? - Q: What are the doublet-atom model's numbers (Li 0.32 and 0.035 cm^-1) and the data they are compared with?
4. Book, PDF pp.80-106 (Ch. III sections 4-7) (Sonnet; IA OCR, page images for Tables 11-16, 21-22). - Q: Give Moseley's law as printed, with slope and screening constant. - Q: What gaps are predicted? - Q: Give the 1916 constant-Delta-lambda doublet law and the K-L doublet equality test (Table 16). - Q: Give the Barkla J-radiation passage, and the list of withdrawn earlier views (A-doublets, theta = x').
5. Book, PDF pp.250-257 (Ch. VIII section 4 footnotes) (Sonnet; IA OCR lines about 42390-43100). - Q: Quote the footnote table of direct H-alpha, H-beta and H-gamma measurements in full, the Birge 1921 citation, and the "relativity correction" passage (p.488). - Q: Did the book state Doppler and Stark blurring as reasons the direct doublet is uncertain?
6. Book, PDF pp.29-32 and 41-45 (Ch. I sections 6-7; Ch. II section 2) (Sonnet). - Q: Give the Sommerfeld-Debye accumulation theory and its stated failure (accumulation time for X-rays). - Q: Give the nebulium, coronium and protofluor exclusion. - Q: Give Bohr's He model (28.8 against 25.4 V) as stated in Ch. II.
7. Book, PDF pp.54-58 (Ch. II section 6, nuclear physics) (Sonnet; page images). - Q: Read the garbled mass-defect energy ("6.3 x 10^? major calories"), and give the Lenz He-nucleus model and Rutherford's disintegration list as printed.

What each later file must change

• facts.json
• Add to key_claims and summary:
  • Paschen's circular-orbit term (item 3.1, with the interested-party note);
  • Paschen's own blending remark (3.2);
  • He+ electron-impact tests (3.3);
  • field-blamed selection breaks (3.4);
  • J-radiation (3.5);
  • nebulium and coronium (3.6);
  • the Sommerfeld-Debye accumulation theory (3.7);
  • the five withdrawals (3.8);
  • the doublet-atom numbers (3.9);
  • Birge 1921 (3.10).
• Apply arbiter corrections 2-3 (blend wording; Ch. V sections 6-7 now read).
• Update how_read after the deep reads.
• claims.md
• Claim 2: replace "only partly explained" with the arbiter's blend wording, and add Paschen's 1916 remark.
• Claim 6: add the circular-orbit term as the Weber discriminator, with Paschen's figure.
• Claim 1: add the electron-impact He+ checks.
• Source-gap note: Ch. V sections 6-7 read; Ch. III, VI and VII pending deep reads 2-4.
• Add the translation slip to the misprint list.
• arbiter.md: "QE revision" section
• Revise verdict 6b to a split, roughly: "Reported once (Paschen 1916, He+, circular-orbit term 0.569 +/- 0.25 against 0.590; Weber predicts 0): weak evidence for relativity over Weber from an interested party; never repeated." Use scale wording: Never properly tested for an independent test, with the Paschen figure stated beside it.
• Fix section 5 row 2 and the claim 6 text ("not measurable then").
• Add Paschen's 1916 blending remark to claim 2.
• Replace "Tested" for 2d with Tested, not supported (for the claim "0.365 is 25 per cent too large").
• Add the field-blamed selection breaks as context to 2e.
• Apply corrections 2, 3 and 5 (section 7).
• Add Birge 1921 and Paschen 1916 to the "what would settle it" table.
• Align the 77 K cell wording with example.py.
• primer.md
• Section 4 (Weber paragraph) and Check-yourself answer 3: say that the book and Paschen 1916 report the l-independent term with the right sign and size (0.569 +/- 0.25 against 0.590; Weber 0), with the caveats. Add a sentence that this is the measurement that separates Weber from relativity.
• Step 5(a) or (d): quote Paschen's 1916 "probably too small" remark.
• Section 6: row 2d verdict on the scale; row 6a citation (Schaefer and Neumann, not Bucherer); row 6b per the QE revision; optionally row 1a with the He+ electron-impact checks (79.3 against 79.5 V; 75.4 against 75-80 V).
• Section 7: "several retractions" in place of "two"; one bullet on the 1924 "doublet riddle" (Millikan-Bowen and Landé; Sommerfeld's "ebenso unverständlich"); one bullet on J-radiation and nebulium as cases where theory and replication set aside a reported effect; one line that Sommerfeld himself wrote "If ... Paschen has not under-estimated the accuracy of his measurement".
• Section 2 or 3: one-line definitions of WKB, parity and the 6j (angular-momentum coupling) coefficient.
• example.py. Optional: add a Part G that prints the circular-orbit shifts for N = 2 under relativity (-alpha^2/128 hartree = 0.0913 cm^-1), Weber (0) and Abraham (4/5 of relativity), and compares them with Paschen's 0.569 +/- 0.25 He+ figure once deep read 1 fixes its units and meaning.
• sites.md (next Investigator run). Add as leads:
• Birge, Phys. Rev. 17, 589 (1921);
• Paschen 1916, "Das Relativitätsglied" (in hand);
• Franck and Knipping, Phys. Zeitschr. 20, 481 (1919);
• Horton, Proc. Roy. Soc. 95, 408 (1920);
• Grossmann, Z. Phys. 5, 280 (1921).

Recheck

Date: 2026-10-09. QE recheck (STEP 4b). I re-read arbiter.md section 11, and grepped primer.md, claims.md, facts.json and example.py against each defect. I did not re-run example.py: this machine's python3 has no sympy (the first QE run had it). I checked only that it compiles and that Part G is present and matches the deep read.

Fixed: 1. Retention defect, circular-orbit term (3.1, 7.1): fixed. arbiter 11.1-11.2 and the 11.13 list now give 0.569 +/- 0.25 against 0.590 and Weber 0, with the interested-party and error-bar caveats. Verdict 6b is split: Never properly tested as an independent test, with the one Paschen result stated beside it. Fixed in primer sections 4 and 6b, answer 3, claims.md and facts.json. The "not measurable then" wording survives only inside the correction notes. 2. Paschen's own "probably too small" remark (3.2): fixed. It is in arbiter 11.3 and primer Step 5 and section 7, and its source is cited. 3. Electron-impact He+ checks, 79.3 against 79.5 and 80 V, and 75.4 against 75-80 V (3.3, 7.6): fixed. Present in arbiter, primer 1a, claims.md and facts.json, with the 79.8 misprint noted. 4. Field-blamed selection breaks (3.4), J-radiation (3.5), nebulium (3.6), accumulation theory (3.7), doublet-atom numbers and Fues (3.9), Birge and records named but not examined (3.10): fixed. Each is in facts.json and claims.md, and in primer rows 3e and 7c and the section 7 bullets. 5. Five withdrawals instead of two (3.8, 7.5): fixed in arbiter, primer and facts.json. 6. Off-scale "Tested" (section 6, arbiter claim 2, primer 2d): fixed. Both now read Tested, not supported. 7. Letters merged (7.3): fixed. "Harter Schlag" is cited to Paschen, 23 May 1924, and the arithmetic-regularities quote to Landé, 20 April 1924. 8. Bucherer citation (7.4, spot check 9): fixed. Primer 6a now cites Schaefer and Neumann 1914 and Guye and Lavanchy 1916. 9. Glitscher figures (7.2): resolved and recorded in arbiter 11.5. 10. Digest 79.8 against 79.3 V (7.6) and the "higher the temperature" slip (7.7, 3.11): both recorded in claims.md and arbiter 11. 11. Pending arbiter corrections 2-3 (blend wording; Ch. V sections 6-7 now read): applied in claims.md and facts.json. facts.json still parses. 12. 77 K cell wording (spot check 10): reconciled by a note in arbiter 11. The table text itself was left as it was. 13. Doublet riddle bullet (section 5): fixed. It is in primer section 7. 14. Undefined terms (WKB, parity, 6j, line strength) (section 6): the primer says they are now defined where first used. I confirmed WKB (primer line 54). The others I did not check individually, so I count this as fixed on the primer's own statement. 15. Optional example.py Part G: added, using Paschen's numbers. 16. sites.md leads (Birge, Franck-Knipping, Horton, Grossmann): not changed. sites.md is for the next Investigator run, and arbiter 11 lists them as unobtained.

Remaining: 1. Deep reads 2-7 were not done: Ch. VI (both parts), Ch. III sections 4-7, the Ch. VIII footnotes, Ch. I-II, and Ch. II section 6. Only deep read 1 (Paschen 1916) exists in deep/. The affected facts now rest on the IA OCR with line citations plus digest, and arbiter 11 marks them "pending". The deep reads are therefore disclosed rather than hidden. Nothing in the verdicts depends on them. Items that still depend on [memory] are the Moseley's law verdict (claim 5), the later identification of nebulium lines, and the half-integer outcome. They are tagged as such.

No retention defects remain.

Final: OPEN (1 issues)

Orchestrator fix (2026-10-09)

What was done, against "Remaining" item 1 of the Recheck: - Deep reads 2-7 done (Sonnet deep readers, IA OCR plus folder OCR, page images for every table and formula cited), written to deep/: - Sommerfeld-AtomicStructureAndSpectralLines-0c4636.ch6-part1.md: PDF pp.167-187, Ch. VI sections 1-3 (read 2, and the first half of read 3); - .ch6-part2.md: PDF pp.188-216, Ch. VI sections 4-7 and Addendum (rest of read 3); - .ch3.md: PDF pp.76-106, Ch. III sections 4-7 (read 4); - .ch8-notes.md: PDF pp.250-257, Ch. VIII section 4 footnotes (read 5); - .ch1-2.md: PDF pp.29-32 and 41-45 (read 6; the nebulium and He-model passages are in Ch. II section 3, not section 2); - .ch2-s6.md: PDF pp.54-58, Ch. II section 6 (read 7). - arbiter.md section 12, "QE revision 2 (orchestrator fix, 2026-10-09)", folds the results in; the "pending" marks in section 11 now point to it (and section 0, open question 6 and the 11.8 list are annotated). - [memory] items settled. Moseley's law (claim 5): [read] book p.157 plus [web] arXiv 1809.10480 (relativistic curvature at high Z, which the book itself notes). Nebulium and coronium: [web] Wikipedia (Bowen 1927, doubly ionised O; Grotrian and Edlén, ionised Fe); protofluor not found and stated so. Half-integer outcome: [web] arXiv 2203.07833 (Landé's half-integer j, m, resisted by Sommerfeld and Bohr, vindicated with spin). - facts.json (how_read, key_claims 35, 38, 41-43, 52-59, summary, sources), claims.md (source gap, claims 1, 4, 5, 7, peripheral claims, corrections and misprints) and primer.md (source note, section 3.5 Moseley, evidence-table rows 1a, 2e, 3e, 5c, 7c, section 7 bullets, section 9 Birge, corrections 10-14) updated. No entry file exists for this project in work/rankings/entries/. The site was not re-rendered (not run in this fix); the orchestrator should run STEP R.

Check of the additions (as QE)

Spot checks I made myself:

Process: - Source tags: present on every new statement; [web] items carry URLs; second-hand web items are marked (the Fe XIV attribution is "search summary only, not fetched"). Remaining [memory] items (He 79.0 eV, He-4 28.3 MeV, deuterium and helium-3, half-magneton trunk as a spin forerunner) are high confidence and no verdict depends on them. - Web checks: 5 searches and 7 fetches (3 failed), slightly over the arbiter's budget of 8; logged in arbiter 12.6. - Verdicts: none changed category; the arbiter says so plainly and explains why the evidence did not require a change. The scale is applied consistently (Moseley Established as an approximate law; J-radiation and accumulation Tested, not supported; 2e Never properly tested). - Retention: nothing was dropped. The half-integer correction keeps Fues's argument, the author's rejection and the Addendum's use of half-integers side by side; the withdrawals list keeps others' withdrawals (Franck, Rutherford) as well as the author's. - Corrections stated plainly (arbiter 12.7, items 18-22; claims.md and primer corrections lists). They include errors in this file's own earlier text, which I record here rather than edit: section 3 item 4 named the Hg lines 2P0/2P2 (the book prints 1S-2p1 and 1S-2p3) and placed the 2x/3x Zeeman components in Ch. VI (they are in Ch. V); section 3 item 8 attached "refuted by Hoyt" to the A-doublets and said "half-integers later proved right" without qualification; section 3 item 10 called Birge 1921 a retest of the H-alpha components. All are corrected in the source-of-truth files. - Stale copies: grep of review/Summerfield for the corrected phrasings finds them only inside correction notes and in the original reviewer files (physicist.md, mathematician.md, contrarian.md do not contain the withdrawals, half-integer or Birge wording; checked by grep). facts.json parses. - Minor, not a defect: the deep read of Ch. VI part 2 leaves one OCR ambiguity unresolved ("(S p1)" against "(S p3)" in the 0 -> 0 passage, book p.367); nothing in the review uses it. Ch. VII and the unread parts of Ch. I-III remain digest-only; no claim depends on them, and claims.md, facts.json and the primer say so.

No open issues remain from the Recheck.

Final: PASS