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 | Criterion | Revelle factor | pH cost per carbon | Overall | |---|---|---|---| | Strict full sweep (DIC 1900–2300 µmol/kg) | not supported as stated (falls at DIC ≥ 2285) | not supported as stated (falls at DIC ≥ 2290) | — | | Ocean-relevant domain (DIC ≤ 2250 µmol/kg) | supported (strictly monotone, all four temperatures) | supported (strictly monotone, all four temperatures) | **supported** | The overall verdict is **supported**, with the explicit note that the strict pre-specified full-sweep criterion fails only at a chemically extreme end state (DIC ≥ 2285 µmol/kg, pH ≤ 7.42) that the ocean does not occupy. ## 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. - Revelle factor at 20 °C: **8.32** at DIC 1900, **11.94** at DIC 2100, **16.97** at DIC 2250 (top of the ocean-relevant domain) — buffering weakens strongly and monotonically everywhere the ocean is. - The RF peak sits at DIC ≈ 2285–2290 (pH ≈ 7.41–7.43, the CO₂ equivalence point where DIC ≈ TA); RF then falls to **17.30** at DIC 2300. - **Fine-step verification** (1 µmol/kg grid, central differences d = 1.0 vs d = 0.25, agreement < 1e-3 everywhere): RF at 20 °C is **17.1613** at DIC 2260, **17.3679** at DIC 2280, **17.3680** at DIC 2290 and **17.2965** at DIC 2300. The peak-and-fall is a physical feature, not a numerical artefact. - pH cost per carbon at 20 °C: **0.147 → 0.214 → 0.302** pH units per 100 µmol/kg at DIC 1900 / 2100 / 2250, then 0.307 at 2290 and 0.305 at 2300. ## What this shows and what it cannot show The claim's mechanism is reproduced over the entire ocean-relevant range: as DIC rises at fixed alkalinity, the Revelle factor more than doubles and each additional unit of carbon costs more pH. The stated *monotonic* prediction fails only past the CO₂ equivalence point (pH ≈ 7.41), where the solution becomes CO₂-dominated and buffering recovers; that regime (DIC ≥ 2285 at TA = 2300) lies beyond preindustrial (~2000–2050) and RCP8.5 end-of-century (~2150–2250) ocean states. This is a pure equilibrium computation: it tests the chemical mechanism, not an observed ocean trend, and it says nothing about uptake rates, mixed-layer dynamics, or the airborne fraction. ## 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 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 verdict turns on the domain definition.** Strict monotonicity over the full pre-specified sweep (1900–2300) fails in the last 15 µmol/kg, beyond pH 7.43. The ocean-relevant-domain criterion (DIC ≤ 2250) was added after the first run (disclosed in `hypothesis.md`), because the failing region is unreachable by any realistic ocean trajectory; the strict criterion is retained and reported alongside it. 3. **Fixed alkalinity and temperature.** The sweep holds TA = 2300 and one temperature fixed per curve; real trajectories couple DIC, TA and temperature, which can move the equivalence point. 4. **Rival explanation for any observed weakening.** If a measured water column shows a rising pH cost per carbon, changing temperature, changing alkalinity (freshwater input, calcification, nutrient effects) or the DIC/TA ratio could produce it; this computation controls all of those and so cannot attribute any real-world trend to uptake alone. ## Reproducing `python3 run.py` (pure computation, no downloads) re-derives `results.json`, `data/*.csv` and `figures/*.png`. Figures: full-sweep RF, pH vs DIC, pH cost per carbon, the ocean-relevant domain, and the fine-step zoom.
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). ## Post-run amendment (added after the first run, at the coordinator's direction) The first run found that both pre-specified criteria fail over the full sweep, because RF and |dpH/dDIC| turn down at DIC ≥ 2285 µmol/kg. Two refinements were then made, both disclosed here rather than edited into the pre-specified section: 1. **Fine-step verification.** The Revelle factor was recomputed on a 1 µmol/kg grid over DIC 2240–2310 with central differences at two step sizes (d = 1.0 and d = 0.25 µmol/kg). The turn-down is unchanged — the two step sizes agree to well under 10⁻³ everywhere — so it is a physical feature (the CO₂ equivalence point, pH = (pK1+pK2)/2 ≈ 7.41, where DIC ≈ TA), not a numerical artefact of the finite difference. 2. **Ocean-relevant domain.** The strict criterion is retained and reported, and a second criterion is added alongside it: monotonicity over DIC ≤ 2250 µmol/kg, the domain the ocean actually occupies (preindustrial surface DIC ≈ 2000–2050; RCP8.5 end-of-century ≈ 2150–2250). The overall verdict is **supported** when RF and |dpH/dDIC| rise monotonically on this domain at all four temperatures, with the explicit note that the strict full-sweep criterion fails only at the chemically extreme end state DIC ≥ 2285 (pH ≤ 7.42), beyond any realistic ocean trajectory. Both criteria, the fine-step numbers and the ocean-relevance justification are reported side by side in `results.json`.