Brown-Paul: Step 3 Arbiter

Inputs: facts.json, claims.md, physicist.md, mathematician.md, contrarian.md. Source folder (read only): source folder: Brown-Paul. Numbers recomputed in .venv (numpy).

Tags: [read] = from the folder documents (as reported by the reviewers; I did not re-render pages); [web] = URL given; [memory] = recalled, confidence stated.

Source gap (repeated and updated)

The folder holds only two documents: the 1990 Tesla Symposium bundle (a symposium paper with a clean text layer, the front page only of US Patent 4,835,433, figure sheets, and a later CV) and a 1999 Wired news item by Charles Platt. Step 1 said the patent and figures could not be read; all three reviewers rendered the pages and found the front page and figure equations legible, so Step 1 understated what is readable. Even so: no document in the folder contains a measured power, efficiency or data table. The patent body and claims, Brown's four cited papers (1987 to 1990), his 1991 to 1993 papers, and any record of the gamma-transmutation work beyond the Wired item are not in the folder. The only quantitative performance statement in the whole project comes from the patent text on Google Patents (a [web] source, not the folder). Claims 4 and 5 rest on a news article plus [web]/[memory] physics; no Brown document describes that scheme. Where a conclusion below rests on [memory] alone, it says so.

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1. Facts the arbiter checked on the web (budget 8; 5 calls used, 1 refused for search budget)

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2. Numbers where reviewers differed, recomputed

Patent example (Claim 1). Output 23 A x 400 V = 9,200 W (taking the values as real power into a resistive load, as the patent says). Decay power, upper bound, all energy absorbed:

The three reviewers differ only in how generously they count daughters and betas. The conclusion is identical: the claimed output exceeds the available decay power by roughly seven to eight orders of magnitude (about 5e7). The radium needle dominates; the 300 g of U and Th are irrelevant. To reach 9.2 kW from 5 MeV alphas you would need 1.1e16 decays/s (about 300 kCi) [mathematician; I agree: 9200 / (5 x 1.602e-13) = 1.15e16].

Kr-85 (Claim 3). Power per curie 3.7e10 x 0.251 MeV x 1.602e-13 = 1.49 mW/Ci [recomputed]. Specific activity 392 Ci/g; 0.58 W/g (the contrarian's 0.60 W/g used 400 Ci/g, fine). Needed for 0.25 W/cm^3 at 100% conversion: 168 Ci/cm^3 = 0.43 g/cm^3. Pure Kr-85 gas at 1 atm, 0 C holds 1.49 Ci/cm^3, so about 113 atm of pure Kr-85 (ideal gas; real-gas deviations at that pressure are not modelled). Liquid Kr at about 2.4 g/cm^3 [memory] medium holds at most about 940 Ci/cm^3 = 1.40 W/cm^3 thermal. So electrical 0.25 W/cm^3 needs conversion efficiency of at least 0.25/1.40 = 17.8% (the contrarian's "at least 18%") even at liquid density of isotopically pure Kr-85; real betavoltaics reach about 10% at best [web: https://en.wikipedia.org/wiki/Betavoltaic_device]. The physicist's 1,680 Ci/cm^3 (at 10%) and the contrarian's 18% are the same fact stated two ways. Reactor krypton is not isotopically pure [memory] medium, which makes it harder.

Whole US/world Kr-85 inventory (Brown's 42 MCi). 42e6 x 1.49 mW = 62 kW total thermal power (mathematician and contrarian agree). 1 MCi/yr = 1.5 kW.

Waste-photon bill (Claim 4/5, physicist's Check E). 1 MCi Cs-137 = 5.08e25 atoms = 11.6 kg [recomputed]. At the minimum of one 9 MeV photon per nucleus and 100% photon use: 7.3e13 J = 2.0e7 kWh, i.e. 2.3 MW sustained for one year per MCi. For the physicist's illustrative 80 MCi that is about 190 MW (the 80 MCi inventory is unverified; the 9 MeV threshold is [memory] medium). Per-MCi scale is the robust form: millions of watts per megacurie per year at the floor, before any photon-efficiency loss.

Energy balance, my own tightening (Claim 5), independent of cross-sections. For one (gamma,n) event on Cs-137: beam energy in E_b >= S_n (about 8 to 12 MeV [memory] medium). Heat out = E_b - S_n (neutron leaves with its binding cost) + neutron capture elsewhere (returns about S_n, [memory] medium) + daughter Cs-136 decay (about 2.5 MeV, [memory] low) = roughly E_b + 2.5 MeV. Electricity out <= eta x (E_b + 2.5 MeV) with eta about 0.35 (thermal engine) [memory] high. For net gain you need 0.35 (E_b + 2.5) > E_b, i.e. E_b < 1.3 MeV, which is impossible because E_b >= S_n. So photon-only operation cannot make net electricity. Neither the unverified cross-section (physicist/mathematician) nor the unverified 1% pair-production fraction is needed; they only make it worse.

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3. Claim-by-claim arbitration

Claim 1. A tuned LC tank with a built-in radioactive source sustains itself and delivers net electrical power after a one-time start-up pulse (US 4,835,433)

Agree (all three): the circuit equations Brown shows (f = 1/(2 pi sqrt(LC)), R < 2 sqrt(L/C), dU/dt = -i^2 R) are correct [read: page images]; Brown's own Fig. 7 ("Beta flux >= i^2 R") is an energy budget that caps output at the decay power [read]; the patent example fails that budget by about 5e7; no independent test or replication was found; Brown's own paper admits "a frequency stability problem" and "material degradation" and shows no data [read p.3].

Disagree (weak form): physicist calls the weak form Established (betavoltaics), mathematician Plausible, untested, contrarian Never properly tested. Resolution: these describe different things. (i) Radioactive decay adding microwatts to a circuit through a junction or ionisation collector: Established (betavoltaic and alphavoltaic cells, microwatt to sub-milliwatt, single-digit efficiency) [web: https://en.wikipedia.org/wiki/Betavoltaic_device]. (ii) Brown's specific addition, that placing the source in a resonant tank improves or sustains the output: Never properly tested. It is a testable claim with no neutral controlled test on record. The mathematician's point that decays are a Poisson process uncorrelated with the tank phase (so a passive source adds noise, not a resonant drive, unless a nonlinear gating element is present) is the strongest theoretical reason to doubt any resonance benefit, and I accept it as an argument, but it is [memory]/reasoning-based, not a measurement. Hence not "Refuted".

Internally inconsistent? The mathematician notes the text mixes a fixed-power injection (decay power, Fig. 7) with a current-proportional gain ("amplified by an amount proportional to the activity" [read p.2]); these cannot both hold. I accept this as a real tension in the exposition but treat it as secondary to the energy-budget refutation.

Which argument is stronger. All reviewers' strong-form arguments reduce to energy conservation, and the patent's own sentence gives the number. The contrarian's "strongest honest case" (the paper's own market section needs only 10 to 5,000 mW, and a very high-Q tank needs little power) is fair, but milliwatts from about 0.1 mW of source is at best a microwatt-level claim, and there is no data. Where the contrarian and physicist differ on tested status: Brown and Nucell tested it themselves, unreported; INEL experts reportedly judged it without merit and the Idaho Department of Finance sued over the offering [web, secondary: https://www.deseret.com/1988/11/30/18786157/oregon-firm-is-a-step-closer-to-patenting-nuclear-battery-br-revolutionary-device-could-produce-cent/, as cited by the physicist; I did not re-open it]. What INEL actually ran is unknown. So: not dismissed without any look, and not subjected to a published neutral test.

Caveat on the patent number. The innocent reading is that "23 A at 400 V" is circulating reactive tank current (volt-amperes), not real power. The patent says "into a resistance load" [web, confirmed], so as written it is real power. A reactive-power reading would be consistent with milliwatts of real power, but is not what the patent says, and the patent gives no measurement method.

Final verdict, claim 1 (split): - Strong form (net output beyond decay power; kilowatts from a millicurie radium needle plus 300 g of U and Th): Refuted by calculation. Secondary label: Internally inconsistent (fixed-power vs current-proportional gain). - Weak form, conventional: radioisotope adds power up to its decay power through a collector: Established. - Weak form, Brown's resonant benefit at milliwatt or microwatt level: Never properly tested (not tested neutrally; not shown dismissed without testing).

Claim 2. Radiation in a current-carrying conductor "amplifies" its current in proportion to activity and lowers its resistance (Beta Voltaic Effect, Burke Cell)

Agree: all three compute the same carrier-count result and the same energy ceiling. Brown's own text says "the energy is contributed by the ion generator" and no energy comes from field, electrodes or medium [read p.2]; with 80,000 ion pairs from one Sr-90/Y-90 beta [read p.2], the whole beta energy is spent making ions (80,000 x about 25 to 30 eV = 2 to 2.4 MeV, matching Y-90's 2.28 MeV endpoint / 0.93 MeV mean [web: Y-90 page]; the mathematician's range-formula check puts it near 1.4 MeV electrons, also Y-90). All reviewers find ionisation conductivity in gases, insulators and junctions Established and a measurable resistance drop in a metal wire negligible.

Recomputed effect size. 1 Ci Sr-90 (+ Y-90, two betas per decay chain) makes about 6e15 excitations per second. With relaxation time tau, standing excess = rate x tau against 8.5e22 electrons/cm^3 [memory] high. tau = 1e-13 s [memory] medium gives about 6e2 extra carriers in 1 cm^3; fraction about 1e-20 (contrarian), 4e-19 (physicist, different wire volume), and 1e-20 (mathematician). Even tau = 1 s gives under 1e-6 (mathematician). The spread in the stated exponent comes from different wire geometries and tau, not from disagreement in method. Conclusion unchanged: not measurable in a metal wire. The only real confound the physicist adds is heating by the source (milliwatts to watts), which changes resistance far more than ionisation could.

Disagree: only on emphasis. The physicist adds "Never properly tested" next to Refuted; the contrarian adds "Internally inconsistent" for the "flux cutting / collapsing magnetic field" mechanism (Fig. 4) versus his own statement that the energy comes from ionisation work; the mathematician adds Kirchhoff's current law: in a series circuit the same current flows through battery, radioactive conductor and load, so "all of the power dissipated in the load is not drawn from the battery" [read p.2] cannot be true unless the conductor acts as its own source, which caps it at the decay power. I accept all three as compatible. Which is stronger: the carrier-count calculation, because it quantifies the effect at a factor of about 1e-20 and uses only accepted metal physics. The contrarian's honest uncertainty (if Burke cells used gas or semiconductor in the current path, a small real effect is expected) is correct and is why the weak form stays Established. The Burke patents 3,409,820 and 3,530,316 were read by only the physicist [web: https://patents.google.com/patent/US3409820A/en: no measurements, "It is not known how this amplification physically occurs"]; the contrarian and mathematician did not read them.

Tested? No data in the folder; none in Burke's patent; no independent test found. The metal-wire resistance effect is not dismissed without testing; it is excluded by arithmetic, and a bench test (four-wire resistance with a source, temperature-controlled) was apparently never published.

Final verdict, claim 2 (split): - Ionisation raises conductivity in gases, insulators, semiconductors and junctions (the weak, real form): Established. - Measurable "amplification" of current and resistance drop in a metal wire in proportion to activity: Refuted by calculation (carrier fraction about 1e-20; output capped at decay power). A direct neutral bench test was never run, but is not needed to settle the strong form. - The "flux cutting / collapsing magnetic field" explanation (Fig. 4): Internally inconsistent with Brown's own energy statement.

Claim 3. Direct conversion can reach about 0.25 W/cm^3 with Kr-85, with better efficiency and less shielding than conventional radioisotope generators

Agree: the paper says only "Preliminary data suggests that energy densities on the order of .25 watt per cubic centimeter is achievable" [read p.3]; no data; "energy density" is a misnomer for power density; the sentence names no isotope (the contrarian's correction; it follows the Kr-85 paragraph) and does not say thermal or electrical; no efficiency figure or shielding figure is given; no independent test.

Disagree: physicist and mathematician say Refuted by calculation (electrical); contrarian says Not testable as stated because the paper does not define thermal vs electrical. Resolution: the contrarian is right that the sentence is ambiguous, and Step 1's claims.md wording ("0.25 W per cm3 with Kr-85 fuel", "direct conversion of beta/alpha decay") should carry that ambiguity. But the physicist and mathematician are right that the ambiguity can be resolved by reading each way against the budget, so "Not testable as stated" is too generous for the electrical reading. Splitting by reading: - Thermal: 0.25 W/cm^3 needs 168 Ci/cm^3 (about 113 atm pure Kr-85, or 18% of liquid density). Arithmetically fine; this is a property of the isotope, not Brown's circuit and not an electrical output. - Electrical, at realistic betavoltaic efficiency (about 10% or less) from gaseous Kr-85: needs above 1,680 Ci/cm^3 (above liquid-density pure Kr-85 at 940 Ci/cm^3). Refuted by calculation for conventional conversion. - Electrical at 100% to 18% conversion from liquid pure Kr-85: not excluded by energy conservation, only by the absence of any demonstrated efficiency near that level. That residual is Never properly tested.

The 1.5 kW per MCi/yr and 62 kW for the 42 MCi inventory also show the "greenhouse effect" mitigation framing (Brown's cited 1989 title) cannot be supported on scale [calculation; Brown's 42 MCi from the paper, [read p.2-3], unchecked].

Efficiency / shielding advantage: no number given; shielding is set by the isotope's emissions (Kr-85 has a 0.43% 514 keV gamma branch [web: Kr-85 page]), not by the converter. Never properly tested (and not supported by any figure).

Final verdict, claim 3 (split): - Thermal reading (0.25 W/cm^3 from very dense pure Kr-85): Plausible, untested (arithmetic; not what a battery delivers). - Electrical reading at realistic efficiency (10% or less): Refuted by calculation. Electrical at 18% or higher with liquid pure Kr-85: Never properly tested. - "Better efficiency, less shielding than RTGs" (RTGs about 5 to 7% [memory] medium): Never properly tested. - As a single sentence with the thermal/electrical ambiguity unresolved: Not testable as stated.

Claim 4. Gamma irradiation can transmute long-lived radioactive waste into short-lived or stable species within months, for under a quarter of the DOE estimate (Wired, 1999)

Agree: the mechanism (photonuclear (gamma,n) reactions, giant dipole resonance 7 to 40 MeV [web: https://en.wikipedia.org/wiki/Giant_resonance]) is real physics; Cs-137 (gamma,n) to Cs-136 (13 d) to stable Ba-136 and Sr-90 to Sr-89 (about 50 d) to stable Y-89 are "months" cases [memory] medium to high; three named physicists in Wired (Schiffer, Park, Doolen) agree it is not far-fetched or that it could convert isotopes but is expensive [read: Wired]; Wired gives no cross-section, beam, yield, inventory or cost model; no results of the promised University of Illinois or MIT tests were found; "all waste" fails for nuclides such as Tc-99 (daughter Tc-98 is about 4 million years [memory] medium) and for transuranics.

Disagree: physicist Established in principle / Plausible, untested at scale and Refuted by calculation for the "months, $5M plant" package; mathematician Established (principle), Never properly tested (package); contrarian Plausible, untested (physics), Never properly tested ("all waste"), Not testable as stated (cost). Resolution: the three agree on the content and differ in how they label it. The strongest part of the physicist's case is the photon-energy floor (about 2.3 MW sustained per MCi per year, Check E recomputed above), which uses only the [memory] medium 9 MeV threshold and does not need the cross-section. It means that a "within months" processing of waste inventories in the MCi range needs beam power in the megawatts to hundreds of megawatts, and a $5 million plant cannot house that [accelerator costs [memory] low; not verified]. The part of the physicist's package refutation that depends on unverified inventory (80 MCi Hanford) is illustrative only. The cost-only half ("under a quarter of $150 billion", i.e. under $37.5 billion) is not excluded by energy cost alone: the physicist's own numbers give about $80 million of electricity at the 100% photon-use floor ($0.05/kWh [assumed]) and up to billions at 0.1 to 1% photon use. The mathematician's factor-100 loss from pair production rests on unverified [memory] medium cross-sections (check failed).

Contrarian's useful points kept visible: Brown's "I found no earlier proposal" is not supported; Eremeev proposed photoneutron/bremsstrahlung transmutation of Sr-90, Cs-137 and actinides in 1999 [web: https://www.osti.gov/etdeweb/biblio/20064919, via contrarian, not opened by me]; it is an active research field (laser-Compton, Gamma Factory) [web search listings, abstracts not read]. Nuclear Solutions' 2002 statement that "the fundamental mechanism works on the laboratory scale" has no data [web: https://www.power-eng.com/nuclear/nuclear-solutions-inc-regrets-loss-of-dr-paul-m-brown/, via contrarian]. Tests: the Wired claim "soon run tests" is unconfirmed; I found no source that they occurred or failed.

Tested / never tested / dismissed: Never properly tested as an engineering package; not dismissed without testing (no source shows anyone rejected it formally; apparently never funded or published); the underlying physics has small-scale and simulation studies (not Brown's).

Final verdict, claim 4 (split): - Mechanism for selected nuclides (Cs-137, Sr-90): Established as nuclear physics; Plausible, untested at waste-plant scale. - "All waste safe within months": Never properly tested, and not supported for Tc-99, I-129 and actinides [memory] medium (not web-checked). - Whole-inventory processing in months by a $5 million plant: Refuted by calculation conditional on an inventory in the MCi range and a threshold of about 8 to 12 MeV (the beam-power floor); a much smaller stream is not excluded. - Cost "under a quarter of $150 billion": Not testable as stated (no cost model; energy cost alone does not exclude it).

Claim 5. Gamma-driven transmutation heat can generate more electricity than the plant consumes, enabling a $5 million plant

Agree: photon-only operation cannot yield net electricity (all three, using slightly different arguments); Schiffer's "enormous excess heat" in Wired is the deposited beam energy, not a surplus [read: Wired]; the $5 million figure has no cost basis.

Disagree: physicist Refuted by calculation; mathematician Refuted (but warns that its conclusion rests on medium-confidence cross-sections and would weaken to Never properly tested if they were wrong) and Not testable for cost; contrarian splits off a fission-multiplication variant as Plausible, untested. Resolution: my energy balance (Section 2) shows photon-only net gain fails by conservation of energy using only S_n and a heat-engine efficiency below 1, so the mathematician's caveat does not apply. The contrarian's split is right: with photofission of actinides in a subcritical multiplying system the net energy argument is different (accelerator-driven systems with fission multiplication can in principle give net energy [memory] medium; Nuclear Solutions later described "HYPERCON ADS" [web via contrarian]), but that is a different device from the one described in Wired, no cost or yield is shown, and the cost still isn't supported ($5 million versus a gamma beam in the megawatt class [memory] low).

Final verdict, claim 5 (split): - Photon-only net electricity (as Wired describes it): Refuted by calculation (E_b >= S_n; eta below 1; also beam-generation efficiency below 1). - With fission multiplication of actinide waste: Plausible, untested as net energy; as a $5 million plant: Not testable as stated. - Never tested on record: no test, no data.

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4. Summary table of final verdicts

5. The contrarian's distinction, kept visible (tested vs never tested vs dismissed)

• Tested and failed: none. No controlled negative experiment on any Brown device appears in any source, so nothing is "Tested, not supported".
• Never properly tested: Brown's resonant benefit at low power (Claim 1 weak resonant form); the direct bench measurement of a resistance change in a source-irradiated wire (Claim 2); an electrical efficiency of 18% or more from Kr-85 (Claim 3); the engineering package for waste transmutation (Claims 4, 5). Brown's own tests exist but report no data [read p.3]; the "independent nuclear engineering firm" is unnamed and its work unreported [read p.3]; INEL experts reportedly judged it without merit [web, secondary], details unknown.
• Dismissed without testing: no source documents a dismissal without evaluation. The only adversarial record is the Idaho Department of Finance lawsuit over the stock offering [web, secondary]. No suppression or blocked-publication story was found by any reviewer; Brown published in magazines and conference talks, not refereed journals [read p.3, p.6].
• Refuted by calculation (no test needed): the strong forms of Claims 1, 2, 5, the electrical form of Claim 3, and the whole-inventory/$5M package of Claim 4. These are not experiments failing; they are accepted laws applied to the numbers (energy conservation, carrier count, beam-energy floor).
• Researcher rigour (contrarian, accepted): Brown states the right energy source (ionisation work) and the right power criterion (Fig. 7); the betavoltaic principle and photonuclear transmutation are real. Against him: unit slip (W/cm^3 as "energy density"); "amplification" language contradicting his own energy statement; no measurement table in any folder document; one patent example that fails the energy budget by about 5e7; "all sources worked" including tritium and promethium betas of tens of keV [read, as reported]; unverified CV credentials; a granted patent is not evidence of operation.

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6. Corrected claim list

(replaces claims.md where it differs)

1. A tuned LC tank circuit whose inductor core is radioactive (in the patent, alpha emitters: radium, uranium, thorium; in the 1990 paper's experiments, Sr-90 beta sources) is said to sustain and amplify oscillations and deliver net power after a start-up pulse (US 4,835,433, filed 8 Feb 1988, granted 30 May 1989, 10 claims; the patent states 23 A at 400 V into a resistance load at 86 kHz from a 1 mCi radium needle plus 200 g uranium plus 100 g thorium, with no efficiency or input power). The abstract adds that a core of a mixture of three alpha-emitting nuclides gives a greater flux of decay products than the equivalent amount of a single nuclide (QE addition). The paper's own design (Sr-90 source beside the coils) differs from the patent's radioactive core.
2. Ionizing radiation absorbed in a current-carrying conductor "amplifies" its current in proportion to source activity and lowers its resistance (the "Beta Voltaic Effect" in the "Burke Cell"; mechanisms listed in Fig. 4 include "flux cutting" and "collapsing magnetic field").
3. A power density "on the order of" 0.25 W/cm^3 is achievable ("preliminary data suggests", no data; the paper does not say thermal or electrical, nor name the isotope in that sentence, though it follows the Kr-85 paragraph), with better efficiency and less shielding than conventional radioisotope generators.
4. Gamma irradiation can transmute long-lived nuclear waste into short-lived or stable species within months at under a quarter of the DOE's $150 billion estimate (Wired, Feb 1999, Charles Platt; patent pending, company "Nuclear Solutions", tests "soon" at Illinois or MIT, DOE pilot plant under discussion). Wired says Brown "showed" waste is transformed, but no demonstration, data or publication is on record (QE). His example of waste with a 24,000-year half-life matches Pu-239.
5. The heat from that process would generate more electricity than the plant uses, allowing a plant costing about $5 million (Wired).

Other corrections to Step 1 (all confirmed by two or three reviewers): the bundle holds the patent's front page only; figure sheets are legible and contain the circuit equations; the Wired item has a byline; 0.25 W/cm^3 must not be read as "electrical with Kr-85" without caveat; CV post-dates 1990 (Aug 1992/Jan 1993 events; lists a 1991 IECEC paper "Current status and future research with resonant nuclear generators", not in folder); Moseley's 1913 beta cell is credited in the paper [read p.2]; Brown died 7 Apr 2002 [web: power-eng link above, via contrarian].

7. What would settle it

8. Open questions

1. What exactly did Brown and Nucell measure to arrive at "23 A at 400 V"? Was it circulating reactive current in the tank (volt-amperes), a transient, or a calculated value? The patent gives no method [web]. Obtaining the patent body from the USPTO and Brown's 1991 IECEC paper would help. The "75 W from a tiny Sr-90 source" figure repeated in secondary sources has no verified origin.
2. What did the Idaho National Engineering Laboratory experts actually evaluate, and what did the unnamed "independent nuclear engineering firm" test? Neither is documented in the folder.
3. Does any real, small effect exist when a radioactive source sits inside a high-Q inductor (induced noise, charging of the core, microphonics)? The Poisson-timing argument says it cannot drive the resonance coherently, but this is argument, not measurement.
4. At what electrical efficiency could a Kr-85 liquid or high-pressure cell operate? 18% from betas of 251 keV mean is a high bar; no source shows it.
5. Which fission products and actinides could a photon-only plant treat with a favourable energy ledger, and what is the real electricity cost per transmuted MCi? The inventory (e.g. 80 MCi at Hanford) and the photonuclear cross-sections (check failed here) should be pinned down at source.
6. Did the Wired-announced tests at the University of Illinois or MIT or the DOE pilot-plant negotiations ever take place? No result was found by any reviewer (absence in a search is not proof of absence).

9. Where conclusions rest on [memory] alone

Alpha energies and half-lives of Ra, U, Th; copper electron density and electron relaxation time; giant-dipole cross-section magnitudes; pair-production share; (gamma,n) thresholds of 8 to 12 MeV; RTG efficiency; liquid krypton density; Cs-136 and Sr-89 half-lives; Tc-99 daughter lifetime; accelerator cost. None of these changes the strong-form verdicts (the patent ratio is about 5e7; the carrier fraction about 1e-20; the Claim 5 energy balance holds for any E_b above 1.3 MeV). The cost half of Claim 4 and the fission-multiplication variant of Claim 5 do depend on [memory] and unverified inputs, which is why they are labelled Not testable as stated or Plausible, untested.

10. Web sources used by the arbiter

• https://patents.google.com/patent/US4835433A/en (patent quotation confirmed; no efficiency or input power given)
• https://en.wikipedia.org/wiki/Yttrium-90 (mean beta 0.9336 MeV, endpoint 2.28 MeV)
• https://en.wikipedia.org/wiki/Caesium-137 (half-life 30.04 y, 0.512 MeV beta plus 0.662 MeV gamma)
• https://en.wikipedia.org/wiki/Photodisintegration (no cross-section or S_n numbers; generic endothermic/exothermic remark)
• Check failed (search budget exhausted): giant-dipole cross-section magnitudes; Cs-137 and Sr-90 neutron separation energies; Hanford inventory; accelerator cost.
• Via reviewers (not re-opened by me): https://en.wikipedia.org/wiki/Krypton-85, https://en.wikipedia.org/wiki/Betavoltaic_device, https://en.wikipedia.org/wiki/Giant_resonance, https://patents.google.com/patent/US3409820A/en, the Deseret 1988 article, https://www.osti.gov/etdeweb/biblio/20064919, https://www.power-eng.com/nuclear/nuclear-solutions-inc-regrets-loss-of-dr-paul-m-brown/

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QE revision (after qe.md, verdict MINOR)

Inputs added: qe.md and the new deep read deep/telsasymposium1990paperbypaulbrown-74ab16.md (pp.4-5 page images, tagged [read: page image p.N]). Two web checks used (budget 8; earlier 5 plus 2 here).

New web facts. Pu-239 half-life 24,110 y [web: https://en.wikipedia.org/wiki/Plutonium-239]. Pu-238 half-life 87.7 y [web: https://en.wikipedia.org/wiki/Plutonium-238]. A (gamma,n) hit on Pu-239 gives Pu-238 [memory, high: mass number drops by one, same Z]. Photofission competition on actinides is [memory, medium], not checked.

New evidence from the deep read (all [read: page image p.4-5]). - Patent front page: Appl. 153,070, filed 8 Feb 1988, continuation of Ser. No. 855,607 of 23 Apr 1986 (abandoned), assignee Nucell Inc., granted 30 May 1989. This corrects physicist.md, which gave 22 Apr 1986; no verdict depends on it. Abstract wording confirmed verbatim, including "a mixture of three radioactive materials which decay primarily by alpha emission". - The patent's design (radioactive inductor core of three alpha emitters) differs from the paper's (an Sr-90 source beside the coils, Fig 7, Fig 11). The paper never mentions the three-nuclide core. - Fig 9 and 11 output network: a centre-tapped transformer secondary feeds a symmetric LC filter whose centre line goes to ground (not a battery). A voltmeter sits in parallel across the load; an ammeter is in series in the lower return lead. No phase measurement, wattmeter or calorimeter is drawn, and no component values appear. The 10 kV supply connects through a diode to the tank capacitor (Fig 9); in Fig 11 the start inputs are open terminals. No switches are drawn. - The only operating frequency on the sheets is "50 KHz" (Fig 8), versus 86 kHz in the patent text [web]. Fig 12 is a photo, not the economic comparison the text cites; Fig 11 is a schematic, not "actual wiring".

Changes and additions to verdicts. 1. Claim 1 (new item, patent abstract): "a mixture of three radioactive materials gives greater flux than a single nuclide": Refuted by calculation. Decay activities of independent nuclides simply add; mixing cannot exceed the sum of the separate activities. Brown's own recipe makes the point: 200 g U and 100 g Th contribute about 3.6e-6 W plus about 1e-6 to 3e-6 W against about 1.4e-4 W for the 1 mCi radium needle (Section 2 table), i.e. only a few percent (QE's figure is about 4%). Not tested on record, but no test is needed. Headline Claim 1 verdicts are unchanged. 2. Claim 4, "all waste": split. Still Never properly tested in general. For Brown's own headline example, Wired p.3 "Some waste products have half-lives of 24,000 years" [read], the match is Pu-239 (24,110 y [web]) [inference: Wired does not name the isotope]. If so, (gamma,n) gives Pu-238 (87.7 y [web]), not "safe within a few months" (a century-scale, heat-emitting nuclide), and photofission competes and creates new fission products [memory, medium]. That reading is Refuted by calculation (half-life arithmetic). This reinforces the existing note that transuranics fail. The Cs-137/Sr-90 mechanism verdicts are unchanged. 3. Claim 4 evidential status. Wired's "Brown showed that when nuclear waste is showered with gamma rays..." implies a demonstration. No data, publication or test report is on record in the folder; the same article says tests will run "soon". Treat as an unsupported assertion, not as a test. Verdict unchanged (Never properly tested). 4. Open question 1 (what produced "23 A at 400 V") updated. The paper's measurement set-up is a voltmeter across the load and an ammeter in series, after a centre-tapped LC filter, with the power also "determined by measuring the voltage drop across a resistor of known value". This is a V and A product with no phase, so a reactive volt-ampere reading of circulating or filter current remains possible; the figures do not show it was real power. Still unresolved. Note also that the patent says "into a resistance load" [web].

Smaller points recorded, no verdict change. Kr-85 as "environmentally the most acceptable" source (paper p.3) sits oddly beside the Claim 3 budget of about 113 atm of pure Kr-85 for 0.25 W/cm^3 thermal. The 1987 reference "The Moray Device and the Hubbard Coil were Nuclear Batteries" [read p.3] links Brown to free-energy lore; it is context only. The 42 MCi cited as [read p.2-3] is on p.3 only. The paper's economic claims (competitive with chemical batteries beyond two years at remote sites; 10 to 5,000 mW target) are mainstream-compatible and are not assessed.

Net effect. No headline verdict changes. Two refinements: one added Claim 1 item (mixture claim, Refuted by calculation) and a Pu-239 sub-verdict under Claim 4 "all waste".