QE (Step 4b): Langmuir-Irving (Tonks and Langmuir, "Oscillations in Ionized Gases", Phys. Rev. 33, 195-210, 1929)

QE agent (Opus), 2026-10-04. I read prompt.txt, the manifest, the single digest, the deep read, facts.json, claims.md, sites.md, all 11 research notes, the three reviews, arbiter.md, primer.md and example.py. I also read the full extracted text of PDF pp.1-2, 5-6 and 8-17 myself. I rendered PDF p.8 at 150 dpi to check one citation ([read: page image p.8]) and made two web checks (Crossref) on the identity of "Webb".

Verdict: MINOR. Every central verdict holds. The theory (claims 1-3) was checked from page images by four readers, and the arbiter's verdicts match the text. The defects are these:

• one factual error that bears on how independent the 1939 replication was (the "Webb" identity);
• an inconsistency inside the paper (abstract against body) that nobody noticed;
• some points about energy transfer and thermal effects (pp.2, 5-6) that the reviews and primer missed or underplayed;
• a few misquotes and mislabels that came from the digest;
• stale wording in claims.md and facts.json.

None of these needs Steps 2-4 redone.

1. Coverage

• The manifest lists one document and nothing was skipped. Coverage is complete.
• PDF p.17 is only the Fig. 1 photo caption. The photo itself appears on p.8.
• Figs. 4-10 were never read as data. The reviewers used only the captions and the text that describes them.

2. Shortcuts

1. Step 1b put the experimental part (pp.9-17) on the digest alone (defect, mostly remedied). Claims 4 and 5 rest on these pages. The reviewers read pp.11-17 from page images, so most of the gap was closed during Step 2. - What remains: pp.9-10 (apparatus and detector calibration) are still digest only, apart from my reading of the text layer below. - Figs. 8-10 were not extracted as data.
2. Fig. 10 is the paper's only quantitative in-plasma test of Eq. (6) (claim 4(ii)). Every reviewer judged it from the authors' sentence ("13 of 15 within accuracy"). - The physicist and mathematician each estimate the axis ranges from the figure, and their estimates disagree. The physicist has wavelength at "roughly 15-90 cm" and calls the span "a factor of about 3". The mathematician has wavelength "about 10 to 100 cm" and ionization "about 2 to 6, less than one decade". - A reading of the 15 points, with a fitted slope and its uncertainty, would replace these impressions. That is deep read DR1. - The verdict (Plausible, untested) is not expected to change, but its stated basis should be measured, not estimated.
3. Using abstracts only for the Investigator's later papers is stated openly everywhere. Acceptable.

3. Accuracy spot checks (against the extracted text, PDF pp.10-16)

The theory-part numbers (8980, 33 cm, 12.2e8 Hz, 4.6e-4 cm, 8.3 V/cm, 1.5e6 Hz, 6.5e4 cm/s, 4.4e-2 cm) were verified by the deep read and by all three reviewers. example.py reproduces them, so I did not repeat those checks.

4. Missed material (from the digest and text, absent from or underplayed in facts, claims, reviews, arbiter and primer)

1. The abstract and the body disagree. The abstract (p.1) says: "Another observed frequency of 50 to 60 megacycles may correspond to oscillations of the beam electrons." The body (p.16) concludes: "it seems to be impossible to identify the 55 with the theoretical 18 megacycle oscillation." - The abstract was evidently not updated after the Doppler argument failed. - The abstract also says "the theory offers no explanation of the cause of the observed oscillations" and calls the correlation "tentative until simpler experimental conditions can be attained" [read: p.1]. - None of this is in facts.json, the reviews, the arbiter or the primer. It bears on claims 4 and 5 and on how the paper is usually summarised.
2. The authors themselves say the amplitudes are small. p.2: "although their voltage-amplitude appears to be very small we believe that they play a fundamental role in high current gaseous discharges." - The reviews and primer say "the paper never shows its oscillations reach" Dittmer's 20 V. That is true, but the authors went further and acknowledged it. - The measured crystal voltages are about 9 mV, 30-50 mV and about 90 mV (pp.10, 11, 16). The amplitude gap is about two to three orders of magnitude, so the primer and the claim 5 text should state these figures.
3. The authors' own thermal argument (pp.5-6) was not analysed. The paper argues as follows: - "Fast" electrons cross a disturbance within one cycle and do not add to the effective density. - So the effective density depends on wavelength, giving "a decrease of frequency with decreasing wave-length". - This leads to "a kind of cumulative action which may make oscillations below a certain minimum size impossible".

Two points follow, and neither the reviews nor the primer makes them: - The predicted direction is the opposite of Bohm-Gross: in Bohm-Gross the frequency rises as the wavelength shrinks. - The "minimum size" idea foreshadows the strong damping near the Debye length (the length where the next deep read places the change of behaviour).

The reviews only say the authors "gesture at thermal effects". This is instructive for the reader, and it bears on claim 2. 4. Beam-plasma resonance idea (p.6). The paper says that waves on the moving beam may strike the ultimate electrons ("ultimates": the slow, thermalised plasma electrons) at their natural frequency and "give rise to resonance". This is the energy-transfer mechanism behind claim 5. It is an early form of the beam-plasma (two-stream) interaction that the physicist names from [memory]. The three energy-transfer factors on p.5 (beam motion, unsymmetrical fields reaching outside the tube, fast electrons crossing local oscillations) are mentioned once by the mathematician. They are absent from the primer. 5. Experimental details missing from the primer and arbiter [read: pp.11-16]: - Below 19.5 °C the 115 MHz peak dropped sharply and its frequency jumped to about 900 MHz. - A magnetic field turned the 115 MHz wave into a 730 MHz wave. This is in facts.json and the contrarian review, but not in the primer. - In the 300+ MHz range, reversing the heating current left frequency and amplitude unchanged. This contrasts with the 115 and 230 MHz waves, which it stopped, and it is a control for plasma origin. - The 1.38 MHz line had a peak of about 90 mV. It was found with a 2 mH coil at "practically the condition for the 230 or 115 megacycle oscillation", and the amplifier used to recheck it was a Radiola 17 (550-1450 kc). - The authors note that "frequencies higher than this were not sought with an amplifier". - Between 26 and 42 V on the anode there were oscillations of about 90 mV whose wavelengths could not be found. 6. People and record: - The affiliation and date are printed on p.16: "Research Laboratory, General Electric Company, Schenectady, N.Y., November 20, 1928". The primer and deep read tag the affiliation [memory, high]; it is [read: p.16]. - H. M. Mott-Smith Jr. is credited with help on the theory and with an unpublished theory of infinite plane trains of oscillations, which gives ν_p as the minimum frequency a stationary observer sees (pp.15-16). S. Sweetser helped with the experiments. - Neither person is in facts.json or the primer. 7. Pardue and Webb's 1928 paper is titled "Ionic Oscillations in the Glow Discharge". Phys. Rev. 32, 946 (1928), DOI 10.1103/physrev.32.946 [web] https://api.crossref.org/works?query.bibliographic=Pardue+Webb+1928. - This is earlier, independent experimental work on the ion branch (claim 3). Tonks and Langmuir compared it with their sound-wave range on p.8. - The Investigator did not list it, and the primer does not mention Webb and Pardue at all.

5. Errors in the reviews, arbiter and primer

1. The "Webb" identity (physicist; arbiter Web check 1 and Claim 5; primer §6 and §9). The physicist writes that "Webb was also the co-author of the 1928 oscillation papers cited by Tonks and Langmuir" and treats Merrill and Webb (1939) as possibly a "related-group replication". - The paper prints J. S. Webb [read: page image p.8]. Crossref agrees: "Pardue, L. A. & Webb, J. S., Ionic Oscillations in the Glow Discharge, Phys. Rev. 32, 946 (1928)" [web] https://api.crossref.org/works?query.bibliographic=Pardue+Webb+1928. - The 1939 authors are Harrison J. Merrill and Harold W. Webb [web] https://api.crossref.org/works/10.1103/PhysRev.55.1191. - Different initials do not prove they are different people, but the overlap the physicist asserted has no support. The arbiter rested part of its "shared research line" caveat on [memory, medium] that the 1928 author was H. W. Webb. - Remediation: remove the overlap assertion; state that the printed and Crossref initials differ (J. S. against H. W.); keep the shared-detector-method caveat, which is independent of this. - The primer's "Merrill and H. W. Webb" should read "H. J. Merrill and H. W. Webb". - Effect on verdicts: none. If anything it makes the 1939 replication stronger as independent evidence for claims 4(i) and 5.
2. The 300+ MHz control range is "−80 V (to cathode) to 5 V above anode potential", not "−80 V to +5 V" (§3, item 6). Correct this in the contrarian-derived text in the arbiter, in the primer §6 "Controls" bullet, and in facts.json.
3. The crystal "frequency variation factor" quote (physicist; mathematician) should be the paper's "frequency conversion factor for the crystal". The point is that amplitude comparisons between runs are unreliable (§3, item 7). This affects only wording.
4. example.py, Step 3 labels 810 and 880 MHz as "Fig. 10 example". These are the cathode-g against cathode-d measurements at 33 V and 30 mA (p.13). Nothing shows they are among the Fig. 10 points. Relabel them "cathode g / cathode d, p.13 (journal p.207)". The primer table does not repeat the mislabel.
5. Contrarian page labels. The 60-75 V correlation quote is tagged "[read: page image p.14, journal p.207]". By the contrarian's own rule (PDF page = journal page − 194) that is PDF p.13. The arbiter's "p.13/14" carries the ambiguity forward. Cosmetic.
6. Primer §9 tags the Baalrud et al. title "[memory, medium]". The Investigator read the title on the APS page ([web], research/2026-10-04-aps-journals.md). The tag understates the source.
7. Physicist and arbiter disagree on the Bohm-Gross shift (2.5e-6 against 5.2e-6 at 33 cm). The arbiter identified the cause: k_w = 2π/λ, and example.py gives 5.2e-6. Resolved; noted only for completeness.

6. Retention check

• Investigator leads. Every lead in sites.md "Leads for review" is in arbiter.md: Merrill and Webb 1939, Baalrud 2009, Godyak and Alexandrovich 2015, Gabor/Ash/Dracott 1955, Martin and Emeléus 1956, Linder 1936, Hernqvist 1955, Peterson and Puthoff 1959, Tonks 1931-34, the LOC notebooks, Collected Works vol. 5, Tonks 1967 and PNAS 1928.
• The negative lead (Godyak 2015, against the premise of claim 5) and the supportive one (Merrill and Webb) are both kept, each with its stake and its source level.
• Leads the primer leaves out: Hernqvist 1955, Peterson-Puthoff 1959, Martin and Emeléus 1956, Ash and Gabor 1955 (Proc. R. Soc. A), Tonks 1931 ("The High Frequency Behavior of a Plasma"), Tonks 1933 (Nature, applying the plasma frequency to the ionosphere), Tonks 1932 (Lecher wires), and the 1940s-50s experimental list (Armstrong, Neill, Wehner, Emeleus, Dawson).
• None was left out because a reviewer judged it negatively. Most are neutral or supportive.
• The primer's further reading should still carry the supportive ones for claims 1 and 3: Tonks 1933 and Hernqvist 1955.
• Source material with negative judgements is all kept: the irreproducible 1.38 MHz line, the two-state arc, the 19-21 °C window, and the failed 115 MHz and 55 MHz identifications. The arbiter's absence-of-evidence analysis treats the three observations that go quiet as anomalies with competing explanations, as the rule requires.
• Gaps that are not caused by negative judgement:
• The source material in §4 (items 1-6) is missing from the primer. These look like oversights, not dismissals.
• The authors' own admission of small amplitude (§4, item 2) cuts against claim 5. It should be stated next to Dittmer's 20 V so the reader can weigh it.
• The abstract's 50-60 MHz beam statement (§4, item 1) is the inventors' own claim. It should be kept and shown next to the body's withdrawal of it, not dropped.
• Result: no retention defect of the kind STEP 4b defines (material dropped for a negative reason). There are omissions, listed under remediation.

7. Process

• Source tags are present and honest throughout, with the source level stated each time an abstract or a single page is used. Exceptions:
• the affiliation is tagged [memory] where it is [read: p.16];
• the Baalrud title is tagged [memory] where it is [web];
• a digest paraphrase appears inside quotation marks (§5, item 3).
• Web checks:
• Physicist: 2 (Merrill and Webb; Bohm and Gross).
• Arbiter: 3. It retagged Alexeff and Neidigh 1963 as [web] and corrected the year from 1962.
• Mathematician: none. It states that no verdict rests on a medium- or low-confidence [memory] fact, and that is accurate.
• Contrarian: no new checks reported. It relied on the Investigator's notes, which is acceptable because its verdict-bearing facts are all [web] or [read].
• The one medium-confidence [memory] fact that did bear on a caveat (the Webb identity) was not checked until this QE. It is now [web] (§5, item 1).
• Verdict scale: applied consistently. The split verdicts on claims 2, 3 and 4 are explained. "Established qualitatively" for 4(i) is a qualified use of a scale label, and the arbiter justifies it.
• Source gap: the note is repeated in all of claims.md, the reviews, the arbiter and the primer.
• Primer: follows STEP 4 order sections 1-9, with answers at the end.
• Symbols are defined. The Gaussian/SI translation and Landau damping are explained for the reader profile.
• The worked example uses real numbers and matches example.py.
• example.py: runs cleanly (exit 0) with the project venv. All printed values match the primer, and its sympy assertion that Eq. (12) equals the modern ion-acoustic relation passes.
• Stale files.
• claims.md claim 4 still says "a ratio near 1:2", and claim 5 omits the authors' word "inadequate".
• facts.json key_claims repeats "1:2" and "−80 to +5 V" (in the summary). Its how_read still says the experimental pages were read as "digest only".
• The arbiter's "Corrected claim list" asks for these updates, but they were not carried back into the files.

8. Remediation

Deep reads (most important first; slug Osc-In-Ionized-Gas-a7691d)

1. DR1. Figs. 8, 9, 10, PDF pp.13-15 (Opus) - Fig. 10 (main task): render at ≥200 dpi and read off all 15 points (wavelength in air against relative ionization, with the axis ranges). Fit the log-log slope with its standard error, and test whether −1/2 is distinguished from, for example, 0 and −1. Say which two points are the outliers. - Figs. 8-9: give the collector currents in the two states and the emission ranges. - This decides whether claim 4(ii)'s "consistent, not discriminating" is quantitatively right.
2. DR2. PDF pp.5-6, text and page images (Opus) - State exactly the authors' qualitative argument about fast and slow electrons and effective density: the predicted sign of dν/dλ and the "minimum size" claim. - Do the same for the beam-to-ultimate resonance idea and the three energy-transfer factors. - Compare each with Bohm-Gross dispersion, Landau damping near kλ_De ~ 1, and the beam-plasma (two-stream) instability.
3. DR3. PDF pp.9-12 and Figs. 2-7, page images (Sonnet) - Verify the apparatus and detector-calibration text (slope 0.5, the crystal "conversion factor" caveat). - Verify the 100-300 MHz section: the 9 mV, 30-50 mV, ~900 MHz and 730 MHz values, and the conditions for heating-current reversal. - Describe what Figs. 4-7 show (amplitude against position, the phase-interference curves, the effect of filament c's potential). - No reviewer read pp.9-10 from images.
4. DR4. PDF p.1 (abstract) against pp.15-16, and p.2 (Sonnet) - Confirm the abstract's statements: "50 to 60 megacycles may correspond to oscillations of the beam electrons", "theory offers no explanation of the cause", and "tentative". - Confirm p.2's "voltage-amplitude appears to be very small". - Confirm the p.16 conditions for the 1.38 MHz line (90 mV, 2 mH coil, 25 mA and 63 V, Radiola 17) from the page images.

Changes to later files (MINOR route)

• claims.md
• Claim 4: "frequencies 1080 and 660 MHz (ratio 1.64; authors: 'almost twice'), taken at 26 V and 28 V"; the scaling rests on relative ionization only.
• Claim 5: add that the authors call their correlation runs "inadequate", that the observed amplitudes were mV-scale against Dittmer's 20 V, and that the abstract (but not the body) still offers a beam-oscillation reading of 50-60 MHz.
• Remove the "[read: digest only]" tags once DR3 and DR4 are done.
• facts.json
• Update how_read to "digest + deep read pp.1-9 (page images) + reviewers' page images pp.11-17 + QE text check pp.9-17 (+ DR1-DR4)".
• Fix "1:2" and "−80 to +5 V".
• Add the abstract/body inconsistency, the authors' admission of small amplitude, the p.6 thermal argument, the p.16 affiliation and date [read], Mott-Smith and Sweetser, and Pardue and J. S. Webb 1928 "Ionic Oscillations in the Glow Discharge" [web Crossref].
• arbiter.md: add a "QE revision" section covering:
• the Webb identity (§5, item 1). Remove the related-group caveat that rests on it and keep the shared-detector caveat. No verdict change.
• the corrected control range;
• the authors' small-amplitude admission under claim 5 (it reinforces "Never properly tested"; no change);
• the abstract/body inconsistency under claims 4 and 5;
• the DR1 slope result under claim 4(ii). Change the verdict only if the fit shows the data cannot tell −1/2 from 0, in which case the basis for "Plausible, untested" is restated, not the label.
• the DR2 findings under claim 2. Note that the 1929 qualitative thermal argument has the opposite sign to Bohm-Gross. Verdict unchanged.
• primer.md
• §4: state the authors' "very small" amplitude admission and the 9-90 mV figures beside Dittmer's 20 V.
• §6 "Other observations": fix the control range; add the 115 to ~900 MHz jump below 19.5 °C, 115 to 730 MHz under a magnet, heating-current reversal not affecting the 300+ MHz waves, and the abstract's 50-60 MHz statement against the body's withdrawal.
• §7 "Wrong, and instructive": add a short box on the p.6 thermal argument against Bohm-Gross (from DR2). It is good teaching material: a correct instinct about the role of thermal electrons, with the wrong sign.
• Change the affiliation tag to [read: p.16] and add the Mott-Smith credit.
• §9: fix "H. J. Merrill and H. W. Webb"; retag the Baalrud title [web]; add Pardue and J. S. Webb 1928, Tonks 1933 (Nature 132, 101) and Hernqvist 1955.
• If DR1 changes it, update the description of Fig. 10's span in the evidence table, which is currently "less than one decade".
• example.py: relabel the 810 and 880 MHz entries as "cathode g / cathode d (p.13)". Optionally add a Step 3b that fits the DR1 Fig. 10 points.
• Investigator (next run): follow up Pardue and J. S. Webb 1928 (Phys. Rev. 31, 1122 and 32, 946) and H. W. Webb's affiliation, to settle whether the two Webbs are the same person. The remaining high-value reads still await the owner's approval: the PNAS 1928 PDF, the Phys. Rev. 33, 990 Note, and the Collected Works vol. 5 text.

Recheck

Rechecked 2026-10-04 against the current claims.md, facts.json, arbiter.md, primer.md and example.py (by grep and a run of example.py with the project venv; exit 0). The original reviews (physicist.md, contrarian.md) were left as written; the arbiter's "QE revision" section carries their corrections.

Remaining: one cosmetic item (page-label ambiguity in the original contrarian review), with no effect on any verdict or live deliverable.

Final: PASS