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arxiv: 2606.04114 · v1 · pith:ACPLCAVTnew · submitted 2026-06-02 · 📊 stat.ME

Global Warming Has Been Accelerating Since At Least 1990

J. Eduardo Vera-Valdes This is my paper

Pith reviewed 2026-06-28 08:37 UTC · model grok-4.3

classification 📊 stat.ME
keywords global temperatureaccelerationsupralinear trendlinearithmic modelstructural breakstrend analysisclimate statistics
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The pith

A linearithmic model detects supralinear acceleration in global temperatures since at least 1990.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests whether global temperature increases have been supralinear, meaning faster than linear over time. It introduces a linearithmic statistical framework to detect this acceleration. Results show significant evidence for acceleration beginning no later than 1990, becoming more pronounced with newer data. In comparison, quadratic specifications only detect significance over the longest periods examined. The work also demonstrates that supralinear trends can produce apparent slope changes in linear models, accounting for reported structural breaks.

Core claim

We develop a statistical framework using a linearithmic specification to test for supralinear trends in global temperature. Our results provide evidence of acceleration since at least 1990, with the significance increasing as more recent data are added. Evidence under a quadratic model is significant only for the longest window. If the true trend is supralinear, standard break-point tests will detect changes in the slope of a linear trend model.

What carries the argument

The linearithmic specification, a model that combines linear and logarithmic components to identify supralinear acceleration in time series data.

If this is right

  • Standard linear trend models may show spurious breaks when the underlying trend is actually supralinear.
  • Evidence of acceleration strengthens as the estimation window includes more recent observations.
  • Quadratic specifications detect acceleration only over the longest available periods.
  • Reported structural breaks in global temperature may arise from fitting linear models to supralinear data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the linearithmic model holds, temperature projections based on linear trends will increasingly underestimate future values.
  • The same testing approach could be applied to other climate time series to check for consistent supralinear patterns.
  • Longer historical reconstructions might allow the quadratic model to show significance over additional windows.

Load-bearing premise

The linearithmic specification is an appropriate and correctly specified model for detecting genuine supralinear acceleration without being driven by data artifacts or model misspecification.

What would settle it

Finding that the statistical significance of acceleration does not increase when including data after the most recent observation in the study, or detecting systematic misspecification patterns in the linearithmic model residuals.

read the original abstract

We investigate acceleration in global temperature, defining acceleration as a supralinear (greater-than-linear) increase over time. We develop a statistical framework to test for supralinear trends using a linearithmic specification. Our results indicate evidence of acceleration in global temperature since at least 1990, with significance strengthening as more recent data are included. In contrast, evidence for acceleration under a quadratic specification is significant only in the longest estimation window. We also show that, if the true temperature trend is supralinear, standard break-point tests will eventually detect changes in the slope of a linear trend model, which may explain reported structural breaks in global temperature trends.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper develops a statistical framework using a linearithmic specification to test for supralinear (greater-than-linear) trends in global temperature records. It reports evidence of acceleration since at least 1990, with statistical significance strengthening as more recent data windows are used. Results are contrasted with a quadratic specification (significant only in the longest window), and the authors argue that a true supralinear trend would cause standard break-point tests to detect slope changes in linear models, potentially explaining reported structural breaks.

Significance. If the linearithmic specification is shown to be robust and not an artifact of functional form or serial correlation, the work would offer a methodological contribution to trend testing in climate data and a possible reconciliation with prior break-point findings. The explicit comparison to quadratic models usefully illustrates specification sensitivity.

major comments (2)
  1. [Abstract / statistical framework] Abstract / statistical framework description: The central claim that the linearithmic model detects genuine supralinear acceleration since 1990 requires that the specification is not driven by unmodeled autocorrelation or functional-form artifacts in temperature series. No derivation or simulation evidence is referenced showing that the supralinear coefficient test statistic remains correctly sized under linear-plus-AR(1) noise, which is load-bearing for interpreting the reported strengthening significance with recent windows.
  2. [Abstract / results on significance strengthening] Abstract / results on significance strengthening: The finding that evidence strengthens with more recent data is presented as support for acceleration, but without explicit checks (e.g., against alternative trend forms or pre-whitening) that the linearithmic form is minimal or correctly specified for supralinear detection, the contrast with the quadratic result alone does not establish that the acceleration signal is robust rather than specification-dependent.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief statement of the exact functional form of the linearithmic specification and the data source(s) used for the temperature series.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major point below and will revise the manuscript to incorporate additional validation and robustness checks.

read point-by-point responses

  1. Referee: [Abstract / statistical framework] Abstract / statistical framework description: The central claim that the linearithmic model detects genuine supralinear acceleration since 1990 requires that the specification is not driven by unmodeled autocorrelation or functional-form artifacts in temperature series. No derivation or simulation evidence is referenced showing that the supralinear coefficient test statistic remains correctly sized under linear-plus-AR(1) noise, which is load-bearing for interpreting the reported strengthening significance with recent windows.

    Authors: We agree that explicit validation of the test statistic's size under AR(1) errors would strengthen the framework. Although the current manuscript emphasizes the empirical application, we will add Monte Carlo simulations in a revised methods section demonstrating that the supralinear coefficient test maintains correct size under linear trends plus AR(1) noise. This directly addresses potential concerns about serial correlation artifacts. revision: yes

  2. Referee: [Abstract / results on significance strengthening] Abstract / results on significance strengthening: The finding that evidence strengthens with more recent data is presented as support for acceleration, but without explicit checks (e.g., against alternative trend forms or pre-whitening) that the linearithmic form is minimal or correctly specified for supralinear detection, the contrast with the quadratic result alone does not establish that the acceleration signal is robust rather than specification-dependent.

    Authors: The reported strengthening of significance with recent windows is consistent with a supralinear process, and the quadratic contrast illustrates specification sensitivity. To further establish robustness, we will add pre-whitening procedures and comparisons to additional trend specifications in the revised results section. These checks will confirm that the acceleration signal is not an artifact of the linearithmic choice alone. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical application of new specification to data

full rationale

The paper defines acceleration explicitly as supralinear trend, introduces a linearithmic specification as the testing framework, and reports empirical results on temperature series with comparisons to quadratic alternatives. No load-bearing step reduces the acceleration claim to a fitted parameter by construction, self-citation chain, or imported uniqueness theorem; the central findings rest on applying the model to external data rather than tautological re-expression of inputs. This is the standard case of a self-contained statistical analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on the abstract alone, the central claim rests on the appropriateness of the linearithmic specification and the statistical properties of the temperature series; no explicit free parameters, axioms, or invented entities are described.

pith-pipeline@v0.9.1-grok · 5628 in / 1042 out tokens · 27917 ms · 2026-06-28T08:37:59.439341+00:00 · methodology

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Reference graph

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