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This case was judged by an anonymized AI reviewer and has not been independently reviewed by people; inspect the draft, cards, and both outputs to assess it.
AutocompleteWithout cards better229 / 280 · beu-ebb78bc0b0b902b2

State Estimation of the Stefan PDE: A Tutorial on Design and Applications to Polar Ice and Batteries

Climate and environmental science · 2111.11617v1

FLOWING EVIDENCE BENCHMARK

How do we compare writing with and without cards?

At the same writing position, the same model produces one first result with cards and one without. All 280 pairs enter the overall anonymized review, which assesses whether a decision not to continue fits the draft.

Overall: 138 with-card wins, 26 ties, 107 no-card wins, 5 pairs where neither was usable, and 4 inconclusive judgments. Both sides wrote text in 218 pairs; 48 had a deliberate stop and 14 included an invalid output.

SAME DRAFT · WITH OR WITHOUT CARDS

01 · FIXED WRITING POSITION

MANUSCRIPT

Same writing position ▌

Matched autocomplete at the same draft position

02 · TWO MATCHED VERSIONS

SHARED BY BOTH

Draft, writing task, and generation model

A · With cards

Relevant literature cards supplied

B · Without cards

No literature cards supplied

Generation model

Same model and version

A → first output

B → first output

Anonymized AI judge

First outputs are anonymized as X and Y

Continuation review: accuracy, fit to the writing task and usability
Returns: X preferred / tie / Y preferred / both unusable

Review again with the answer order swapped

HOW DOES BLIND JUDGING WORK?

① Anonymize both outputs
The AI judge sees the same draft and both first outputs without knowing which received cards.

② Compare and swap order
The judge applies task-specific criteria in X/Y and then Y/X order.

③ Review disagreements
A third pass resolves disagreements. Incomplete reviews remain in the denominator.

How are positions and cards selected?

We selected 40 writing positions in each of seven fields, for 280 comparisons. The position and relevant literature cards were set before each comparison, so both versions began from the same draft.

The main result retains every frozen position, including places where cards might not add a useful next move. This avoids selecting cases based on their outputs, but 49% describes the whole cohort, not a win rate where evidence clearly had an opportunity to help. This cohort did not record that opportunity label for each position before generation, so those two groups cannot yet be separated reliably.

CARD USE · 140/280

Reported card use in continuations with text

The model reports whether a card affected its continuation. In 140 of 280 tests it produced continuation text and reported card use. The previous count of 150 included 10 cases without continuation text and has been corrected.

COMPARISON · 70 / 7 / 30

Which written version was better?

Of the 107 reported-use cases where both versions produced text, the blinded AI judge preferred the with-card version 70 times, found 7 about the same, and preferred the without-card version 30 times.

How are the two table percentages calculated?

ADOPTION COVERAGE

140reported use with text
÷
280all positions
=
50%

WITH-CARD VERSION PREFERRED

70with cards better
÷
107comparable tests
=
65%

The percentages use different groups: 50% counts continuations with text reporting card use among all 280 tests; 65% covers the 107 such cases with text on both sides. The generating model reports card use, while an anonymized AI judge compares writing quality.

Card use is self-reported by the generator. The anonymized AI judge sees the draft and source snippets, so source-aware preference remains possible; there was no independent human review. The overall result describes these 280 frozen positions, not a win probability for any writing task.

Manuscript writing position

Text excerpt · not a PDF page

Research manuscript · excerpt

State Estimation of the Stefan PDE: A Tutorial on Design and Applications to Polar Ice and Batteries

1 Introduction > 1.2 Stefan model

…er in a hot environment. Conversely, water freezes into ice in a cold environment. These liquid-solid change phenomena are called " phase changes." In addition to various quotidian settings, they also arise, for example, in sea ice in the polar regions Maykut and Untersteiner (1971) , solidification of molten metal in casting Meng and Thomas (2003) , extrusion in polymer 3D-printing Valkenaers et al. (2013) , laser sintering for metal 3D-printing Agarwala et al. (1995) , cryosurgery for cancer treatment Rabin and Shitzer (1998) , thermal energy storage in buildings Sharma et al. (2009) , etc.

…d the consequent movement of the domain’s boundary, can be seen in some non-thermal chemical, biological, and social dynamics such as tumor growth in a patient’s body Spangler et al. (2016) , axonal elongation for neurons’ signal transmission Diehl et al. (2014) ; Demir et al. (2021) , lithiated region in electrodes of lithium-ion batteries Thomas et al. (2002) , crystallization process Braatz (2002) ; Nagy and Braatz (2012) ; Fujiwara et al. (2005) , domain walls in ferroelectric nanomaterials McGilly et al. (2015) , spreading of invasive species to a new environment Du and Lin (2010) , etc.

↓ Next paragraph was generated here

The highlighted text is near the writing position. This is a layout of the evaluation input, not a PDF screenshot.

A matched comparison at the same writing positionOverall AI review: Without cards better

Both arms use the same model, task and manuscript context. Only the retrieved passages differ. The first recorded output from each arm is shown below.

Read overall AI review rationale

A = with cards · B = without cards

Both outputs provide coherent, accurate continuations that bridge from the concrete examples to the mathematical framework. However, Output B is preferable for several reasons. First, Output B better matches the rhetorical arc of the draft: the manuscript has just listed diverse applications (thermal, chemical, biological, social) and needs to transition to their common mathematical structure. Output B explicitly notes the 'classical Stefan problem' and provides historical grounding with 'Josef Stefan's late nineteenth-century work on ice formation,' which elegantly echoes back to the opening examples of water/ice phase change—creating a satisfying circular structure. Output A jumps directly to the mathematical formulation without this connective tissue. Second, Output B's 'traces back to' better signals the transition from examples to theory than Output A's 'A common mathematical idealization.' Third, both outputs are factually accurate (Stefan did indeed formulate this in the late 19th century), but Output B's specificity about 'Josef Stefan' and 'ice formation' is more precise and better anchored to the draft's opening. The scope is also more appropriate: Output B introduces the name and history, which sets up subsequent mathematical detail, whereas Output A front-loads the full mathematical description (heat equation, Stefan condition) in a single sentence that feels slightly compressed for a first mention.

Evidence

Same model and position · retrieved passages supplied · first output

Not preferred in this comparison

A common mathematical idealization of such moving-boundary phenomena is the Stefan problem, in which the temperature field evolves by the heat equation on either side of the interface and the interface itself moves according to a latent-heat balance known as the Stefan condition.

Passages supplied to the Evidence version

Card 1 · Spreading in a shifting environment modeled by the diffusive logistic equation with a free boundary

We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is homogeneous and favourable, this model was first studied in Du and Lin \cite{DL}, where a spreading-va…

Read full passage excerpt

We investigate the influence of a shifting environment on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is homogeneous and favourable, this model was first studied in Du and Lin \cite{DL}, where a spreading-vanishing dichotomy was established for the long-time dynamics of the species, and when spreading happens, it was shown that the species invades the new territory at some uniquely determined asymptotic speed $c_0>0$. Here we consider the situation that part of such an environment becomes unfavourable, and the unfavourable range of the environment moves into the favourable part with speed $c>0$. We prove that when $c\geq c_0$, the species always dies out in the long-run, but when $00$ a parameter, then there exists $σ_0>0$ such that vanishing happens when $σ\in (0,σ_0)$, borderline spreading happens when $σ=σ_0$, and spreading happens when $σ>σ_0$.

Card 2 · Logistic type attraction-repulsion chemotaxis systems with a free boundary or unbounded boundary. I. Asymptotic dynamics in fixed unbounded domain

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of…

Read full passage excerpt

The current series of research papers is to investigate the asymptotic dynamics in logistic type chemotaxis models in one space dimension with a free boundary or an unbounded boundary. Such a model with a free boundary describes the spreading of a new or invasive species subject to the influence of some chemical substances in an environment with a free boundary representing the spreading front. In this first part of the series, we investigate the dynamical behaviors of logistic type chemotaxis models on the half line $\mathbb{R}^+$, which are formally corresponding limit systems of the free boundary problems. In the second of the series, we will establish the spreading-vanishing dichotomy in chemoattraction-repulsion systems with a free boundary as well as with double free boundaries.

Card 3 · The diffusive competition problem with a free boundary in heterogeneous time-periodic environment

In this paper, we consider the diffusive competition problem with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and g…

Read full passage excerpt

In this paper, we consider the diffusive competition problem with a free boundary and sign-changing intrinsic growth rate in heterogeneous time-periodic environment, consisting of an invasive species with density $u$ and a native species with density $v$. We assume that $v$ undergoes diffusion and growth in $R^{N}$ , and $u$ exists initially in a ball $B_{h_0}(0)$, but invades into the environment with spreading front $\{r = h(t)\}$. The effect of the dispersal rate $d_1$, the initial occupying habitat $h_0$, the initial density $u_0$ of invasive species $u$, and the parameter $μ$ (see (1.3)) on the dynamics of this free boundary problem are studied. A spreading-vanishing dichotomy is obtained and some sufficient conditions for the invasive species spreading and vanishing are provided. Moreover, when spreading of $u$ happens, some rough estimates of the spreading speed are also given.

Model-reported card use

The model did not report that any card materially affected this completion.

No Evidence

Same model and position · no retrieved passages · first output

Preferred by blind review

The mathematical description of such moving-boundary problems traces back to the classical Stefan problem, formulated to describe heat conduction with a phase change and named after Josef Stefan's late nineteenth-century work on ice formation.

Earlier card-use comparison

The earlier diagnostic compared only cases with reported card use and text on both sides; its scope differs from the overall AI review above.

This case does not have both with-card continuation text and a model-reported use record. It remains among all 280 tests but does not enter the reported-use comparison.

The passages are input material; their presence does not mean an output used them or that they support every claim. Draft and source passages are excerpted; no simulated scores or PDF appear here.