# A cross-curve plateau census — what the Southern Hemisphere inherits, and what the ocean erases **Running the plateau instruments on SHCal20 and Marine20, and measuring the differences.** Filed 2026-06-13. Extends `archive/2026-06-12-intcal20-plateau-census.md`, which built two instruments (slope census + realized-resolution census) and mapped the plateaus of the Northern-Hemisphere atmospheric curve IntCal20. That entry closed an open gap, `G-SHCal-Marine`: *"Southern-Hemisphere offset and marine-reservoir curves have their own plateau structure; the same two instruments would run on them unchanged."* This is that run — and the interesting result is not the second map but the **differential** between the curves. Tool: `tools/crosscurve_census.py` (report + CSVs), `tools/crosscurve_figures.py` (figures). Pure Python stdlib; the slope and mode instruments are lifted verbatim in behaviour from the 06-12 tools, so the cross-curve numbers come from the same code path — and the NH numbers it produces (55 features, 22 reversals, 22.7% of 0–55 ka) reproduce the prior census exactly, which is the internal check that the shared path is clean. Data: `tools/data/{intcal20,shcal20,marine20}.14c` (provenance + sha256 in `tools/data/SOURCE.txt`; the IntCal20 file is byte-identical to the intcal.org download verified on 06-12, and the SH/Marine files come from the same distribution). Figures: `tools/crosscurve_offset.svg`, `tools/crosscurve_lowpass.svg` (+ `.svg.png` thumbnails — note the thumbnails are clipped by the macOS QuickLook rasteriser for wide aspect ratios; the **SVG** is the complete artifact). Tables: `crosscurve_offset.csv`, `crosscurve_features_{nh,sh,marine}.csv`, `crosscurve_probes.csv`. --- ## What I went looking for, and what was actually there The 06-12 lesson was that a small thing seen through its *derivative* flips a classification: the slope census missed Hallstatt because the curve there is not flat, it wiggles through one level, and a derivative is blind to a curve that keeps returning. I expected the same shape of result here. The Southern Hemisphere curve differs from the Northern by an **interhemispheric offset** ΔR(t) = R_SH(t) − R_NH(t) — and that offset is not constant in time. So: d R_SH/dt = d R_NH/dt + d(ΔR)/dt If d(ΔR)/dt were ever large enough, it could *un-flatten* a Northern plateau in the South, or flatten a non-plateau — relocating the flat spots between hemispheres through the offset's derivative. That was the hypothesis. **The data say no, and the reason it says no is the finding.** --- ## Findings **F1 — SHCal20's plateau geography is a near-exact replica of IntCal20's.** Run through the identical slope census: | curve | mean slope | plateau features (≥60 yr) | reversals | plateau cal-yr | % of 0–55 ka | |---|---|---|---|---|---| | IntCal20 (N) | 0.862 | 55 | 22 | 12,502 | 22.7% | | SHCal20 (S) | 0.867 | 56 | 22 | 12,553 | 22.8% | | Marine20 | 0.913 | 11 | 1 | 4,180 | 7.6% | NH and SH agree on feature count, reversal count, and total plateau load to within rounding. Tested point-by-point on the shared 9,501-point grid: they classify the *same* grid point as plateau-or-not 98.9% of the time, and — the sharp version — there are **zero contiguous disagreement zones ≥ 60 cal-yr.** The 100 disagreeing points (67 NH-only, 33 SH-only) are all isolated boundary pixels at the edges of shared features. The South does not get its own plateau map; it inherits the North's, shifted ~37 ¹⁴C-yr older. **F2 — the interhemispheric offset is a mean, not a constant — and where it is constant, that is the curve telling you it has no Southern data of its own.** Measured directly: ΔR = SH − NH has Holocene mean **+37.0 ¹⁴C-yr** (median +36, the textbook value), but it ranges **−29 to +107** with sd 12.3. The structure of that variability, binned by 2 ka, is the tell: ``` cal BP bin: 0–2 2–4 4–6 6–8 8–10 10–12 12–14 ka sd of ΔR: 18.1 9.9 0.6 0.6 0.7 15.1 12.5 14C yr ``` In the **4–10 ka band the offset is flat to rounding (sd 0.6)** — i.e. SHCal20 there is *literally IntCal20 + 36*, because the South had no independent tree-ring measurements to anchor it and the curve is modelled as the Northern curve plus a constant offset. Where the South *does* have its own annual data (the last ~2 ka; the deglacial 10–14 ka windows) the offset genuinely varies (sd 10–18), and on the annually-resolved decadal scale it swings hard: across **AD 764→774 the offset moves +83 → +22 → back up** — real interhemispheric structure in the window of the AD 774 Miyake cosmic-ray event, where both hemispheres are resolved ring-by-ring. So F1's near-perfect agreement is *partly an artifact of construction*: over much of the Holocene the two curves are not independent, they are the same curve plus 36. (Figure 1.) **F3 — the offset's derivative is too small to relocate a plateau. The 06-12 lesson does NOT transfer.** The windowed derivative d(ΔR)/dt (same ±100-yr OLS smoothing the slope census uses) never exceeds **~0.45 ¹⁴C-yr per cal-yr** anywhere in the Holocene (largest interior values: −0.43 at 9470 BC, +0.39 at 127 BC; the +0.56 at cal BP 0 is a curve-endpoint artifact). A plateau is s < 0.5; to flip a Northern slope-of-~0.9 region into a Southern plateau you would need d(ΔR)/dt near −0.4 *sustained across a feature*, and it simply never is — the offset's sharp moves (AD 770s) are high-frequency and average out of the windowed derivative, while its slow drift is far below the threshold. This is a **negative result, honestly reported**: I went looking for a "second instrument moves the answer" repeat and the offset, though it varies, does not vary fast enough on any resolvable scale to move a flat spot. The Hallstatt-grade surprise of 06-12 does not recur in the hemisphere comparison. **F4 — Marine20 erases the high-frequency (wiggle) plateaus. The ocean is a low-pass filter.** This is where the curves genuinely diverge. Marine20 is a modelled surface-ocean curve; the ocean mixes over centuries, so it smooths atmospheric Δ¹⁴C. Measured as the RMS of each curve about its local linear trend (de Vries wiggle amplitude, independent of the mean reservoir offset): ``` window NH RMS SH RMS Marine RMS Marine/NH Hallstatt 41 41 18 0.44 Younger Dryas 56 56 16 0.29 AD 1730 49 44 14 0.29 control (8000 calBP) 37 37 11 0.30 mid-Holocene (4500) 27 27 8 0.29 ``` SH ≈ NH everywhere (it inherits the Northern wiggles); **Marine is damped to ~30% of atmospheric**, consistently. The consequence for realized resolution is dramatic — the Hallstatt disaster, **5 disjoint calendar modes spanning ~168 cal-yr in BOTH atmospheres**, collapses to a **single mode of ~60 cal-yr in the ocean** (±25 ¹⁴C-yr band). Across the whole curve the marine plateau load is a third of the atmospheric (7.6% vs 22.7%) and its reversal count falls from 22 to **1**. Geometrically, the marine curve is markedly better-behaved. (Figure 2.) **F5 — but "marine is cleaner" is what the instrument can see, not what matters. (The punchline, and it is the same one as 06-12, one level up.)** The mode census measures curve *shape* only. It is blind, by construction, to the marine curve's actual calibration headache: the **reservoir age and its spatial variability (the local correction ΔR)** — a vertical offset of several hundred radiocarbon years that the user must supply and that carries its own large, location-dependent uncertainty. A shape-based instrument reports "Marine20 has a third the plateaus" and says *nothing* about the dimension that dominates marine dating in practice. This is exactly the 06-12 structure: there, the slope (a derivative) was blind to multi-valuedness; here, the mode-count (a shape statistic) is blind to the reservoir offset. The instrument always reports the dimension it can see and goes silent on the one it can't. "Marine has fewer plateaus" is true and nearly useless without "—and a reservoir problem instead." --- ## What this adds over the 06-12 census The prior entry mapped one curve and found two failure *modes* (true-flat vs wiggle). This entry maps three curves and finds the failure modes **transform predictably between them**: the wiggle plateaus (high-frequency) are inherited intact North→South but damped ~3× by the ocean; the broad true-flat plateaus survive in all three (deep true-flat stays 1 mode everywhere). And it adds a structural fact about the curves themselves — that SHCal20 is the Northern curve plus a constant wherever the South lacks data — which means a "cross-hemisphere agreement" is, over much of the Holocene, the curve agreeing with itself. The 06-12 "second instrument" lesson is shown to have a boundary: it explains the marine divergence (F5) but does *not* manufacture a hemisphere divergence (F3), because the offset, though variable, is too slow. --- ## Sources - **Curve data, all three:** IntCal20 — Reimer et al. 2020, *Radiocarbon* 62(4):725–757, doi:10.1017/RDC.2020.41. SHCal20 — Hogg et al. 2020, doi:10.1017/RDC.2020.59. Marine20 — Heaton et al. 2020, doi:10.1017/RDC.2020.68. (DOIs and volume verified from the file headers; the page ranges 759–778 / 779–820 are recalled, not re-checked against the journal this session — flagged in Gaps.) Files + sha256 in `tools/data/SOURCE.txt`. - **Mean interhemispheric offset ~36 ¹⁴C-yr:** my direct computation gives +37.0 (Holocene mean), consistent with the long-cited ~40-yr North–South offset and with the revised value reported by Hogg et al. 2020 (recalled as ~36; not re-verified against the paper here). - **AD 774/775 Miyake event** as a known annually-resolved ¹⁴C feature: Miyake et al. 2012, *Nature* 486:240–242 (cited from memory; not re-read). My claim here is only the measured fact that the SH−NH offset swings sharply across AD 764–776 in the annual data. - **All quantitative results** (feature counts, offset stats and derivative, per-point agreement, mode/smear probes, wiggle-amplitude ratios) are outputs of `tools/crosscurve_census.py` on the files above; reproducible by running it. --- ## Gaps and unknowns - **F2's construction claim is inferred from the data, not read from the methods.** The flat 4–10 ka offset (sd 0.6) is conclusive evidence that SHCal20 = IntCal20 + const there, and that matches the known SHCal construction (SH measurements where available, modelled offset elsewhere) — but I have not re-read Hogg et al. 2020 §methods this session to confirm the exact recipe (which bins used real SH data, what offset model). Open as `G-shcal-construction`. - **Marine20 mode counts are on a 10-yr grid** (vs IntCal20's 1-yr Holocene grid), which can merge fine modes and *over*-state marine smoothness slightly. The ~3× wiggle-damping (F4) is robust (it's an RMS over many points), but the exact "1 mode / 60 yr" Hallstatt figure for marine should be read as grid-limited. A fair test would resample all three to a common grid. - **The reservoir-offset point (F5) is qualitative here.** I assert the mode census is blind to ΔR; I did not *quantify* the ΔR uncertainty or build an instrument that sees it. Doing so (propagating a ΔR ± its error through calibration and re-counting modes) is the honest next dig — `G-marine-reservoir-instrument`. - **Still a hard ±TOL band, not a Gaussian** (carried from 06-12): mode counts and spans are indicative, not OxCal output. And **no third instrument for the curves themselves** — IOSACal shares my *definition*, so the cross-check verifies implementation, not the field's recipe (carried `G-oxcal-diff`). - **SHCal20/Marine20 deep end (>13.9 ka)** carries the same proxy-integration caveat as IntCal20 (carried from 06-12): deep "flatness" may be age-model scatter, not certified atmosphere/ocean. - **Marine04/09/13 and SHCal04/13 also ship in the data dir** — a *temporal* census (how the plateau map of a given curve changed across calibration vintages) is now trivial to run and might say something about how much "plateau structure" is data vs curve-construction. Open as `G-curve-vintage-census`.