DLHotson: Arbiter (Step 3)

Project: Donald L. Hotson, "Dirac's Equation and the Sea of Negative Energy", Parts 1-3 (Infinite Energy #43, #44, #86). Inputs: facts.json, claims.md, physicist.md, mathematician.md, contrarian.md. Tags: [read] document; [web] URL; [calc] my own computation (scratch script, NumPy); [memory] with confidence.

Source gap note (repeated from claims.md)

No source gap. All three PDFs have a full text layer and were read. Equations are sparse, so nothing important was lost in text extraction. Two cautions apply: - Everything said about other people's experiments (Reznik, Sherwin-Rawcliffe, Graneau, Pappas, Urutskoev, Radin, Hudson, Majorana/Allais) is known only as Hotson quotes it, unless a [web] tag says otherwise. - Hotson gives almost no derivations. Many verdicts below are therefore "Not testable as stated". That is a verdict on the form of the claim, not a finding that the claim was tested and failed.

How the arbiter worked

I read the three reviews, then re-read the Hotson passages where they disagreed (Part 2 neutrosynthesis, strong force and gravity-range sections; Part 3 scale-model passage). I recomputed the contested numbers and web-checked what I could. The WebSearch budget for this session was exhausted, so I used WebFetch on specific pages only. Check log:

Reviewer web sources I accept as cited, without re-fetching: - GW170817 speed of gravity: https://arxiv.org/pdf/1710.06394 - Pion-nucleon coupling g^2/4pi = 13.73: https://arxiv.org/pdf/nucl-th/9910040 - AV18 and HAL QCD nuclear force: https://link.aps.org/doi/10.1103/PhysRevC.51.38 and https://link.aps.org/doi/10.1103/PhysRevLett.99.022001 - Carlip on aberration: https://arxiv.org/pdf/gr-qc/9909087 - Mandelstam-Tamm time: https://pmc.ncbi.nlm.nih.gov/articles/PMC7515176/ - Urutskoev (authors' own reports): https://www.osti.gov/etdeweb/biblio/20813985

Corrections all three reviewers agree on (these supersede claims.md and facts.json)

1. 9180 is a count of electron-positron pairs (18,360 charges), not 9180 charges. [read: Part 2, "a combination of 9180 electron-positron pairs"]. Hotson also writes "packing 9180 charges of like polarity" once [read: confirmed by me], meaning 9180 of each sign, so he is loose about it.
2. tau = 2e^2/3mc^3 is Hotson's own bracketed insertion, not Treiman's. [read: Part 1, "Smoking Gun"]. Value 6.266e-24 s [calc] (Hotson truncates to 6.26). c x tau = 1.879 fm. He calls this "the measured diameter of the proton". The measured charge radius is about 0.84 fm, so the match is loose (about 10 percent).
3. The 99.78 percent is an R-squared value, not an accuracy. It is the lowest R-squared (0.9978 to 0.9993) of Hotson's exponential fits.
4. GW170817 bound on the speed of gravity is verified [web, as above]: between -3e-15 and +7e-16 of c.
5. Pion-nucleon g^2/4pi = 13.73 [web], not 15. Hotson's 15 is about 9 percent high and uses an unstated convention.
6. The gravity range is quantitative. Hotson predicts about 2 kiloparsecs and says this removes dark matter [read: Part 2, gravity-range section, confirmed by me].
7. Hotson denies the neutrino is a particle [read: Part 2]. Step 1 did not record this.
8. Pair-production "paradox": hbar/tau = 105.0 MeV [calc] = 1.5 x 0.511 MeV / alpha. His own relation gives about 100 times the 1.022 MeV needed for a pair, so "none to spare" fails on his own number.

Recomputed numbers where reviewers differed

A. Satellite R-squared (physicist vs mathematician vs contrarian). The three numbers answer different questions. I reran all three null models, 14 points between 60.33 and 12,952 as in Saturn's case [calc]:

Reconciliation: - The physicist and contrarian are right that R-squared of 0.998 is unusual for consecutive ranks. The mathematician is right that Hotson's procedure is not consecutive ranks: he assigns the integer per satellite, skips integers, and (as the mathematician reproduced) fits an exponent. Under that freedom the statistic is close to automatic. - Caveat none of them stated: the random sets rarely fit distinct integers at all (1 to 7 percent acceptance). Real satellite systems are roughly geometrically spaced, which is what packing and resonance already produce (Hayes and Tremaine [web, via Wikipedia]). - So R-squared cannot separate "wave" from "dynamical packing". The 95 percent figure is conditional on that acceptance, and I would not quote it without the condition. - I did not independently verify the Saturn integer table from Hotson's figure. I rely on the mathematician's page-image reading [read: page image p.10, as reported].

B. Coulomb self-energy of the nucleon (mathematician: 8e7 MeV vs 939 MeV). I do not carry this into the verdict. It assumes 9180 like-sign charges packed into a real-space radius of 0.9 fm. Hotson says the sea is neutral overall and that about 90 percent of the epos are pure one-dimensional vibrations "in imaginary directions" [read: Part 2]. If charges of opposite sign interpenetrate, the electrostatic energy is not N^2 e^2/R. The confinement argument (hbar c / 1 fm = 197 MeV per lepton) has the same dependence on real-space localization. Both are valid objections to a literal-particles reading, but Hotson's reading is not literal. The firm refutations are the experimental ones in Claim 4.

C. Gravity range (physicist: force factor 0.09). Recomputed: e^(-r/L)(1 + r/L) at r = 8 kpc, L = 2 kpc gives 0.0916 [calc]. The exact factor depends on the shape of the cutoff, which Hotson does not give (the contrarian rightly said "qualitative"). The sign does not depend on it: any cutoff makes gravity weaker than Newton at large radius. Flat rotation curves need more force than the visible matter supplies, so the cutoff goes the wrong way. I accept "Refuted by calculation" for the dark-matter claim, with the exact factor marked as illustrative.

D. Scale model, 490 AU and "13,000 times". Bohr radius divided by proton radius times Sun radius [calc]: 492 AU at 0.5 fm, 293 AU at 0.84 fm, 263 AU at 0.935 fm (Hotson's own 1.87 fm diameter). Volume ratio (490/39)^3 = 1983 [calc]. 13,000 would follow from (980/39)^3 = 15,900, a diameter used as a radius. I cannot confirm that this is Hotson's slip. The qualitative point (the atom is mostly empty at nuclear scale) is conventional.

E. Other numbers, all agreed and reproduced [calc]: - 136 x 135 = 18,360; 18,360/10 = 1836.0. Real proton 1836.15, neutron 1838.68 (0.14 percent above the model). - Hyperon divisors 9, 8, 7, 6 give 2040, 2295, 2623, 3060 versus 2183, 2328, 2573, 3273: errors -6.6, -1.4, +1.9, -6.5 percent. - 15 x 137 = 2055. Using g^2/4pi = 13.73, the ratio to alpha is 1881. This is 2.5 percent from 1836 numerically. It is two unrelated dimensionless numbers, and a coupling ratio is not a force ratio at a given distance. - G m_e^2 / Coulomb for two electrons = 2.4e-43. The g-2 anomaly is about 1.2e-3, so about 40 orders of magnitude separate them. - Pion Compton wavelength = 1.41 fm.

Verdicts, claim by claim

Verdict scale as in the prompt. "Tested / Never tested / Dismissed" status is tracked explicitly, because that is the contrarian's distinction. Nothing here was documented as "dismissed without testing". Hotson's only evidence of resistance is Zebuhr's commentary that he was pushed out of physics for asking awkward questions [read: IE86]. That is one source, anecdotal and undocumented, and it is not evidence about correctness.

Claim 1. The Dirac negative-energy solutions were wrongly discarded; all four roots are physical.

• Agree: The mainstream already keeps all the Dirac solutions (hole theory 1930, Anderson 1932, Feynman-Stueckelberg). "Discarded in 1934 by a trick" misstates history. The "imaginary direction" and "ten dimensions" steps are not derived. Dirac theory is among the best-tested structures in physics (hydrogen fine structure, electron g-factor, positron physics) [memory: high].
• Disagree: Headline verdict. Physicist: split with Established (antiparticle reading). Mathematician: Internally inconsistent. Contrarian: Not testable as stated.
• Stronger argument: The mathematician found specific defects. A negative real root is not an imaginary number. "Ten" counts the independent components of a symmetric 4x4 tensor (4 x 5 / 2 = 10), not dimensions. Hotson's "four kinds of electron" double counts the solutions. I take the first two as established. The double-count point depends on how Hotson sets out the four roots, and I did not re-read that passage, so I treat it as likely rather than certain. The physicist and contrarian are right that the epo reinterpretation as a whole has no measurable difference from standard theory, so it is not testable as stated.
• Tested / never tested / dismissed: Standard reading: tested for about 90 years, passed. Hotson's reading: never tested because it makes no distinct prediction; not dismissed without testing, because nothing testable was offered.
• Final verdict (split):
• Four solutions physical in the antiparticle sense: Established (mainstream content, not Hotson's reading).
• Literal filled negative-energy sea as history: Historically superseded but instructive.
• "Wrongly truncated in 1934": incorrect as history.
• The epo/"imaginary dimension" reinterpretation: Internally inconsistent at the three named steps; where it is consistent it is Not testable as stated.
• What would settle it: A calculation of the electron g-2 (1.0011596522) or Lamb shift from the epo picture. None is offered.

Claim 2. A universal BEC of epos, alternating at tau = 6.26e-24 s, restores energy conservation in pair production and "is" zero-point energy.

• Agree: The tau argument fails on Hotson's own number (105 MeV available vs 1.022 MeV needed). The relation he borrows is a state-dependent characteristic time (Mandelstam-Tamm [web]), not a universal quantum of time. tau is the Abraham-Lorentz classical radiation time, (2/3) r_e/c, alpha-suppressed relative to the Compton time. The pair-production "paradox" does not exist: spin angular momentum is not an energy, and energy, momentum, angular momentum and charge are each conserved with a nucleus taking up momentum. No condensate temperature, density or Hamiltonian is given.
• Disagree: Whether the BEC itself is "Never properly tested" (mathematician, contrarian) or "Not testable as stated" (physicist). Also whether the contradiction with measured short lifetimes is direct (physicist) or only a test gap (contrarian: attosecond timing does not reach 1e-24 s).
• Stronger argument: The physicist, with a correction. The Z width 2.4955 GeV [web] gives a lifetime of 2.64e-25 s [calc], 24 times shorter than tau. That is an indirect inference from a width, not a time-resolved measurement, but Hotson claims a universal "minimum time of any interaction", and the measured widths contradict it. On the BEC, the scale definition decides it. "Never properly tested" is for a claim that could be tested; Hotson names no observable, coupling or density, so "Not testable as stated" fits. The contrarian is right that the BEC has been ignored rather than tested and failed.
• Tested / never tested / dismissed: Never tested; no test can be built from the text. Not "tested and failed". Hotson cites Reznik as support; whether Reznik's result is a calculation or a laboratory demonstration is unverified (check failed). Entanglement of probes would not show a BEC either way.
• Final verdict (split):
• "Pair production violates conservation unless a sea exists": Refuted by calculation.
• The tau argument ("no energy to spare"): Internally inconsistent (his own formula gives 105 MeV).
• tau as a universal minimum interaction time: Refuted by calculation against measured widths (Z, [web] + [calc]).
• The epo BEC and "zero-point energy is negative energy": Not testable as stated.
• What would settle it: A stated Hamiltonian, condensate density and a prediction for one measurable (for example a Casimir force or a high-energy time-structure signature). Failing that, nothing can be run.

Claim 3. EM, photon, gravity and inertia are non-local, instantaneous epo structures; gravity range-limited (about 2 kpc), no dark matter.

• Agree: GW170817 contradicts instantaneous gravity [web]. Range-limited gravity points the wrong way for flat rotation curves. "Magnetogravitation" has no coupling constant and Hotson says "further analytical work will have to be done" [read]. Chains attach to charges, so gravity would not scale with mass-energy. Laplace's aberration argument is answered in GR (Carlip [web]).
• Disagree: (i) Instantaneous EM: physicist "Tested, not supported"; mathematician and contrarian "Never properly tested". (ii) The contrarian calls the dark-matter refutation "qualitative" and flags it as his own reasoning.
• Stronger argument: (i) The mathematician and contrarian. The physicist's support for "Tested, not supported" is [memory medium], and my web check of Sherwin-Rawcliffe failed. The sources I do have say the Graneau wire work was met with conventional rebuttals (pinch effect, thermal expansion; contrarian's [web] links) and that Sherwin-Rawcliffe's reading as "instant Coulomb action" is an inference, not a measurement. I will not state a test outcome I cannot source. (ii) Recomputed above: the sign holds for any cutoff, so "Refuted by calculation" stands for the dark-matter claim, with the 0.09 as illustrative.
• Tested / never tested / dismissed: FTL gravity: tested (GW170817), not supported. Instantaneous EM near-field propagation: no neutral propagation-speed test on record from the sources in hand; the exploding-wire work was engaged by critics (not ignored). Epo chains: never tested, no observable.
• Final verdict (split):
• Gravity acts instantaneously: Tested, not supported.
• Range-limited gravity replaces dark matter: Refuted by calculation.
• Gravity as a g-2 residual: Refuted by calculation on magnitude (about 1e40 off, no mechanism).
• EM acts instantaneously: Never properly tested (neutral propagation test), with the disputed Graneau/Pappas readings noted.
• Epo chains, photon as epo wave, gyroscopic inertia: Not testable as stated.
• What would settle it: A measured speed of the near-field Coulomb or Ampere interaction between moving charges, with retardation effects separated from the standard Lienard-Wiechert result; and for gravity, a worked rotation curve with Hotson's cutoff.

Claim 4. The nucleon is 9180 epo pairs (136 modes, ten dimensions); explains the neutron, charge equality and the strength and shape of the strong force.

• Agree: The arithmetic is right (136 x 135 = 18,360; /10 = 1836). It is numerology: the "/10" comes from "time is one of ten dimensions", with no derivation. The model gives the proton mass but is said to be of the neutron (1838.68), and Hotson answers "mass is a tricky business". Divisors 9, 8, 7, 6 were chosen after the fact. Sirag himself called it "mere number-juggling" [read]. No force law or potential V(r) is written. Hotson's claim that the nuclear force "has never been successfully modeled" is false: AV18 fits more than 2000 scattering data and has a repulsive core, and lattice QCD reproduces the core and well [web, physicist]. DIS found fractional-charge point constituents, neutrinos exist (Cowan-Reines), and a 9180-pair nucleon would need a magnetic moment near 2.79 nuclear magnetons by cancellation, with no mechanism [memory: high].
• Disagree: (i) Physicist: "Internally inconsistent" for the counting. Mathematician: "Internally inconsistent" and "Refuted by calculation" by energy budget. Contrarian: "Refuted by calculation" on the neutron mass and confinement. (ii) Hotson's coupling ratio: physicist says the "2000" is not a force ratio; contrarian says convention-dependent; mathematician says "near 2000 only roughly".
• Stronger argument: (i) The mismatch of 2.68 electron masses is acknowledged by Hotson and is an approximation he accepts, not a self-contradiction and not a "refutation by calculation" (0.14 percent). The energy-budget refutation fails for the reason in Correction B above. The strong arguments are the experimental ones and the absence of any derivation. (ii) The physicist: with the measured coupling, ratio 1881 vs 1836 is a numerical near-match of unrelated numbers, and Hotson's step "918 pairs give 1836e" has no force law behind it. A strength coupling ratio is not a force ratio at a given distance. The physicist's estimate of about 30 for the potential-depth to Coulomb ratio at about 1 fm is [calc], loose.
• Tested / never tested / dismissed: Hotson's model was not designed to be tested, so it was never tested as such. But existing data on record (DIS, neutrino detection, nucleon moments) were not run against it either. They conflict with it, so "Tested, not supported" is accurate only in the sense of existing experiments, not a test aimed at his model. Not suppressed in any documented way; ignored.
• Final verdict (split):
• The 136/9180/1836 count as a derivation of nucleon mass: Not testable as stated (numerology: free divisors, ad hoc 1/10, neutron/proton mismatch; not a derivation).
• Nucleon composed of epos (e+e- pairs): Tested, not supported by existing experiments (DIS, neutrino detection, magnetic moments), noting these were not designed against his model.
• The "about 2000 times Coulomb" strength argument: Refuted by calculation (coupling ratio is not a force ratio; 15 was high; match of unrelated numbers).
• "No other model explains the force shape": Refuted by calculation (AV18 and lattice QCD are calculations; relabelled in QE revision).
• Equal electron and proton charge as a consequence: follows only if the construction is accepted; Plausible, untested only in a trivial sense (restatement), not worth testing given the above. Neutrality is tested to about 1e-21 [memory: medium, web check failed].
• What would settle it: Compute the proton and neutron magnetic moments (+2.79, -1.91 nuclear magnetons) and a deep inelastic scattering structure function from the 9180-pair model. Hotson says this analysis "should also yield exact agreement" [read] but does not do it.

Claim 5. Atoms are held in shape by a crystal-like Atomic BEC of epos; plasmas and double layers organised the same way.

• Agree (all three): No equations, spacing, energy levels or spectrum. The five "miracles" attack the Bohr orbit model abandoned in 1925-26. Stationary states do not radiate, atoms are neutral by spherical symmetry, and Pauli exclusion comes from antisymmetry [memory: high]. Hydrogen spectra agree with Dirac theory and QED to about 1e-12 [memory: medium, level of agreement]. Plasma double layers are covered by standard plasma physics.
• Disagree: Only emphasis. The contrarian notes the neutrality of atoms really is an unexplained accident in the standard picture (partly addressed by anomaly cancellation [memory: medium]), but Hotson's answer rests on Claim 4.
• Stronger argument: All three converge. The mathematician's extra point holds: the scale-model numbers are inconsistent with Hotson's own proton size (see Correction D).
• Tested / never tested / dismissed: Never tested; never put in a testable form.
• Final verdict (split):
• Critique of the Bohr orbit: Historically superseded but instructive.
• The Atomic BEC lattice: Not testable as stated.
• What would settle it: A lattice model that outputs the hydrogen Rydberg series and the 21 cm line. Nothing short of that.

Claim 6. Standing "waves of polarization" set satellite and planetary spacing at harmonics ("at least 99.78 percent determined").

• Agree: R-squared is misread as the fraction of the value "attributed to" a wave. Hotson chooses which integer each satellite gets, with gaps, and excludes Neptune. A Schroedinger wave with "1/r^2 amplitude" is not derived. Io-Europa-Ganymede is a 1:2:4 resonance, a standard tidal-resonance effect (Io tidal heating powered by it [memory: high]). No advance prediction exists, though many moons discovered since 2002 would have been a free test [memory: high; whether he tried is unknown].
• Disagree: How strong the statistical refutation is: physicist (0.01 to 0.2 percent of random sets reach 0.9978, consecutive ranks), mathematician (95 percent, free integers), contrarian (0.95 for real moons; refutation "weak, partial").
• Stronger argument: The mathematician's null is closer to what Hotson actually did, and I reproduced it (A and B above). The physicist's null removes Hotson's freedom. The key conclusion is the same: the statistic cannot distinguish a wave from packing. One further point from the mathematician, which I did not re-derive: if nodes were harmonics of the radius, spacing would be linear in N, not exponential, so the wave picture disagrees with the fit.
• Tested / never tested / dismissed: The statistic was tested (by reviewers, not by Hotson's critics in print; I know of no published reply, search not exhaustive). The physical claim was never tested out of sample. Titius-Bode itself is treated as coincidence or packing [web, via Wikipedia].
• Final verdict (split):
• R-squared as proof of a wave: Refuted by calculation (uninformative under Hotson's free-integer procedure).
• Epo-sea standing waves set the spacings: Never properly tested (post hoc fit; no advance prediction; not dismissed after a test).
• Titius-Bode spacing in general: Historically superseded but instructive.
• What would settle it: Pre-register Hotson's formula with its parameters for exoplanet systems or new moons, then compare against a packing-based null. Or compute whether a Schroedinger-type wave around a plasma body gives nodes exponential in N.

Claim 7. LENR, biological transmutation, psi and Hudson's "monatomic" superconductors are real and explained by the BEC.

• Agree: "Removing the label" is a metaphor with no mathematics. "Outcomes depend on the experimenter's mind-set" makes the claim unfalsifiable. Radin's 10^104 odds is a combined meta-analysis figure and says nothing about effect size or reality when there is any systematic bias [memory: high, statistical point]. Hotson's own platinum-group "separation from sea water" is anecdote: no instrument, data or procedure in the paper [read].
• Disagree: Psi: physicist and contrarian "Tested, not supported"; mathematician "Not testable as stated". Kervran-type transmutation: physicist "Tested, not supported" (memory, no source); contrarian and mathematician "Never properly tested".
• Stronger argument: On the rule that I may not state a test outcome without a source. For psi, extensive controlled testing exists and is disputed. The only critiques retrieved are skeptical (skepdic, philarchive), so I can say the mainstream does not accept it, not that neutral tests definitively failed. For Kervran I have no source at all, so "Never properly tested" is the safe label, with the mainstream non-acceptance noted.
• Tested / never tested / dismissed:
• LENR titanium-foil: tested by the originating group (about 5 percent 48Ti deficit vs 0.4 percent error [read, quoting Urutskoev/Lochak]); claimed confirmed at Dubna by the authors' side [web: osti.gov]; no independent neutral replication found by two reviewers (neither of us found one; not proven none exist). Contamination and isobaric mass-spectrometry artefacts are not excluded in what Hotson quotes.
• Psi: tested extensively, dispute unresolved; not dismissed without testing.
• Hudson: no neutral test found.
• Final verdict (split):
• Urutskoev-type transmutation: Never properly tested (no neutral replication; not dismissed without testing).
• Kervran biological transmutation: Never properly tested (no source retrieved; mainstream does not accept it [memory: high]).
• Psi as an established, BEC-mediated effect: the effect, Tested, not supported (controlled experiments disputed; mainstream non-acceptance, with skeptical-only web sources); the BEC mechanism and "mind-set dependence": Not testable as stated.
• Hudson monatomic superconductors: Never properly tested (the test is cheap: resistivity and magnetization on a purified sample).
• What would settle it: Blinded, independent isotope-ratio mass spectrometry of Ti foil before and after discharge, with blank controls and a second lab; and, for Hudson, zero-resistance and Meissner-effect measurements on a purified sample.

Corrected claim list (replaces claims.md for later steps)

1. The Dirac equation has four solutions per momentum (two spin states, two energy signs). The mainstream reading (antiparticles; hole theory then Feynman-Stueckelberg) keeps all of them. Hotson holds that they were wrongly discarded in the 1930s and that all four are physical electron/positron states in a literal negative-energy sea.
2. A universal electron-positron Bose-Einstein condensate ("Big BEC" of epos) alternates charge every tau = 2e^2/3mc^3 = 6.266e-24 s (Hotson's insertion), is the real meaning of zero-point energy, and makes pair production a promotion from the sea so that energy conservation is restored.
3. The EM field, the photon, gravity and inertia are non-local, instantaneous epo structures. Gravity ("magnetogravitation", tied to the g-2 anomaly) has a range of about 2 kpc, which Hotson says removes the need for dark matter (a stated prediction; no derivation is given in the paper).
4. A nucleon is built from 9180 electron-positron pairs (18,360 charges; 136 x 135 modes; mass 18,360/10 = 1836 electron masses), accounting for the neutron, equal electron and proton charge, and the strength (about 2000 times Coulomb, via the coupling ratio) and shape of the strong force. Hotson denies the neutrino is a particle.
5. Atoms are held in shape by a crystal-like "Atomic BEC" of epos around the proton, replacing the Bohr atom's "miracles"; plasmas and double layers are organised the same way.
6. Satellite and planetary spacings (Titius-Bode) are set by standing "waves of polarization" at harmonics, supported by exponential regressions with R-squared 0.9978 to 0.9993 (misread as the fraction of the value determined).
7. LENR (Urutskoev titanium-foil transmutation), biological transmutation, psi (Radin's 10^104) and Hudson's monatomic platinum-group superconductors are real and explained by removing the Atomic BEC's "label". (QE extension: reality is "pure information" refreshed every tau, and "I am my information", which survives bodily death.)
8. (Added by QE revision; wording updated in Round 2) Cosmological redshift is tired-light energy loss to the epo medium, which Hotson says the Second Law requires; the Doppler reading is said to violate conservation; the universe is static with continuous creation; the Big Bang and the Standard Model have "failed every observational test"; redshifts are quantized (no step size given).

Extensions from the QE revision (they sit under the claims above): claim 6 also includes the tau / 10 tau octave fits (R-squared above 0.999999), the Sun = 10 x Jupiter coincidence, Sirius, the Jupiter-satellite 137 recurrence and Io shout, the 160-minute solar pulsation, the planetary-orbit and Pioneer anomalies, and the Music of the Spheres 2 items (length of day, decay rates, Allais). Claim 2 also includes the ZPE numbers (1.6e23 Hz, 660/330 MeV, 2.7 K interface). Claim 3 also includes "Lorentzian relativity passes Sagnac and Silvertooth where SR fails".

Summary table

What would settle it (one test per claim)

1. A calculation of g-2 or the Lamb shift from the epo picture.
2. A stated Hamiltonian and density for the BEC, with one measurable prediction. Independently, any measured interaction time below 6.26e-24 s (the Z width already implies one, indirectly).
3. A measured propagation speed of the near-field Coulomb or Ampere interaction between moving charges; and a rotation-curve calculation using Hotson's 2 kpc cutoff.
4. The nucleon magnetic moments and a DIS structure function derived from the 9180-pair model.
5. A lattice model that yields the Rydberg series and 21 cm line.
6. A pre-registered out-of-sample test on new moons or exoplanet systems against a packing null.
7. Blinded second-lab mass spectrometry of Ti foil before and after discharge; resistivity and Meissner tests on purified Hudson material.

Open questions

• Is Reznik's vacuum-entanglement result a theory paper or a laboratory result? Hotson writes "has demonstrated" [read]; my check failed. Unknown.
• Did any independent lab replicate Urutskoev's isotope shift? Two reviewers found none; neither has proven none exist.
• Do the Sherwin-Rawcliffe, Graneau and Pappas results admit conventional explanations, as the Lienard-Wiechert argument suggests? The sources I retrieved are partial; I could not settle it.
• Why does the electron charge equal the proton charge to about 1e-21? This is a real open question, partly addressed by anomaly cancellation [memory: medium]. Hotson's answer rests on Claim 4, which fails.
• Is there a version of Titius-Bode regularity that is not explained by packing? Hayes and Tremaine suggest not [web], but I did not read the paper itself.
• The Majorana, Allais and Saxl eclipse and shielding anomalies Hotson cites are known here only as he quotes them. Not checked.
• Hotson's "Zebuhr: pushed out of physics" story is anecdote with no documents.

What is worth keeping

• The genuine tension: pair production is described by operators that "create" particles, and the electron-proton charge equality and the size of the vacuum energy are real puzzles. Dirac's hole theory was once exactly the sea picture Hotson revives.
• The contrarian's honest case: Graneau-type wire experiments are real laboratory phenomena with contested interpretations. A neutral Urutskoev replication would be cheap.
• The lesson: a model that forbids nothing (massless, inertialess, "virtually undetectable" epos) cannot be tested by anything, however many numbers it matches. The numbers it matches (1836, 918, 99.78 percent) were all in hand before the model was built.

QE revision (after qe.md, verdict MINOR)

QE found the seven reviewed claims sound but flagged a missing cosmology claim, un-reviewed octave numerology, and the separate "Music of the Spheres 2" article. Three deep reads now exist in deep/ (IE86 pp.11-16, Part 1 pp.15-19, Part 2 pp.12-18). I did not have the three reviews re-run. Every verdict below is mine, from the deep reads plus the web checks logged here.

Gap that remains. No deep read covers Part 2 pp.18-24 (cosmology). Claim 8 rests on QE's quotations from the extracted text [read: Part 2 pp.20-24, via qe.md] and digest 26c938.03. Hotson's own arguments for tired light were therefore not independently re-read by me. Verdicts for claim 8 depend mainly on observations, not on his derivation, so this does not change them.

New web checks (WebSearch budget was exhausted, so WebFetch of specific pages)

New evidence from the deep reads (all [read] unless tagged)

1. Table 1 uses a fitted base, not exact octaves [read: page image, Part 2 p.13, deep/HotsonPart2]. The intercepts come from base 1.99936 (tau series) or 1.9999 (10 tau series). 6.2517e-24 x 1.99936^76 = 0.46101 reproduces the table; exact 6.2664e-24 x 2^76 gives 0.47348 [calc]. Against exact octaves the tau series is off by up to 4-7 percent (Mercury, Mars, Pluto; Mars -6.6 percent), mean |dev| 0.042 octave. The 10 tau series is off by about 1.4 percent (0.020 octave). Hotson's own text admits Mars is "a fat 6%" off, yet Table 1 prints 0.030.
2. R-squared cannot test octaves [calc]. Any 9 positive numbers spread over 110 octaves, each assigned its nearest whole octave, give R-squared about 0.99993 (median of 20,000 simulations) with no physics. The informative statistic is the deviation from the nearest octave, which under chance is uniform on 0 to 0.5 octave (mean 0.25). Hotson's "chance less than 1 in 1,000,000" [read: p.14] is therefore wrong as stated. With two bases and several quantity types per body (what Hotson uses), the tau series is consistent with chance (P about 0.12 at 3 choices per body, 0.55 at 5). The 10 tau series looks tighter (P about 0.006 at 5 choices) but its 13 rows are not independent (Galilean 1:2:4 resonance, outer-orbit trio, Io shout = P_Io/2, Sun LD = 10 x Jupiter LD by construction, Kepler's third law), leaving about 6-7 effective points. That is the deep reader's own simulation. I have not re-run it, but it agrees with my earlier free-integer result for satellites (A and B above).
3. Sun = 10 x Jupiter works with Hotson's Jupiter value (ratio 10.0004) but is 9.95 with modern radii (1,391,400 / 139,822) [calc; modern radii memory high]. Table 1 gives Sun and Jupiter light-diameters with the same digits, so the factor is built in.
4. Sirius matches 10 tau x 2^77 to 0.03 percent only with Hotson's 2.04 solar diameters. A modern interferometric radius of about 1.71 R_sun (Kervella et al. 2003 [memory medium-high, unchecked]) moves it about 0.25 octave off, near the worst place on the 10 tau grid. Hotson's prediction that all measurable stars sit on tau or 10 tau octaves was testable, and Sirius is the first test.
5. Mercury: text exponents (2^80, 2^84) and table exponents (2^81, 2^85) differ by one octave. The table version fits the one-way light times (153.4 s and 232.9 s [calc]), yet is labelled "x 2". Sidereal period is 4.3 percent from exact tau x 2^100, not "within 1%".
6. Cesium frequency is misprinted (9 129 631 770 instead of 9 192 631 770 Hz). With the correct value the tau x 2^44 match is 1.3 percent, not 0.5 percent [calc].
7. "within 1% of 10 tau x 27" is 2^7 [read: page image p.13, Table 1]: 8.021e-21 s versus h/(m_e c^2) = 8.0933e-21 s, 0.90 percent. This confirms QE's reading. Digest 26c938.03 (tau = h/mc^2) is wrong and no verdict uses it.
8. The 137 recurrence is an artefact of 1976-77 CRC periods [calc, deep read]. Those periods violate the Laplace relation (N1 - 3N2 + 2N3 = 0) by 2.1e-5 per day. Even then, Europa-Ganymede gives n = 135.6, not 137. With modern periods [memory high] the Laplace relation holds to 1.6e-10 per day and the best alignment is n = 136 (973.02 d). The "490-day" period is 1/nu of the Laplace conjunction line (486.81 d modern). So "137 = 1/alpha in Jupiter's moons" does not survive.
9. Io shout and 10.73 years: Table 1's "Io Shout" is exactly P_Io/2, not an independent measurement. The factor 8 in "eight 490-day periods = 10.73 years" is not derived (Jupiter's direction advances 40.7 degrees per 490 d, so a return needs 8.84, not 8 [calc]). With modern 1/nu it is 10.66 years. The sunspot cycle is about 11.0 years and varies from 9 to 14 [memory high].
10. 160-minute oscillation: Kotov's own letter [read: IE86 p.14-15] says P0 = 160.0101 min was present only 1974-1982, P1 = 159.9656 min dominated after that, P1 vanished at solar minima 1985-86 and 1996-97, and "the origin of this phenomenon is unknown". Hotson's "rock-solid for the 35 years" contradicts this. The beat of 399.4 d [calc] matches Kotov's 399(4) d and Jupiter's synodic period (398.9 d [memory high]), which is an interesting coincidence, but only a letter backs it. 9 x P0 = 24.0015 h and 9 x P1 = 23.9948 h, so neither is exactly 24 h. Whether the 160-minute signal is real or an Earth-atmosphere/window artefact is disputed [memory medium, unchecked]. 160 min is exactly 1/9 day.
11. Corona: Hotson writes "50 times" hotter (IE86) and "170 times" (Part 2); 1e6/5800 = 172 [calc]. A slip, not a claim that matters.
12. Length-of-day table (Perry) [read: IE86 p.15]: units are undefined ("-3 seconds"), no data series is named, and the last row is a forecast ("2014 faster ??") whose outcome I did not check. Not testable as stated until units and source are given.
13. Orbital anomalies [read: IE86 p.14; Part 2 pp.19-21 via qe.md]: Hotson says GR explains "only about 17%" of Mars and gives no Venus correction, with no source. The Mercury GR check above contradicts him for Mercury. Pioneer was thermal (Turyshev 2012 [web]).
14. ZPE numbers [read: Part 1 p.16; deep/HotsonPart1]: nu = 1/tau = 1.6e23 Hz, E = h nu = 660 MeV per epo, 330 MeV per mode. The numbers follow from one input, tau x c = 1.87 fm (the proton diameter), since 660 MeV = hc / 1.87 fm = 1240 MeV fm / 1.87 fm = 663 MeV. Nothing independent is predicted. Hotson also uses 2 m_e c^2 = 1.022 MeV as the threshold below which an epho (photon-carrying epo) is "unstable" [read: Part 1 p.18], while assigning 660 MeV to an epo. The two use different energy scales without comment. Note also hbar/tau = 105 MeV (earlier arbiter figure), and 660 MeV is exactly 2 pi times that, because h = 2 pi x hbar. So Hotson's 660 MeV and the reviewers' 105 MeV are the same quantity with and without 2 pi, and both still exceed 1.022 MeV by a wide margin. The ZPE is also fixed to a single frequency for every mode, which standard theory does not do [memory high]. The 2.7 K "interface" is a hedged guess ("perhaps around 2.7 K") equal numerically to the CMB temperature; kT at 2.7 K is 0.23 meV, nine orders below 330 MeV [calc, deep read].
15. Sherwin-Rawcliffe, Graneau, Pappas are cited, not analysed, in Part 1 [read: p.15]. The Graneau references on the list are titled for Ampere (longitudinal) forces in conductors, not propagation speed. Hotson also writes the actions "are not literally instantaneous, but take the finite time tau" [read: p.15], which sits uneasily with "apparently instantaneously". This leaves the Claim 3 verdict (Never properly tested) unchanged.
16. Lorentz versus SR [read: Part 1 p.19]: Hotson says Lorentz's aether passes tests SR fails, naming Sagnac (1913) and Silvertooth (1987, 1989, 1992), giving no analysis. Sagnac is a standard SR result for a rotating frame, and Lorentz theory is empirically equivalent to SR for inertial experiments [memory high, not web-checked]. Silvertooth has no independent replication that I know of [memory medium].
17. IE86 pp.11-13: the Ti-48 5 percent deficit against 0.4 percent error and the 10^3 neutron limit are quoted from an unnamed paper; Hotson's references 1-2 are Ramsey and Reznik, so the Lochak/Kuznetsov data cannot be traced from this article [read]. Radin, Goswami, Sabom, Ring and Cooper, Shoulders, Kervran and Hoyle are all absent from his reference list. Hotson himself concedes NDE studies "may fall short of absolute proof".
18. Music of the Spheres 2 (IE86 pp.14-16) is a separate article with six references, none for Allais, Saxl, Hudson, Mercury/Venus/Mars figures or the satellite regressions. New data are second-hand (Kotov letter, Perry table). Specifics: the 1954 Allais claim says the sun was "almost directly overhead" at Paris, which cannot occur at latitude 48.9 N (maximum elevation about 64.5 degrees [calc]); the Hernando 10^3 T figure is an effective anisotropy field in thiol-capped gold, not a measured field around a sample, and the step to Pd and to Hudson's single atoms is Hotson's inference; Hudson is offered as confirmation of a prediction built from Hudson's own claims (circular); Hotson says he isolated "stealth atoms" from sea water himself with no procedure or data; Arata's 5 nm Pd work is asserted ("reliable excess heat and neutron bursts") with a 2003 website as the only reference, and the claim that replication failed because of particle size is Hotson's "apparently".
19. Neutron "gravitational quantum": the real experiment (Nesvizhevsky et al. 2002 [memory high, unchecked]) shows neutrons in quantized states in Earth's gravity. Hotson reads it as showing neutrons are "90% negative energy" [read: Part 2 p.22, via qe.md]. That reading is his and no calculation is offered. I did not read this passage in depth.

Claim 8: cosmological redshift is tired light; static universe; no Big Bang; quantized redshifts

(a) Mathematics: Hotson gives no mechanism equation for energy loss to the epo medium, and no stated loss rate per unit distance, so no dispersion or blurring prediction can be derived. His objection that the Doppler reading "violates conservation and the Second Law" confuses a local Doppler shift with cosmic expansion, where global energy is not conserved in GR [memory medium-high, unchecked]. Judged as an argument, it does not establish a contradiction. (b) Consistency with experiment: tired-light models are contradicted by supernova time dilation (light curves stretched by 1 + z), by the Tolman surface-brightness test, and by the CMB's thermal spectrum [web: Wikipedia Tired light]. (c) Tests: the first two were run by independent groups [memory high for existence; details not fetched]; tired light is the model that failed them. Quantized redshifts (Tifft, Arp, Guthrie and Napier) are disputed [memory medium, unchecked]. (d) If true: the CMB spectrum, SN Ia time dilation and structure growth would all need new explanations.

• Agree (my own reading, no reviewer assessed this claim): The argument has historical standing (Zwicky 1929 proposed tired light, and Nernst 1921 is the date Hotson cites) but has lost to specific observations.
• Tested / never tested / dismissed: Tested, not supported. It was not dismissed without testing.
• Final verdict (split):
• Tired-light redshift: Tested, not supported.
• "Doppler/expansion violates conservation": Internally inconsistent as stated (conflates local and global energy), not strictly refuted.
• "All versions of the Big Bang have failed every observational test": Refuted by calculation and observation (the thermal CMB spectrum alone contradicts it).
• Quantized redshifts: Never properly tested (disputed; not web-checked).
• Static universe: Tested, not supported.
• What would settle it: Already run: SN Ia light-curve widths versus z. A tired-light model with a stated loss law must predict (1 + z) stretching, which it does not.

Changed or added verdicts

Corrections to earlier arbiter statements

• (Superseded by Round 2 below: Part 2 pp.18-24 now also has a deep read.) Source-gap note above is no longer complete: pp.12-18 of Part 2, Part 1 pp.15-19, and IE86 pp.11-16 now have deep reads. Part 2 pp.18-24 does not.
• "The arbiter's Open Question on Reznik" is closed (theory).
• Any earlier mention of tau = h/(m_e c^2) from digest 26c938.03 is wrong; the 8.09e-21 s time is a separate Heisenberg "fundamental time", which Hotson says is 10 tau x 2^7 within 1 percent.

Open questions added

• Does the 160-minute solar oscillation persist in modern helioseismic data, and with what amplitude? Web check not done.
• Are Hotson's Mercury 41.24 +- 1.35, Venus 10.14 +- 1.86 and Mars 8.04 +- 2.43 residuals taken from any ephemeris paper? His text cites none.
• Do the Io shout and the 160-minute oscillation have any phase relation after a 43-minute lag, as he predicts? Needs raw data.
• Does the Part 2 pp.18-24 text hold further numbers on redshift quantization that bear on the verdict? Answered in Round 2 below: no. Hotson gives no step size, sample size or significance.

QE revision, Round 2 (Part 2 pp.18-24 deep read)

Source: the second deep read appended to deep/HotsonPart2-26c938.md (pp.18-24, full text layer re-extracted page by page, pp.19 and 21 checked as page images) [read: p.18-24]. This closes the gap I flagged in Round 1: Claim 8 no longer rests on QE's quotations and digest 26c938.03. I did no new web checks in this round. Items tagged [calc] are the deep reader's arithmetic, which I spot-checked where noted. Items tagged [memory] were not web-checked.

Headline: no verdict changes. Every Claim 8 verdict stands. The deep read sharpens the reasons for several, corrects two statements I made in Round 1, and adds five items that Round 1 did not cover (all labelled in the table below).

What the deep read found

1. Claim 8 has no quantitative content in Hotson's text [read: p.20-22]. There is no loss-per-distance law, no mechanism equation, and no prediction for supernova light-curve stretching, surface brightness, spectral blurring or the CMB spectrum. The promised BEC explanation of redshift quantization ("we will show that this can only be a BEC characteristic") is never delivered in pp.18-24. Hotson does not mention the CMB's blackbody spectrum at all [read: p.22]. This confirms that the Round 1 verdict "Tested, not supported" rests on observations [web: Wikipedia Tired light, Round 1], not on anything Hotson derived.
2. Hotson makes two separate arguments against Doppler redshift, not one [read: p.20-21]. (i) An energy-source argument: no known source could fuel millions of galaxies accelerating towards light speed, so conservation is "flagrantly" violated. (ii) A Second Law argument: "any transformation of energy must entail a loss of energy". My Round 1 reading ("confuses local and global energy") answers only (i). For (ii), the Second Law requires that total entropy not decrease. It does not require that every transmission lose energy [memory high]. So (ii) is a misuse of the law, and the Doppler reading is not contradicted by it. Argument (i) stays as I judged it in Round 1: stated, not derived, and it confuses a local shift with global energy bookkeeping in GR [memory medium-high, unchecked].
3. Redshift quantization: no figures given [read: p.21-22, p.24]. Tifft, Arp and Sulentic, Guthrie and Napier are cited with no step size, sample size or significance. Guthrie and Napier is cited second-hand through Arp 1998. Tifft's 1990 and 1991 references concern temporal variation of redshifts as well as quantization. The verdict "Never properly tested (disputed)" stands, and Hotson's text cannot support a stronger one. The 4He superfluid ring analogy has no reference. Real rings carry quantized circulation, which is not the all-or-nothing energy storing Hotson describes [memory medium].
4. The "failed every observational test" sentence extends to the Standard Model [read: p.22-23]. The phlogiston line reads "the Big Bang and the Standard Model are to the physics of the future as Phlogiston is to modern chemistry", and the p.21 pull quote calls the Standard Model "an enormity" of the same bad choice. The Standard Model's precision tests (for example the electron g-2 quoted under Claim 1) contradict that clause [memory high]. Hotson also concedes on p.23 that his own picture is "only a model ... lacking in quantitative analysis", which sits badly with "with some finality".
5. The 2 kpc gravity range is stated, not derived [read: p.22]. The only mechanism offered is that epo chains lose coherence below the 2.7 K "critical temperature" (the CMB temperature) and drop back into the BEC. There is no loss rate, coupling or chain length. Hotson says the range "should be calculable" and predicts about 2 kpc. I re-derived the illustrative factor e^(-4) x 5 = 0.0916 [calc], so Claim 3 point C is unchanged. The primer and facts must call it a prediction, not a derivation.
6. Mercury correction to Round 1 [read: p.19]. Hotson's own claim is narrower than I wrote. He gives Newcomb's residual 41.24 +- 1.35 arcsec/century against GR's 42.98, calls this "not quite within the probable error", and concedes "the Mercury anomaly is roughly explained by GR". The gap is 1.74 arcsec, about 1.3 sigma [calc], with GR above the 1890s residual. My Round 1 table compared a modern total (574.10 +- 0.65 observed vs 575.31 predicted [web]) with Newcomb's 1890s residual, which are different data sets. The right statement is that 1.3 sigma is not an anomaly and that Newcomb's residual is superseded by modern ephemerides. Verdict unchanged (Tested, not supported). Venus 10.14 +- 1.86 (5.5 sigma) and Mars 8.04 +- 2.43 (GR gives 1.35, which is 16.8 percent [calc]) come from Newcomb via Spolter 1993, a book, and I did not check them against a primary ephemeris paper. Hotson himself says magnetogravitation "does not in itself explain" Mercury, and that without a quantified wave the anomalies "can not be considered proof".
7. Hotson's self-falsification is empty [read: p.19]. "If Mercury's perihelion did not experience such an advance, it would disprove our hypothesis." A perihelion advance exists with or without the wave (GR alone gives 42.98), so this test cannot fail. A wave with nodes can produce any sign and size, which is why the anomalies are not a test.
8. Pioneer and Ulysses are internally inconsistent with his own scaling [read: p.19-20]. He says the anomalies diminish with distance from the Sun, roughly 1/r^2, and so "clearly" come from the Sun. The Pioneer pull of about 1e-10 g is roughly constant at 20-70 AU, not 1/r^2 [memory high], and a sunward pull far out contradicts the stated decay. He also says Ulysses "completely exited the solar system"; it orbited the Sun in a polar orbit [memory high]. No reference is given. The thermal-recoil resolution [web, Round 1] stands.
9. Earth period 5e-9 [read: p.19]. Hotson calls the optical-radar discrepancy "similar" to an effect of 1e-7 at Mercury. With 1/r^2 scaling, 1e-7 x 0.387^2 = 1.5e-8 [calc], about 3 times larger. That is order-of-magnitude "similar" only. The 5e-9 figure is Van Flandern's, quoted second-hand, and I did not check it.
10. Fifth force [read: p.19]. Hotson cites mine and tower gravity measurements (Stacey 1981, Holding 1984, Eckhardt and Zumberge 1988) and says density variation is implausible. He gives no magnitudes and does not say later experiments largely disfavoured a fifth force. Not testable as stated here. I have not checked the later experimental record.
11. Neutron "gravitational quantum" [read: p.21, p.24]. Closes Round 1 item 19. The source is Van Flandern's 2002 newsletter note (Meta Research Bulletin 11, 16), not the experimental paper. The figure "velocity steps of 1.7 cm/s" is that note's wording, and uniform steps of 1.7 cm/s under g = 981 cm/s^2 would need a step every 1.7 ms [calc]. The "90% negative energy" and "918 boson components" are 9180/10 = 918 from Claim 4, with no derivation in pp.18-24. Hotson himself says that if gravity were quantized this crudely "the effect would have been detected long ago". The real experiment measured quantized bound states of neutrons above a mirror, not velocity steps in free fall [memory medium, not web-checked]. His reading is therefore Not testable as stated, and it inherits Claim 4's problems.
12. Continuous creation [read: p.22]. He claims the "perfect cosmological principle" and "continuing, natural process, without a necessary beginning or end". That is a steady-state commitment, which the static-universe verdict covers.
13. Smaller points. Stellar interferometry "photon larger than a continent" is a misreading of wave-field coherence, not a physical photon size [memory medium]. The Brookes/van der Raay spellings are off ("Brooks", "van der Ray") and Severny is dated both 1966 and 1976 [read, deep reader]. The p.24 page is references only, and the phlogiston line is on p.23, not p.24. Hotson's "von Nernst predicted" story depends on a 1921 book I did not check [memory low].

Verdict table, Round 2

Corrected claim list, Round 2 changes

• Claim 3 (replace the last sentence): "...Gravity has a range of about 2 kpc, which Hotson says removes the need for dark matter. The figure is a stated prediction; no derivation is given in the paper."
• Claim 8 (replace): "Cosmological redshift is tired-light energy loss to the epo medium, which Hotson says the Second Law requires; the Doppler reading is said to violate conservation; the universe is static with continuous creation; the Big Bang and the Standard Model have 'failed every observational test'; redshifts are quantized (no step size given)."
• Extensions line, add: "Claim 6 also includes the solar-wave explanation of Mercury, Venus and Mars residuals, the Earth period discrepancy, fifth-force gravity and the Pioneer pull, all described by Hotson as qualitative. Claim 4 also includes the neutron 'gravitational quantum' (918 bosons)."
• Both lists replace facts.json wording that says the anomalies "are caused by the Sun's polarization wave" with "attributed qualitatively".

Summary table, Round 2 changes

Corrections to earlier statements, Round 2

• The Round 1 "Gap that remains" paragraph is closed: Part 2 pp.18-24 now has a deep read. No remaining gap in the three PDFs, apart from the web checks listed as open.
• Round 1 item 13 ("The Mercury GR check above contradicts him for Mercury") is too strong. See item 6 above: Hotson concedes GR roughly explains Mercury.
• Round 1 item 19 (neutron passage "not read in depth") is superseded by item 11.
• Round 1 said the Claim 8 Doppler argument "confuses local and global energy" as if that covered everything Hotson says. It covers only his energy-source argument (item 2).
• Page references: the neutron argument is on p.21, the 2 kpc and CMB material on p.22, and the phlogiston line on p.23.

Open questions, Round 2

• Do later experiments (after 1988) support or rule out the fifth-force readings Hotson cites? Not checked.
• Do primary sources (Newcomb 1897, a modern ephemeris paper) give the Venus and Mars residuals Hotson quotes via Spolter 1993? Unchecked.
• Did Nernst in 1921 actually predict energy loss from distant light? Unchecked [memory low].