Hilgenberg-OC: Arbiter (Step 3)

Role: weigh the Physicist, Mathematician and Contrarian reviews (and the Investigator's findings they used), settle disagreements, give one final verdict per claim on the Step 2 scale, and name what would settle each open point. Tags: [read] document or Investigator note as quoted by a reviewer; [web] URL; [memory] with confidence; [calculation] my own arithmetic (Python, checked).

Source gap (repeated)

The project folder holds one document: Scalera and Braun (2003), a secondary summary by Earth-expansion advocates (interested parties); it has no equations. None of Hilgenberg's own works is in the folder. The only primary Hilgenberg text any step saw is two page images and OCR of the 1933 book Vom wachsenden Erdball, read by the Investigator (https://archive.org/details/Hilgenberg1933); the reviewers worked from the Investigator's notes. Never read by anyone: the 1929 and 1931 booklets (Met Office Library copy exists), the 1933 Magnus reports (Z. Techn. Phys. 14, 211-214), the 1939 sink/source booklet, the 1965 Geol. Rundschau 55 paper (source of 4590 km), the 1974 Geotektonische Forschungen 45 monograph, the unpublished 1967 "swallowing constant" manuscript, and Scalera 2021 (seen as an abstract note only). Every statement of what Hilgenberg's physics says therefore rests on the advocates' paraphrase or on a partial reading of one book. The verdicts below on the experimental questions (radius change, paleomagnetism, mass growth) rest on independent published measurements and do not depend on the missing documents, but they test Hilgenberg's numbers only as far as those numbers are known.

Recomputed numbers (where reviewers differed or leaned on one source)

All inputs: R = 6.371e6 m, M = 5.972e24 kg, G = 6.674e-11, c = 2.998e8 m/s, mean density 5513 kg/m3, 1 yr = 3.156e7 s [calculation].

One more orbit remark. The physicist notes that mass added at rest would shrink an orbit (r proportional to 1/m^2 at fixed angular momentum), whereas Hilgenberg's 1931 text predicts widening orbits [read: Investigator note]. Nobody read his orbit argument; I record this as an unanswered question for the theory, not a refutation.

Web checks by the Arbiter (7 searches, 1 failed fetch; budget 8)

1. Wu et al. 2011 (Geophys. Res. Lett. 38, L13304): mean Earth radius not changing within 1 sigma of 0.2 mm/yr; best value 0.1 mm/yr [web: https://www.sciencedaily.com/releases/2011/08/110817120527.htm ; bibliographic record via search at https://www-app2.gfz-potsdam.de/grace-references/b2hd-2011GeoRL..3813304W.html]. Retagged from reviewers' [web] to my own check. Caveat I add: this bounds the present rate, and is a statement about a reference-frame origin analysis; it does not constrain episodic growth in the past.
2. McElhinny, Taylor and Stevenson 1978, Nature 271, 316-321: palaeoradius over 400 Myr limits expansion to less than 0.8%; lunar surface static for 4 Gyr (limit 0.06%); Mercury; G decreases by less than 8e-12 /yr (constant-mass cosmologies) and 2.5e-11 /yr (Dirac) [web: https://www.nature.com/articles/271316a0.pdf, abstract text via search; the full paper sits behind the publisher's login, so I read the abstract summary only]. The physicist and contrarian relied on the same abstract.
3. Lunar laser ranging: Hofmann et al. 2010 give Gdot/G = (0.7 +/- 3.8)e-13 /yr; Williams et al. 2004 (4 +/- 9)e-13 /yr [web: https://ilrs.gsfc.nasa.gov/lw18/docs/presentations/Session9/13-0402-Mueller.pdf via search result]. The contrarian's "(7.1 +/- 7.6)e-14" from arXiv gr-qc/0412049 was not reproduced by my search; I use the confirmed order of 1e-13 /yr. Search returned nothing specific on a limit for the Earth's GM alone.
4. Solar mass rate from ephemeris EPM2019: -13.4e-14 < (dM/M)/dt < -8.7e-14 per year [web: https://arxiv.org/pdf/2201.09804]; INPOP check at https://arxiv.org/pdf/2111.04499 (not opened). Confirms the mathematician's number.
5. Earth density structure: PREM mean 5.515 g/cm3, central 13.09 g/cm3 [web: PREM values reported by search result, e.g. https://au1.ucar.edu/what-is-the-most-dense-layer-of-the-earth]. Retags the physicist's inner-core figure [memory, medium] as [web].
6. Length of day: tidal braking about 2.3 ms per century offset by post-glacial rebound, net measured +1.7 ms per century [web: https://astro.uni-bonn.de/~pbrosche/aa/acta/vol03/acta03_100.html]; Devonian corals about 400 daily lines per year, days of about 21.9 h [web: https://lvnhm.org/post/the-days-are-getting-longer-it-s-recorded-in-the-fossils ; https://scienceblog.com/?p=600265]. Retags the physicist's "1.7 ms per century [memory, medium]" (the number is confirmed as the net observed rate).
7. Bjerknes analogy: C.A. Bjerknes (1875) and V. Bjerknes studied pulsating and oscillating spheres in an incompressible fluid; the force falls as the inverse square and is phase dependent [web: https://mathshistory.st-andrews.ac.uk/DSB/Bjerknes_Vilhelm.pdf and search summaries]. The existence of the analogy is confirmed. NOT confirmed, still [memory, medium]: the sign rule (like sinks attract, sink and source repel) and the mathematician's Reading B force law F = rho m u. No verdict below depends on them; they affect only the mathematician's implied ether density and inflow speed, which I carry as a flagged consequence.

Check failed: direct fetch of the Nature paper (redirect to login). Not rechecked: the inverse (negative) Magnus effect literature (JFM and arXiv 2302.11260 are cited by two reviewers; I relied on their [web] tags), the Hamilton and Lisle river model (reviewers cite arXiv gr-qc/0411060; I did not reopen it; it is standard and all three reviewers agree), meteorite infall of about 4e7 kg/yr (Bruhn's point is not verdict-bearing).

Corrections to the reviewers

1. Physicist, claim 6: "Refuted by calculation" for no-new-matter expansion at R = 0.72 (mean density 14.7 g/cm3) is too strong. The density number is right, but a body of the same mass squeezed into 0.72 R has central pressure larger by (0.72)^-4 = 3.7 (scaling of G M^2/R^4) [calculation], so the actual density would be higher than today's at every depth, not equal to it. Whether a rocky mantle and iron core could reach that is an equation-of-state question nobody answered. Present central density is 13.09 g/cm3 and mean 5.515 [web, above]; the mean required (14.74) exceeds anything now found in the Earth, which makes the case implausible but not a refutation by simple arithmetic. I downgrade that sub-verdict to Tested, not supported, on the paleomagnetic and geodetic evidence that bind both growth versions equally.
2. Mathematician, claim 2: "Established" for M/M' = (R/R')^3 is dropped. It is an assumption (constant density) that Hilgenberg himself calls untrue but simplifying [read: Investigator note], not an established result.
3. Mathematician, claim 1: "Refuted by calculation" for Reading A is correct as mathematics but it refutes a reading Hilgenberg does not hold. The Investigator's reading of the 1933 text ("a body accelerates because a sink sits in a stream") is Reading B. Reading A is how the folder document's phrase "accelerated flow of space towards the planetary body" can be taken by a reader. I keep the result in the record (it is a good lesson: incompressible sink flow gives r^-5, not r^-2) but do not assign it to Hilgenberg.
4. Mathematician, claim 6: "Internally inconsistent" for "equivalent in every way" is not established. His flow is shown to differ from the river-model flow only if his flow is the incompressible one; his actual flow law is unread. The claim is unsupported, not self-contradictory.
5. Contrarian, claim 3 weak form "Plausible, untested": keep, but note that "less than 0.8% over 400 Myr" is the McElhinny limit itself, so a change below that is neither excluded nor tested; it is not what Hilgenberg claimed.
6. Contrarian, claim 2: "Refuted by calculation / Tested, not supported". The radius bound is a measurement (Wu et al.), the ephemeris and LLR limits are measurements, so "Tested, not supported" applies. The energy figure alone would not refute (the ether is posited as the reservoir).
7. Physicist and Contrarian agree the "60%" is a diameter ratio (0.62-0.65 in the 1933 book, shelf sphere), not a Permian radius. Adopted into the corrected claim list.
8. Day length (new point). The physicist's 4.7 h Permian day (angular momentum conserved, R^5 scaling) and Hilgenberg's own prediction that days shorten with growth [read: Investigator note] are two different assumptions. Under the first the past day is 4.7 h; under the second the past day is longer than 24 h. Devonian corals show about 21.9 h at 400 Ma [web, above]. Both assumptions conflict with the coral record, in opposite directions. This strengthens the contrarian's and physicist's point.

Final verdict per claim

Claim 1. Gravity is the accelerated flow of space (ether) towards massive bodies, each a sink

• Agreement. All three: no equations in the folder; the verbal sink/stream picture is a recognised hydrodynamic analogy; the river model (Painleve-Gullstrand coordinates, flow at v = sqrt(2GM/r), speed c at the horizon [web: arXiv gr-qc/0411060 per physicist]) shows "flowing space" can be exact mathematics, equivalent to general relativity (GR) for static masses.
• Disagreement. Physicist: Not testable as stated (strong form). Mathematician: split, Reading A refuted, Reading B coherent but forces universal exponential growth. Contrarian: Not testable / Never properly tested.
• Stronger argument. The mathematician's, because it makes the claim precise. Reading B (a sink pushed by the stream) gives an inverse-square force and then forces dM/dt = mu M with G = mu^2/(4 pi rho_e) [reconstruction; force law still [memory, medium]]. Hilgenberg's 1933 phrase that G is the ether volume swallowed per unit mass per unit time [read: Investigator note] supports the reconstruction. That turns "not testable as stated" into a testable consequence: the same mu for every body. The physicist's "not testable" is right for the weak form (a coordinate description) and too pessimistic for the strong form.
• Final verdict (split).
• Weak form, space flow as a reformulation of GR (no ether consumed): Plausible, untested (it is known mathematics, not a competing theory; it makes no new prediction).
• Carried-along incompressible sink flow as the force law: Refuted by calculation (r^-5; Moon off by five orders). Not Hilgenberg's reading as far as seen.
• Strong form, a real consumed ether giving inverse-square attraction via sinks: Never properly tested. No force law is in anything read, his own sink/source tank experiments (1931, 1939) are unread and unreplicated on record, and the thesis built on them was rejected in 1937/38 on conflict with relativity according to three secondary accounts, so the question was not settled by independent experiment. If the reviewer-derived universal-mu consequence is applied, it fails the ephemeris limit by a factor of order 10^4 (and gives an implied inflow speed far above c at the Earth's surface); I report that as a consequence of a reconstruction, not as Hilgenberg's stated prediction, and not as the verdict.
• What would settle it. Read the 1931 and 1939 booklets and the rest of the 1933 book: does he derive a force law and an ether density? Then one calculation: apply his law with universal mu to d(GM_sun)/dt (limit about 1e-13 per year). Experimentally nothing distinguishes the weak form from GR.

Claim 2. Inflowing ether is converted inside planets into new matter; mass grows exponentially

• Agreement. All three: the 1933 law mu = 5.1e-17 /s is arithmetically correct, the "g/sec" unit is a slip for "per second", conversion has never been measured, and no neutral test of the conversion exists.
• Disagreement. Contrarian leans to "Refuted by calculation"; physicist to "Tested, not supported" for the specific rate; mathematician to "Never properly tested" with the universal-rate form tested.
• Stronger argument. The physicist's split. The existence of some conversion at any rate is untestable by the radius data alone; the 1933 rate is excluded by independent measurement: radius (Wu 2011), ephemeris solar GM (about 1e-13 per year), lunar laser ranging Gdot/G (order 1e-13 per year) and my order-of-magnitude lunar-distance estimate (0.7 m/yr drift if Earth's GM grows at 1.9e-9 per year).
• Final verdict (split).
• Existence of ether-to-matter conversion: Never properly tested (no measurement; Hilgenberg himself lists how ether enters atoms as unexplained [read: Investigator note]; it was not tested but also was rejected without test per the secondary accounts of the thesis; the 1974 open letter drew no recorded reply).
• 1933 exponential form (mu about 5e-17 /s, 3-4 mm/yr, 2e35 baryons/s): Tested, not supported.
• Energy: 3e25 W of rest energy, 8% of solar luminosity, is a requirement on the ether, not a refutation; nobody has detected any such reservoir.
• What would settle it. A direct limit on dGM_earth/dt from satellite and lunar laser ranging (not found in this review); the 1967 swallowing-constant manuscript (sent to Runcorn); Scalera 2021 numbers for ether density and flux compared with the fixed product rho x v of about 6e-7 kg/(m2 s).

Claim 3. Radius nearly doubled since the Paleozoic (60%, 4590 km, 4 mm/yr)

• Agreement. All three: the printed figures do not agree as a set; the 60% is a diameter ratio; independent tests exist and the strong form fails them.
• Disagreement. Mathematician rates the printed set "Internally inconsistent"; the others call it two models (1933 and 1965).
• Stronger argument. The two-models reading, with the mathematician's label kept for the printed set. The 1933 law is self-consistent (3.4 mm/yr now). The 4590 km figure (1965 paper, unread) needs 8.4 mm/yr under an exponential. The inconsistency lies in the advocates' combination of numbers from different constructions; whether Hilgenberg reconciled them is unknown.
• Final verdict (split).
• Printed figure set as presented in the folder document: Internally inconsistent (unreconciled until the 1965 paper is read).
• Strong form, R = 0.72 at the Permian or 3.4-4 mm/yr now: Tested, not supported (paleomagnetic palaeoradius limit under 0.8% over 400 Myr, factor 35 to 55 away; geodetic 0.1 +/- 0.2 mm/yr, 17 to 20 times away; coral day counts).
• Weak form (change under 0.8% over 400 Myr, under 0.2 mm/yr now): Plausible, untested (not excluded; not what he claimed).
• What would settle it. The 1965 Geol. Rundschau paper (time base and law); the reader's own calculation: dR/dt = R mu/3 with mu = ln(1/0.216)/t for t = 1 Gyr and 540 Myr against 0.2 mm/yr.

Claim 4. Ether flow to the Sun plus the inverted Magnus effect spins planets up until a ring detaches

• Agreement. The inverse (negative) Magnus effect is a real laboratory fluid effect (viscous boundary layer, Reynolds number about 1e5) [web: JFM and arXiv 2302.11260, cited by two reviewers]. No planet is near break-up (Earth period 84 min needed, 1440 min actual); the folder authors call the ring-expulsion part "less valid today" [read: page image p.10].
• Disagreement. Planetary part: physicist "Tested, not supported"; mathematician "Not testable as stated" and "Historically superseded but instructive"; contrarian both of the latter.
• Stronger argument. Physicist, with the mathematician's point that no torque law is given. A Magnus force is a lift perpendicular to the stream, not a torque on the spin axis; spin-up needs a separate argument that nobody supplies.
• Final verdict (split).
• Inverse Magnus effect in laboratory fluids: Established (general fluid dynamics). Hilgenberg's own 1933 experiment: Never properly tested by others on record (apparatus, data and witnesses unread; no sign it was challenged either).
• Planetary spin-up and ring detachment, observable consequences (spin-up, shorter days, a ring): Tested, not supported (observed spins, tidal slowing, fossil days; the advocates' own concession). The mechanism, with no torque law given: Not testable as stated. Historically superseded but instructive, by the advocates' own judgement. [revised by QE revision: the earlier combined label put two verdicts on one part]
• Note: the link between the "completely proven" effect in the 1933 reports and the inverse Magnus effect is an inference from titles; the document does not say which effect was proven.
• What would settle it. The 1933 report (Z. Techn. Phys. 14, 211-214): apparatus, Reynolds number, measured lift sign.

Claim 5. Reconstructions on smaller globes with paleopoles; trenches, rifts and Benioff zones without subduction

• Agreement. The geometry is legitimate; the Pacific solution conflicts with later paleomagnetic data by the advocates' own admission [read: p.11]; tomography shows cold slabs to about 700 km and deeper [mainstream, reviewers' memory high].
• Disagreement. On "no subduction needed": physicist "Tested, not supported"; mathematician "Never properly tested".
• Stronger argument. Physicist, for the no-subduction statement, because tomography, seafloor ages (oldest in-place crust about 180 Myr [memory, high, not rechecked]) and paleomagnetic radius are independent observations that Hilgenberg's dunite-uplift model must explain and does not. The mathematician is right that no neutral, blind comparison of the two reconstructions was ever run, and I keep that in the record. The mathematician's calculation also shows how weak a "good fit" is: shelf area of 35% of the surface gives R'/R = 0.59 (his 0.62-0.65 allows 9-21% area slack), two cut lines (the 2000 km Mackenzie-Florida shear, an Alaska line) are free, and the transformation law is a free choice (7% tangential strain at 3000 km).
• Final verdict (split).
• Outlines can be fitted on a sphere of about 0.6-0.65 present diameter with modest gaps: Plausible, untested as geometry (low information given the free parameters).
• That the Earth really was that small and that paleogeography is correct: Tested, not supported.
• Trenches, rifts and Benioff zones without subduction: Tested, not supported (tomography and paleomagnetic evidence), with the caveat that no controlled head-to-head test of the two reconstructions exists on record and the reconstructions were reproduced only by advocates (Scalera's replica globes, workshops in more than ten countries).
• What would settle it. A blind reconstruction: fit continental outlines on a 0.62 sphere against random cuts with the same slack, and compare misfit with the fit on the present sphere (Bullard-type); then test Hilgenberg's predicted rising dunite against slab seismology.

Claim 6. The real question is expansion with or without new matter; ether view analogous to GR; ether inflow at c is a black hole

• Agreement. The river model gives an exact correspondence in which the flow speed reaches c at the horizon; it is a coordinate reformulation with no measurable difference from GR; the reported Riemann-to-GR step ("set ether energy to zero, add a fourth coordinate") is not shown and is not how Einstein's equations arise [memory, high]. No reply to the 1974 open letter is reported.
• Disagreement. Mathematician calls "equivalent in every way" internally inconsistent; the others "not testable as stated".
• Final verdict (split).
• Analogy to GR and black hole as flow reaching c: Not testable as stated (interpretation with no measurable difference); the correspondence itself is Plausible, untested as mathematics.
• "Equivalent in every way" and the derivation of GR: Not testable as stated for the strong wording (derivation not shown; his flow law unread). Not rated Internally inconsistent. [revised by QE revision: replaces "unsupported as presented", which is not a scale term]
• Expansion with no new matter: Tested, not supported (paleomagnetic palaeoradius, geodesy, Mercury and Moon limits in McElhinny et al. 1978; limits on Dirac-type G change below 8e-12 /yr). Not "Refuted by calculation" (see correction 1).
• Note for the reader: on the reviewer-derived Reading B, the inflow speed at the Earth's surface exceeds c by about 6e8, which would breach Hilgenberg's own black-hole criterion; this depends on the unverified force law and is a red flag, not a finding.
• What would settle it. The 1974 monograph's text and any reply in the correspondence of Wilson, Beloussov or van Bemmelen; a full flow law from the 1931/1939 booklets.

Corrected claim list (for claims.md, Step 1)

1. Gravity is the flow of space, or a real ether, into masses acting as sinks; in 1933 Hilgenberg argues from relativity of motion and the equality of heavy and inertial mass, and says a body accelerates because a sink sits in a stream [read: Investigator note]. No force law or equation is in the folder.
2. Swallowed ether becomes matter; mass grows as exp(mu t) with mu about 5.1e-17 /s (not "g/sec") for t = 1 Gyr and a volume ratio 0.216 [read: Investigator note, 1933 book]. The folder document gives no rate.
3. In the 1933 book the "60%" is a diameter ratio (0.62-0.65, shelf sphere), not a Permian radius. 4590 km (0.72 R) and 4 mm/yr come from other constructions (1965 paper, unread); the 1933 law itself gives 3.4 mm/yr now and 5570 km at 250 Myr. These do not form one law with one rate.
4. The 1933 reports are said to prove one of four fluid-dynamic effects; the document does not say it is the inverted Magnus effect (an inference from titles). The ring-expulsion cycle is called "less valid today" by the advocates [read: page image p.10].
5. Outlines fitted on smaller globes with paleopoles (1965: 5 reconstructions, 30 projections [read]); advocates concede the Pacific solution disagrees with up-to-date paleomagnetic data.
6. The 1974 letter [read: p.13-15] states "expansion with or without new matter" as the question and the ether-GR analogy; no reply reported. Publisher of the 1933 book is Verlag O. Hilgenberg, printed by Giessmann and Bartsch [web: archive.org, Investigator]. Also add to claims.md (QE revision): the 1934 metre-prototype paper as an unread empirical claim; the lineage in the folder document (Mantovani, Yarkovski, Lindemann 1927); the authors' own caveat that the lineage is "unsolved". Also: Hilgenberg's own admissions (constant density "not true but simplifying", how ether enters atoms unexplained) [read: Investigator note], and the "Penzias and Wilson 1968" slip (discovery 1964-65 [memory, high]).

Absence-of-evidence analysis

The record goes dark in six places. Each is an anomaly to analyse, not a neutral gap. None of the competing explanations below is established.

A. The 1937/38 thesis rejection and the refused chair (NSDAP). Present: three accounts of the rejection (Scalera and Braun 2003; German Wikipedia: 1938, Faculty of Mechanical Engineering, mainly over conflict with relativity; Thielmann 2015 and zillmer.com: submitted 1937) and three accounts of a refused professorship tracing to the same advocacy circle (Scalera, Jacob 2001, Wikipedia). Absent: the faculty file, the referees' reports, the personnel file 1934-38. Explanations: (1) a scientific rejection on relativity grounds, as the sources say; (2) political rejection, as Scalera and Braun add; (3) both, or procedural reasons, with later legend. For: three consistent published accounts, each by a source with a stake (advocates) or derived from them; he did later obtain a Dr.-Ing. (1948, TU Berlin, on fault structure), and the university gave him a workroom for decades (supporters Quiring, Zeil), which argues against a lasting institutional ban. Against: none cites the file; one account (Fiedler-Volmer, a TU witness) describes persistence against "sometimes even insulting ignorance", which is a witness account that fits (1) or (2). Decider: TU Berlin Universitaetsarchiv Promotionsakte 1937/38 and personnel file (not reached).

B. His own flow and Magnus experiments (1929-1939) and the 1933 Z. Techn. Phys. paper. Absent: any independent replication, any citation trail, any datasets. Explanations: unremarkable fluid dynamics nobody needed to repeat; the link to gravity was never accepted; wartime Germany; published outside refereed venues (booklets) apart from the 1933 paper. For the "never taken up" reading: Westphal had done earlier one-dimensional sink/source work [read: Investigator note], so the effects were within known hydrodynamics. Decider: citation search of the 1933 paper; the 1931 booklet at the Met Office Library (loan available); Gerlands Beitr. Geophys. 42 (1934).

C. No reply to the 1974 open letter to Wilson, Beloussov and van Bemmelen. Explanations: not sent or not received; answered privately and not preserved; ignored because plate tectonics had consolidated by 1974. The physicist adds the last as most likely but it is untested. Decider: those authors' correspondence archives; the Hilgenberg estate (held by his daughter Helge [read: p.11]).

D. The 1967 swallowing-constant manuscript, sent to Runcorn and unpublished [read: p.17]. This is the one place where Hilgenberg may have supplied the missing number (ether swallowed per unit mass per unit time). Explanations: lost; held in Runcorn's papers (Newcastle) or the estate; never completed. Decider: Runcorn's archive and the Hilgenberg estate.

E. No quantitative ether theory after 1933 until Scalera 2021. Explanations: the idea is not developable into numbers; the community that held it was small and dispersed; the numbers exist in the unread 1931/1939/1974 texts. Scalera is the interested party offering the first numbers; geoneutrino "corroboration" is his characterisation, not analysed by anyone neutral.

F. The investigative record itself stops at the time limit. Not reached: Gallica (Yarkovsky 1888), TU Berlin Universitaetsarchiv, Schweizerbart table of contents of the 1974 monograph, Google Books/HathiTrust, Springer (Geol. Rundschau 1965); DNB blocked by Chrome permissions; nothing downloaded (research/files/ is empty). Several gaps in this review are gaps in the search, not in the world.

What would settle it (cross-claim)

• The one experiment/calculation that matters most. Apply the 1933 growth law to existing limits: mu = 5.1e-17 /s gives 3.4 mm/yr and 1.6e-9 /yr mass growth against 0.1 +/- 0.2 mm/yr and about 1e-13 /yr. This has been done above; strong form fails. Anything weaker needs the 1965 paper.
• Records. 1965 Geol. Rundschau 55, 878-924; 1931 and 1939 booklets; Z. Techn. Phys. 14, 211-214; TU Berlin archive files; Runcorn and estate correspondence; the rest of the 1933 book (reference list naming Westphal and Fricke); the 2001 TU intern follow-ups (June, July "ad acta") and the Nerad appendix.
• Reader's try-it. (1) dR/dt = R mu/3 with mu = ln(1/0.216)/t for t = 1 Gyr and 540 Myr; compare 0.2 mm/yr. (2) Sink flow v = -k/r^2 gives a = v dv/dr proportional to r^-5; compute the Moon/surface ratio (60^-5). (3) Break-up period sqrt(R/g) x 2 pi = 84 min. No example.py exists yet.

Open questions

1. Did Hilgenberg derive an inverse-square force law from sink flow, and with what ether density? (Decides whether his gravity is a theory or an analogy.)
2. Does the universal-mu consequence hold in his text, and how does he handle the Sun, Moon and other bodies?
3. What are the time base and law behind 4590 km and 4 mm/yr in the 1965 paper?
4. Is the equation-of-state of a constant-mass Earth at 0.72 R compatible with a rock-and-iron structure? (Not answered by any reviewer; it bears only on the no-new-matter variant.)
5. What does Earth's GM do over decades in satellite and lunar laser data, and is the limit on its secular change comparable to the solar 1e-13 /yr?
6. Do the 1931/1933 flow experiments measure a real inverted Magnus effect at a specific Reynolds number?
7. What do the TU Berlin files say about 1937/38 and 1934-38?
8. Does a neutral blind fit test favour the 0.62 sphere over the present sphere once cuts and slack are matched?
9. What does the Investigator's unread material add (Scalera 2021 numbers; Farrell's accounts of the 1959 vortex-ring atom models; Krafft; Yarkovsky 1888 in French; Herndon's rival model)? All kept in the record; none changes a verdict.

Material kept in the record whatever the verdict

Hilgenberg's candour about unexplained steps and his invitation to repeat the globe construction; his peer-reviewed geology papers (1960s, Springer, Schweizerbart, Italian journals) and a 194-page 1974 monograph, so publication was not blocked; the variable-radius paleopole method (authors' claim: first use); the river-model correspondence (a real mathematical result his picture resembles); Yarkovsky 1888 and Riemann as the same idea earlier; Krafft (translated by Hilgenberg 1953); Jordan's G-decrease expansion; Herndon's decompression model (interested party); Scalera 2021 (interested party); witnesses Fiedler-Volmer and Oppermann; critics Bruhn (mass conservation, tomography), Seiler, Thorweihe; the 2001 Lautenthal colloquium and Scalera's replica globes (advocates); the arte/ZDF documentary (2007); Farrell's popular accounts (not read, no verdict). The mainstream tests (McElhinny 1978, Wu 2011) were run on expansion in general, not on Hilgenberg specifically, and both come from groups with no known stake in the outcome beyond their discipline's standards.

Verdict summary

QE revision

Inputs: qe.md (verdict MINOR) and the QE deep read of the folder document (deep/2003Book-ScaleraBraun-Hilgenberg-4ae024.md: Appendix on pp.2-6, section 9 on pp.15-18). One web check added (Shankland 1955; running total 8 of 8 budget, counting the earlier 7 plus this one). No verdict changes in substance; two labels are repaired. Tags as above.

Verdict changes (labels only)

Every other verdict stands. The deep read adds no number or experiment that bears on the radius, mass-growth or paleomagnetic tests; the 1934 metre-prototype paper is the only new empirical claim and it is unread (below).

What the new deep reads establish (folder document, authors' statements; interested parties, advocates honouring Hilgenberg)

1. Lineage. Mantovani is called the first to defend expansion as the cause of drift (1889; popular piece 1909); Wegener "made no mention of the central core" of Mantovani's idea and judged expansion "a form of extremism to be avoided" [read: p.3]. Yarkovski (1888) is in the folder's own text and reference list; the authors write that Russian circles "beginning from Yarkovski ... may have had some sort of influence on the ideas of the Germans. Indeed, many of them, including Hilgenberg, knew the language" [read: p.4]. No document is cited showing Hilgenberg read him, so the Investigator's Yarkovsky lead and the folder agree on the idea, and the influence stays a conjecture. This corrects the mathematician's "whether Hilgenberg knew Yarkovsky is unknown": still true, but the folder discusses it and supplies the language point.
2. Tension the authors leave open. "He may very well not have been aware that the expansion theory had come earlier" [read: p.3]; Mantovani's name appears in none of his works [read: p.3]; yet "only the book of Lindemann from 1927 ... was known and quoted by Hilgenberg in 1933" [read: p.4], and its title carries Erdexpansion. The authors call the lineage "unsolved". I keep both statements side by side and do not resolve them; the 1933 reference list (unread) would.
3. Training. The folder says a diploma in Mechanical Engineering and America from May 1925 to Sept. 1928 as an oil-prospecting geophysicist [read: p.2, p.5]; German Wikipedia (via the Investigator) says electrical machine engineering at TH Berlin, 1919-22 [web]. Both stay in the record; the contrarian's "electrical engineer" lacked a tag and its "four years" conflicts with the folder's dates.
4. The reference list names the records the arbiter wanted [read: p.16-17]: 1929 Das Raetsel Gravitation geloest (14 pp.); 1931 Ueber Gravitation, Tromben und Wellen in bewegten Medien (78 pp.); 1933 Z. Techn. Phys. 14, 211-214 and a 28-page Magnus booklet; 1933 Vom wachsenden Erdball (56 pp.); 1939 Ueber Stroemungsversuche mit Senken und Quellen (72 pp.); 1965 Geol. Rundschau 55, 878-924; 1967 swallowing-constant manuscript to Runcorn; 1974 Geotekt. Forsch. 45, 1-194. This confirms bibliographic details only; none was read.
5. Honour-volume texts. The 2003 volume carries an English translation of Hilgenberg's unpublished manuscript ("this volume pag.178-28", page range truncated by OCR) [read: p.9] and "selected parts" of Erdentstehung und Entwicklung (1976, 57 pp., translated at INGV, Rome) [read: p.15], plus the daughter Helge Hilgenberg's biographical paper [read: p.15]. These are Hilgenberg's own words in English, and the first place to look for his flow law and swallowing constant. Not in the folder.
6. Authors' own statements, kept as theirs. "The Technical University was created by him, taking advantage of the confusion in Berlin" is hedged ("could be said") and its only documented content is recovering the library from the Soviet sector and a short time as director in library activities [read: p.15]; cited source is the daughter's paper (kinship stake). Copies of the globes were damaged in 1968 by students [read: p.11]. Egyed 1960 is cited at p.9 but is not in the reference list [read: p.9, p.16-18]; which work is meant is unknown.
7. Authors' reception explanation. The authors say the idea was too general for contemporary physics ("bound not to find support") and do not claim suppression [read: p.6]. That is their account; the thesis-rejection and NSDAP statements (pp.7-8) remain single-source in the folder, corroborated only by the other accounts in claim 1 and section A above.

New items added to the record

• 1934 metre-prototype paper. Hilgenberg 1934, "Vergleich der Laengenzunahme der Meterprototypen mit der errechneten Zunahme des Erddurchmessers", Gerlands Beitr. Geophys. 42, 409-412 [read: p.16]. A refereed-journal comparison of recorded length changes of metre bars with his computed diameter growth. Title only; what data he used and what he concluded are unknown. Relevance to claim 2: a laboratory-scale empirical claim that no reviewer saw. Note that growth of the Earth's diameter would not by itself change a metre bar if matter scaled with it, so how he reasoned is an open question; slow length drift in bars from metallurgical relaxation is a candidate explanation of any drift he saw [memory, medium], not a finding. Open question 10 (added): what did the 1934 paper compare, with what data, and what did it conclude? Decider: the paper itself (HathiTrust or Google Books were not reached).
• Other Hilgenberg works in the folder's list not yet weighed: 1932 vortex-ring nature of cyclones (14 pp.); 1939 sunspot-maxima paper (Ann. Hydrographie, Aug. 1939, 421-424); 1940 drift and ocean permanence (Ann. Hydrographie 68, 262-272; it is a drift paper, not a vortex-atom work); 1959 vortex-ring atom model (36 pp.) [read: p.16-17]. No verdict; kept as records.
• Miller and the ether, both descriptions. The folder's authors call Dayton Miller's results "flawed by spurious effects" [read: p.7]. Thielmann (2015, a media scholar, not an expansion advocate) describes Miller's 1925 Mount Wilson papers as a later successful detection of the ether [web: https://doi.org/10.1515/9783839406106-003, via Investigator]. Both are characterisations: the authors have an interest in ether theories; Thielmann's chapter argues that ether proponents went unheard, so it too has a stance. Mainstream reanalysis: Shankland, McCuskey, Leone and Kuerti (1955) attributed the small periodic fringe shifts partly to statistical fluctuation in reading a very difficult experiment and the rest to local temperature conditions at Mount Wilson [web: https://en.wikipedia.org/wiki/Dayton_Miller, via search; the 1955 paper itself was not opened]. That reanalysis is itself a published characterisation by physicists defending the standard view; it is not a replication of Miller's apparatus. Miller is Dayton Miller, now confirmed [web, same URL]. Bearing: none on a verdict (no claim here depends on ether-drift detection), kept for retention.
• Advocates' replies to the decisive tests, records not yet read. Scalera et al., "Are artificial satellites orbits influenced by an expanding Earth?" (Earth-Prints, via the Investigator) is the advocates' own treatment of the test in open question 5; Maxlow 2002 (cited by Scalera 2021) and the expansionist argument that the 1978 paleomagnetic test assumes fixed-radius reconstructions are the rebuttal to McElhinny et al. Their existence is recorded; their content is not weighed here. The contrarian's point stands that geodesy at 0.1 +/- 0.2 mm/yr constrains the present, not episodic or very slow growth.
• Authors' vacuum-energy argument. The authors quote Michael Turner (2000), "estimates range from the absurdly large to the simply insignificant" [read: p.8], to argue that an ether energy density is not excluded. The underlying difficulty is real in mainstream physics (the cosmological-constant problem [memory, high]). It does not supply the 3e25 W of rest energy the 1933 law needs (see claim 2); that remains a requirement on the ether.
• Arithmetic corrections noted by QE, not in this file: physicist claim 5 new surface is 0.64 km2/yr (not 0.6 million); contrarian claim 2 is about 6e11 times Earth's heat loss (not 5e5); Hamilton and Lisle is Am. J. Phys. 76, 519 (2008) [memory, high]. None affected a verdict.

Retention and source status after the revision

Still unread by any step: the 1933 book beyond two page images and OCR pp.1-18 (archive.org copy not downloaded; needs the owner's approval), the 1931, 1939 and 1965 works, the 1934 paper, the Z. Techn. Phys. 1933 reports, the 1974 monograph, the English texts in the 2003 volume, Scalera 2021. The source gap note at the top stands unchanged. QE's expectation that no verdict changes was met: the two repaired labels change wording, not evidence.

Updated records list additions (for the "Records" bullet in the cross-claim section)

1934 Gerlands Beitr. Geophys. 42, 409-412; the 2003 volume's English Hilgenberg texts (pp.178ff.) and Helge Hilgenberg's paper; Lindemann 1927 (quoted by Hilgenberg); Mantovani 1889/1909; Scalera et al. satellite-orbit paper; Maxlow 2002; Shankland et al. 1955 (to open).