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Audit PDE benchmark with numerical controls and reproducible figures #2

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2e0626d
Revise PDE benchmark paper with audited Kaggle figures
Hydrodynamical Oct 21, 2026
f5b6778
Add numerical controls and validity audit to research paper
Hydrodynamical Oct 21, 2026
ac126c7
Validate fixed-query recovery on 300 fresh task seeds
Hydrodynamical Oct 21, 2026
9eb8b1d
Clarify PDE formulation and measurement protocol for both audiences
Hydrodynamical Oct 21, 2026
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2 changes: 2 additions & 0 deletions .github/workflows/offline-checks.yml
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Expand Up @@ -23,5 +23,7 @@ jobs:
run: python -m pip install -r requirements.txt
- name: Test numerical core, parser, and CLI workflows
run: python -m unittest discover -s . -p 'test_*.py' -v
- name: Verify research output provenance
run: python scripts/verify_paper_artifacts.py
- name: Generate an offline example with its dashboard
run: python main_loop.py --mock --difficulty easy --seed 42 --output-dir runs/ci-smoke
54 changes: 33 additions & 21 deletions README.md
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Expand Up @@ -143,27 +143,38 @@ paths, independently of `--output-dir`.
For a reproducible experiment record, retain the JSON logs, exact command,
`git rev-parse HEAD`, and `python -m pip freeze` alongside your analysis.

## Results and evidence status

This repository contains several historical experiment artifacts with different
scopes:

- The manuscript's preliminary comparison lists **18 attempts / 15 scored runs**
across three OpenAI models, three difficulties, and seeds 42 and 137.
- Checked-in success-rate figures are labeled **180 scored runs across six
models**, with ten runs per model/difficulty combination. This is a different
design from the manuscript's proposed five-seed, two-prompt study.
- Saved Kaggle notebook outputs contain additional exploratory runs under their
own settings.

The complete per-run JSON archive behind those tables and figures is **not
bundled**, so their aggregates cannot currently be regenerated from a fresh
checkout. The manuscript's six-model, five-seed, two-prompt protocol is a proposed
expansion, not a completed result established here. Historical numerical tables
are preserved; no new provider benchmark was run for this reproducibility update.
The previous README's single-seed, 28-query example is omitted because its source
logs and exact settings are unavailable and it exceeds the current default hard
budget of 24 queries.
## Paper, figures, and archived results

The [revised manuscript](paper.pdf) analyzes the public
[Kaggle run archive, version 1](https://www.kaggle.com/datasets/jkmiller/elliptic-differential-equation-llm-reasoning/versions/1):
**180 scored runs**, six models, three difficulties, and seeds 1–10 in each cell.
All records use the standard prompt. The archive contains scored observations,
not a complete history of failed or retried attempts.

The paper's figures are regenerated from the JSON logs, including a correction
to the older strict-threshold chart: GPT-5.4 mini has **2/10** hard successes at
**total absolute coefficient error below 0.01**. This metric is distinct from
function error evaluated on a spatial grid.

[Reproduction instructions](paper_artifacts/README.md) include the pinned source
URL, archive checksum, figure script, and derived summary. Reproducing these
figures requires no new model calls. Historical provider responses cannot be
recreated exactly from the archive because complete settings and source
revisions were not recorded.

The research revision adds fixed and randomized numerical controls, paired
statistical comparisons, joint-matrix spectra, and precision/refinement audits.
Fixed sine queries recover all 30 reconstructed tasks at the strict threshold
using the minimum permitted solve budget. This limits claims of a benefit from
adaptive language-model measurement selection on these instances. A separate
300-task fresh-seed validation reports both strong fixed-policy recovery and
failures from zero excitation and numerical sensitivity; the paper keeps those
results distinct from the archive.

The earlier three-model, two-seed pilot tables are retained separately in
`paper_artifacts/legacy_pilot_tables.tex`. Their source logs have not been recovered, and they are not
pooled with the six-model study. Saved Kaggle notebooks contain further
exploratory outputs under their own settings.

## Repository guide

Expand All @@ -177,4 +188,5 @@ budget of 24 queries.
| `replot.py`, `plot_*.py`, `verify_metacognition.py` | Analysis of saved run logs |
| [kaggle-benchmark.ipynb](kaggle-benchmark.ipynb), [kaggle.ipynb](kaggle.ipynb) | Kaggle-specific exploratory notebooks; require their own Kaggle environment |
| `test_basis.py`, `test_weak_form.py`, `test_parser.py`, `test_cli.py`, `test_sweep.py` | Offline numerical, protocol, and workflow tests |
| [scripts/reproduce_paper_figures.py](scripts/reproduce_paper_figures.py), [paper_artifacts/](paper_artifacts/) | Reproduce the paper figures and audit the archived study |
| [archive/](archive/) | Historical demos and earlier interfaces; outside the supported quick start |
79 changes: 79 additions & 0 deletions algorithm.sty
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% ALGORITHM STYLE -- Released 8 April 1996
% for LaTeX-2e
% Copyright -- 1994 Peter Williams
% E-mail Peter.Williams@dsto.defence.gov.au
\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{algorithm}
\typeout{Document Style `algorithm' - floating environment}

\RequirePackage{float}
\RequirePackage{ifthen}
\newcommand{\ALG@within}{nothing}
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\newcommand{\ALG@floatstyle}{ruled}
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% Declare Options
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}
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}
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\renewcommand{\ALG@floatstyle}{boxed}
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% then numbering convention
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\renewcommand{\ALG@within}{part}
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}
\DeclareOption{chapter}{
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}
\DeclareOption{section}{
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}
\DeclareOption{subsubsection}{
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\setboolean{ALG@within}{true}
}
\DeclareOption{nothing}{
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\DeclareOption*{\edef\ALG@name{\CurrentOption}}

% ALGORITHM
%
\ProcessOptions
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\ifthenelse{\equal{\ALG@within}{part}}
{\newfloat{algorithm}{htbp}{loa}[part]}{}
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\newcommand{\listofalgorithms}{\listof{algorithm}{\listalgorithmname}}

201 changes: 201 additions & 0 deletions algorithmic.sty
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% ALGORITHMIC STYLE -- Released 8 APRIL 1996
% for LaTeX version 2e
% Copyright -- 1994 Peter Williams
% E-mail PeterWilliams@dsto.defence.gov.au
%
% Modified by Alex Smola (08/2000)
% E-mail Alex.Smola@anu.edu.au
%
\NeedsTeXFormat{LaTeX2e}
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%
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%
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%
\ProcessOptions
%
% ALGORITHMIC
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\newcommand{\algorithmicendloop}{\algorithmicend\ \algorithmicloop}
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%changed by alex smola
\newcommand{\algorithmicinput}{\textbf{input}}
\newcommand{\algorithmicoutput}{\textbf{output}}
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%end changed by alex smola

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%changes by alex smola
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%end changes by alex smola
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%changed by alex smola
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%end changed by alex smola
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\leftmargin\labelwidth \addtolength{\leftmargin}{\labelsep}
\ALC@tlm\labelsep
}
}
{\end{list}}














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