========================================================================== CORE LEAKAGE -- CLUB MIXING + MASS-FLUX MODEL Anchor: Messling et al. (2025) Nature 642, 376-380 doi:10.1038/s41586-025-09003-0 This is the club's own simplified model, NOT the paper's analysis. ========================================================================== PART 0 -- THE SIGNAL, IN PLAIN UNITS ------------------------------------ Hawaiian eps100Ru excess = +0.09 +/- 0.03 (2 s.e.) ... same thing in parts per million = +9 +/- 3 ppm Single-measurement 2s reproducibility (OREAS 684) = 0.13 eps = 13 ppm -> one measurement CANNOT see this. The population mean can. Signal-to-noise on a single run = 0.69 Ru core/mantle concentration ratio = 800x (Ru leverage) W core/mantle concentration ratio = 36x (W leverage) PART A -- MIXING FRACTION f (analytic central case) ---------------------------------------------------- eps_mix=0.09, eps_core=0.25, eps_mantle=0.00, Cc=4000 ppb, Cm=5.0 ppb f_central = 7.026e-04 = 0.0703 % core by mass = 1 part in 1,423 PART A -- MONTE CARLO PROPAGATION (200,000 seeded draws) -------------------------------------------------------- draws kept = 200,000 of 200,000 (rejected 0 = 0.00% as unphysical) f (mass fraction) 7.1243e-04 [68% 4.4455e-04 - 1.2943e-03] [95% 2.9361e-04 - 2.4015e-03] f (percent core by mass) 0.07124 % [68% 0.04446 - 0.1294] [95% 0.02936 - 0.2402] Interpretation: the Hawaiian source is ~0.071% core metal, i.e. about 1 part in 1,404. The published paper puts an upper bound of <0.25% (bulk core) or <0.3% (oxide layer); our median sits comfortably inside that, which is the sanity check we wanted. PART A -- SENSITIVITY: what if the excess were smaller? ------------------------------------------------------- eps100Ru ppm f (bulk core) 1 part in 0.05 5 3.124e-04 3,201 0.07 7 4.859e-04 2,058 0.09 9 7.026e-04 1,423 0.11 11 9.812e-04 1,019 0.17 17 2.649e-03 377 (0.05 = a deliberately conservative reading of the anomaly; 0.11 = Kilauea Iki lava lake; 0.17 = Napali Member, Kauai) PART A -- SENSITIVITY: the softest number, eps100Ru of the core --------------------------------------------------------------- eps_core f (bulk core) percent 0.15 1.871e-03 0.1871% 0.20 1.022e-03 0.1022% 0.25 7.026e-04 0.0703% 0.30 5.354e-04 0.0535% 0.35 4.325e-04 0.0433% A factor of ~2.3 in the assumed core composition moves f by ~2.7x. Nobody has ever measured a piece of the core. This is the weak joint. PART B -- INDEPENDENT TUNGSTEN CROSS-CHECK ------------------------------------------ predicted mu182W -5.496 ppm [68% -9.906 - -3.384] [95% -17.99 - -2.182] Observed Hawaiian OIB mu182W ~ -5 to -12 ppm (Mundl+ 2017) Global OIB range ~ 0 to -18 ppm Fraction of our predictions landing inside the Hawaiian window: 47.5% The Ru clock and the W clock were set independently and they agree to within a factor of ~2. That agreement is the paper's real argument -- not either isotope system on its own. PART B -- INVERTED: what f would W alone demand? ------------------------------------------------ mu182W obs f from W alone ratio to Ru f -3.0 3.822e-04 0.54 -5.0 6.428e-04 0.90 -8.0 1.043e-03 1.46 -12.0 1.593e-03 2.24 -18.0 2.459e-03 3.45 PART C -- THE GOLD LEDGER (headline, conservative) -------------------------------------------------- Hawaiian magmatic volume flux Q = 0.15 km3/yr (range 0.08-0.21) erupted+intruded basalt mass 4.2747e+11 kg/yr [68% 3.4213e+11 - 5.0752e+11] [95% 2.7470e+11 - 5.7051e+11] core metal delivered 3.0051e+08 kg/yr [68% 1.7935e+08 - 5.5741e+08] [95% 1.1234e+08 - 1.0611e+09] CORE-DERIVED GOLD 158.5 kg/yr [68% 90.46 - 300.8] [95% 54.25 - 584.9] Median gold flux = 158.5 kg/yr (0.30 g/min) time per 4.0 g wedding band 13.27 minutes [68% 6.994 - 23.26] [95% 3.597 - 38.78] Median: one wedding band's worth of core gold every 13.3 minutes Equivalently 39,626 rings per year, 68% range 22,616-75,206 The core metal itself: 300,506,053 kg/yr -- a cube of iron 33.77 m on a side, every year. PART C -- CUMULATIVE OVER THE HAWAIIAN-EMPEROR CHAIN ---------------------------------------------------- gold over 85 Myr 1.3473e+10 kg [68% 7.6894e+09 - 2.5570e+10] [95% 4.6111e+09 - 4.9716e+10] gold over 85 Myr 1.3473e+07 tonnes [68% 7.6894e+06 - 2.5570e+07] [95% 4.6111e+06 - 4.9716e+07] as multiples of all gold ever mined 61.24 x [68% 34.95 - 116.2] [95% 20.96 - 226] (all gold ever mined taken as 2.2e+08 kg = ~220,000 t) CAVEAT: flux was NOT constant over 85 Myr -- Hawaiian output has grown several-fold along the chain. Treat this as an order of magnitude only. PART C -- MELT-ENRICHMENT VARIANT (generous end) ------------------------------------------------ gold if Au perfectly incompatible 1981 kg/yr [68% 1131 - 3760] [95% 678.1 - 7311] melt fraction F = 0.08; the melt scavenges 12.5x its own mass of source mantle. We do NOT quote this as the headline. Variant median: 1981 kg/yr = one band every 1.06 minutes PART C -- WHAT FRACTION OF HAWAIIAN BASALT GOLD IS CORE-DERIVED? ---------------------------------------------------------------- core share of source-rock gold 17.33 % [68% 11.57 - 27.6] [95% 7.951 - 41.45] Primitive-mantle Au taken as 1.7 ppb (Palme & O'Neill 2014). So even in the leakiest rocks on the planet, most of the gold is still ordinary mantle gold. The core signal is a minority shareholder. FIGURE DATA -- mixing curve (Figure 2) -------------------------------------- log10(f) f eps100Ru mu182W -5.00 1.000e-05 0.0020 -0.08 -4.75 1.778e-05 0.0035 -0.14 -4.50 3.162e-05 0.0062 -0.25 -4.25 5.623e-05 0.0108 -0.45 -4.00 1.000e-04 0.0185 -0.79 -3.75 1.778e-04 0.0311 -1.41 -3.50 3.162e-04 0.0505 -2.49 -3.25 5.623e-04 0.0776 -4.39 -3.00 1.000e-03 0.1112 -7.68 -2.75 1.778e-03 0.1469 -13.31 -2.50 3.162e-03 0.1793 -22.64 -2.25 5.623e-03 0.2047 -37.35 -2.00 1.000e-02 0.2225 -58.85 FIGURE DATA -- histogram of f (Figure 3), 18 bins in log10 f ------------------------------------------------------------ bin 0 log10f -4.117 to -3.976 n = 10 frac = 0.0001 bin 1 log10f -3.976 to -3.836 n = 77 frac = 0.0004 bin 2 log10f -3.836 to -3.696 n = 492 frac = 0.0025 bin 3 log10f -3.696 to -3.555 n = 3202 frac = 0.0160 bin 4 log10f -3.555 to -3.415 n = 14453 frac = 0.0723 bin 5 log10f -3.415 to -3.275 n = 37127 frac = 0.1856 bin 6 log10f -3.275 to -3.134 n = 49163 frac = 0.2458 bin 7 log10f -3.134 to -2.994 n = 41322 frac = 0.2066 bin 8 log10f -2.994 to -2.853 n = 27805 frac = 0.1390 bin 9 log10f -2.853 to -2.713 n = 15828 frac = 0.0791 bin 10 log10f -2.713 to -2.573 n = 7202 frac = 0.0360 bin 11 log10f -2.573 to -2.432 n = 2438 frac = 0.0122 bin 12 log10f -2.432 to -2.292 n = 680 frac = 0.0034 bin 13 log10f -2.292 to -2.152 n = 154 frac = 0.0008 bin 14 log10f -2.152 to -2.011 n = 36 frac = 0.0002 bin 15 log10f -2.011 to -1.871 n = 8 frac = 0.0000 bin 16 log10f -1.871 to -1.730 n = 0 frac = 0.0000 bin 17 log10f -1.730 to -1.590 n = 3 frac = 0.0000 FIGURE DATA -- measured samples (Figure 4 panel) ------------------------------------------------ sample eps100Ru 2s ppm f median Kilauea Iki lava lake, Hawai'i 0.11 0.04 11 9.81e-04 Hawaiian OIB mean 0.09 0.03 9 7.03e-04 Napali Member, Kaua'i 0.17 0.13 17 2.65e-03 Eifel peridotite (ambient mantle) 0.02 0.03 2 1.09e-04 Rhenish picrite (ambient mantle) -0.01 0.13 -1 -- HEADLINE NUMBERS FOR THE ARTICLE -------------------------------- signal : +9 ppm excess 100Ru (eps100Ru = +0.09 +/- 0.03) core mass fraction f : 0.071% (68% 0.044-0.129%; 95% 0.029-0.240%) = 1 part in : 1,404 predicted mu182W : -5.5 ppm (68% -9.9 to -3.4) core metal to surface : 300,506,053 kg/yr core-derived gold : 159 kg/yr (68% 90-301) wedding band interval : 13.3 minutes over 85 Myr : 13.47 million tonnes = 61x all gold ever mined core share of Au in the source rock: 17.3% ==========================================================================