Test 10 — Buffering decreases (Vol XXXI, ocean-acidification-buffer)
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
README.md
# Test 10 — Buffering decreases (Vol XXXI, ocean-acidification-buffer) ## Summary | Prediction | Verdict | |---|---| | Revelle factor rises monotonically with DIC at every temperature | not supported as stated | | pH change per unit carbon (per 100 µmol/kg) increases with DIC | not supported as stated | | Overall | **not supported as stated** | ## Headline numbers - Solver check (S = 35, T = 25 °C, TA = 2300, DIC = 2000 µmol/kg): pH (SWS) = **8.0558** against the canonical 8.06, pCO2 = **397.2 µatm** against 400 (error 0.7%), alkalinity residual < 10⁻⁹ µmol/kg. The solver reproduces the standard carbonate system. - Revelle factor at 20 °C (TA = 2300): **8.32** at DIC 1900, **11.94** at DIC 2100, **17.30** at DIC 2300 µmol/kg — buffering does weaken, strongly, across most of the sweep. - But RF peaks at DIC ≈ 2285–2290 (pH ≈ 7.41–7.43) and **falls** between 2290 and 2300 at every tested temperature, so the strict monotonic prediction is refuted over the full tested range. - pH cost per carbon at 20 °C: **0.147 → 0.307 → 0.305** pH units per 100 µmol/kg at DIC 1900 / 2290 / 2300. The cost doubles, then falls at the very end of the range. ## What this shows The claim's mechanism is reproduced over the whole ocean-relevant range: as DIC rises from 1900 to about 2285 µmol/kg at fixed TA = 2300, the Revelle factor more than doubles and each additional 100 µmol/kg of carbon costs more pH. The stated prediction of *monotonic* weakening fails only past the CO2 equivalence point (pH = (pK1 + pK2)/2 ≈ 7.41), where the solution becomes CO2-dominated and buffering starts to recover; as DIC grows without bound the Revelle factor tends back to 1. The tested sweep (1900–2300 µmol/kg) includes the last 15 µmol/kg of this turnaround, so the pre-specified monotonicity criterion is not met and the verdict is "not supported as stated". The refuting regime (pH below 7.43, pCO2 above roughly 1900 µatm) is one the ocean does not occupy, and the figure makes the location of the turnaround visible. ## What this cannot show This is a pure computation of the equilibrium carbonate system. It tests the claim's chemical mechanism, not an observed ocean trend; it says nothing about how fast real surface DIC is rising, about mixed-layer dynamics, or about the Revelle factor's role in the airborne fraction of emissions. ## Limitations 1. **Constant set.** K1/K2 (Lueker 2000), KSO4/KB (Dickson 1990), KF (Perez & Fraga 1987), KW (Millero 1995), K0 (Weiss 1974) and borate (Uppström 1974) carry laboratory uncertainties of a few per cent; a different accepted set (e.g. Dickson & Riley 1979 for KF) shifts the numbers slightly, though not the shape of the result. Phosphate, silicate and ammonia terms are omitted, as is standard for open-ocean check values. 2. **The refutation sits in an unreachable regime.** The verdict turns on the last 15 µmol/kg of the pre-specified sweep, beyond pH 7.43. The claim is quantitatively right everywhere the ocean actually is; a sweep capped at DIC 2280 would have returned "supported". The pre-specified criterion was strict monotonicity over 1900–2300, and it failed. 3. **Rival explanation for any observed weakening.** If a researcher measures an apparent rise in the pH cost per carbon in a real water column, rising temperature, changing alkalinity (freshwater input, calcification, nutrient effects) or the DIC/TA ratio could produce it; the computation here controls all of those, so it cannot attribute any real-world trend to uptake alone.
hypothesis.md
# Test 10 — Buffering decreases (Vol XXXI, ocean-acidification-buffer) ## Posted claim (verbatim from the notebook) > "The ocean's buffering capacity falls as it absorbs carbon, so each additional unit of uptake costs more in pH." **Prediction:** pH change per unit carbon should increase (buffering weakens). **Refutation:** constant buffering. Source: Incoprea Research library, Volume XXXI, theory entry "ocean-acidification-buffer" (posted 30 October 2026). ## Pre-specified criteria for this test Written before the computation was run. The test is a pure computation: a standard carbonate-chemistry solver (Lueker et al. 2000 K1/K2, Dickson 1990 KSO4/KB, Perez & Fraga 1987 KF, Millero 1995 KW, Weiss 1974 K0) is used to sweep dissolved inorganic carbon (DIC) at fixed total alkalinity (TA) and temperature, and the Revelle factor RF = d ln pCO2 / d ln DIC plus the pH cost per carbon (pH units per 100 µmol/kg of DIC added) are evaluated by finite differences. 1. **Solver check (gate):** at S = 35, T = 25 °C, TA = 2300 µmol/kg, DIC = 2000 µmol/kg the solver must reproduce pH ≈ 8.06 and pCO2 ≈ 400 µatm within a few per cent, otherwise the test is "not testable" (solver failure). Scale note recorded before running: the canonical check value pH = 8.06 for this TA/DIC pair (Lewis & Wallace 1998, CO2SYS program documentation) is quoted on the seawater (SWS) scale; the solver reports pH on the total, SWS and free scales, and the gate applies to the SWS value (|ΔpH| < 0.05) together with pCO2 within 5% of 400 µatm. 2. **Revelle factor:** "supported" on this prediction if RF rises monotonically with DIC at every tested temperature (0, 10, 20, 30 °C). 3. **pH cost per carbon:** "supported" if |dpH/dDIC| (pH units per 100 µmol/kg) increases with DIC at every tested temperature. Overall verdict: - **supported** — criteria 1, 2 and 3 all hold; - **partly supported** — RF rises monotonically but the pH-per-carbon cost is near constant (slope within ±10% of zero across the sweep); - **not supported** — RF is flat or falling. RF is reported at DIC = 1900 / 2100 / 2300 µmol/kg for each temperature, together with the pH per 100 µmol/kg numbers. Monotonicity is judged strictly (each successive step must rise or stay equal; no tolerance).