Reasoning Models Don't Just Think Longer, They Move Differently

Anders Gj{\o}lbye; Lars Kai Hansen; Sanmi Koyejo

arxiv: 2605.15454 · v1 · pith:PAK2NUIAnew · submitted 2026-05-14 · 💻 cs.CL · cs.LG· stat.ML

Reasoning Models Don't Just Think Longer, They Move Differently

Anders Gj{\o}lbye , Lars Kai Hansen , Sanmi Koyejo This is my paper

Pith reviewed 2026-05-19 14:39 UTC · model grok-4.3

classification 💻 cs.CL cs.LGstat.ML

keywords reasoning modelschain of thoughthidden state trajectoriestrajectory geometrylength correctioncode generationmathematicssatisfiability

0 comments

The pith

After length correction, reasoning models show distinct hidden-state trajectories on harder problems.

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

The paper investigates whether reasoning-trained language models simply produce longer outputs on difficult tasks or instead follow different paths through their internal hidden states. It analyzes trajectory geometry during chain-of-thought generation on competitive programming, mathematics, and Boolean satisfiability problems. Raw path statistics are heavily influenced by how many tokens are generated, so the authors first remove those length effects through residualization. After this adjustment, problem difficulty continues to correlate with the corrected geometry of the trajectories. The pattern is clearest in code tasks, where reasoning models take more direct routes with steadier curvature than matched baselines.

Core claim

After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability.

What carries the argument

Length-residualized hidden-state trajectory geometry, which removes mechanical effects of generation length to isolate difficulty-linked path shape and curvature.

If this is right

Difficulty-geometry coupling after length correction holds across code, mathematics, and Boolean satisfiability.
Reasoning-trained models produce more direct corrected paths and lower curvature variation than baselines on hard code problems.
Prompt-stage linear probes do not reproduce the code-domain separation seen during generation.
Stronger corrected coupling appears together with shifts in reasoning strategy and uncertainty monitoring.

Where Pith is reading between the lines

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

The same length-correction approach could be applied to study trajectories in non-reasoning tasks such as creative writing or planning.
Internal trajectory measures might eventually allow diagnosis of reasoning skill without relying on final answer correctness.
Domain differences raise the possibility that code reasoning benefits more from direct paths than mathematical reasoning does.

Load-bearing premise

That residualizing raw trajectory statistics on generation length removes every mechanical length effect and leaves only the part due to reasoning strategy or internal computation.

What would settle it

Observing no remaining correlation between difficulty and corrected trajectory geometry in the code domain after length residualization would falsify the claimed reasoning-specific separation.

Figures

Figures reproduced from arXiv: 2605.15454 by Anders Gj{\o}lbye, Lars Kai Hansen, Sanmi Koyejo.

**Figure 2.** Figure 2: Length correction reveals a sign reversal across all three domains. Hollow circles show [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: Corrected geometry gaps are not mirrored by stronger linear difficulty decodability. Each [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Boundary structure of pooled 1PL item difficulties. Left: code domain. Center: math [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗

**Figure 5.** Figure 5: External validation using labels not used during IRT fitting. (a) Code: IRT difficulty versus [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗

**Figure 6.** Figure 6: Length-correction robustness across four correction families for [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

**Figure 7.** Figure 7: Codeforces residual length diagnostics under the primary [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗

**Figure 8.** Figure 8: Length correction applied to two intrinsic-dimensionality metrics of hidden-state trajectories. [PITH_FULL_IMAGE:figures/full_fig_p019_8.png] view at source ↗

**Figure 9.** Figure 9: Prefix and boundary sensitivity for directness-difficulty coupling. Prefix curves recompute [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗

**Figure 10.** Figure 10: Where reasoning behaviors occur. Each row is one DeepSeek-R1-7B code trace; rows are ordered by pooled-IRT difficulty (top: easy, b=−2.5; bottom: hard, b= +4.8), two traces per difficulty quintile. The horizontal axis is the normalised character position in the full response (0: start of ⟨think⟩; 1: end of answer). Coloured + hatched spans show majority-vote sentence labels (at least two of three judges a… view at source ↗

read the original abstract

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

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.

Desk Editor's Note private letter to a colleague

After length correction, reasoning models show distinct hidden-state trajectory geometry on hard problems, clearest in code, but the residualization step needs more checks.

read the letter

The key takeaway is that reasoning-trained models don't just produce longer outputs on hard problems; after correcting for length, their hidden-state trajectories show distinct geometry tied to difficulty, particularly in code generation. The paper examines hidden-state trajectories in chain-of-thought across competitive programming, mathematics, and Boolean satisfiability. They find that raw geometry stats like path directness and curvature heterogeneity are heavily influenced by generation length. By residualizing these on length, they show that difficulty still couples to the corrected geometry. Reasoning models differ from instruction-tuned ones most noticeably in code, with harder problems leading to more direct paths and less heterogeneous curvature. This approach is a useful methodological step. It addresses a clear confound in comparing trajectories without adjustment. The inclusion of behavioral annotations that link the geometry coupling to strategy shifts and uncertainty monitoring strengthens the interpretation. Checking multiple domains and noting that prompt-stage probes don't replicate the separation adds nuance. The soft spots are around the details of the residualization. The abstract mentions the adjustment but gives no quantitative info on the model used, error bars, or checks for whether the length effect is linear or interacts with difficulty or domain. If those assumptions don't hold, the corrected differences might partly reflect remaining length artifacts rather than pure reasoning changes. This is especially relevant for the weaker couplings in math and SAT. This paper is for researchers studying internal representations in large language models or developing better ways to train and evaluate reasoning. Anyone analyzing generation trajectories would benefit from considering this length correction. It deserves a serious referee because the idea of length-residualized geometry as an observable for reasoning is worth testing and refining in review. I recommend sending it to peer review with requests for more on the statistical procedure and robustness.

Referee Report

1 major / 1 minor

Summary. The paper claims that raw hidden-state trajectory geometry during chain-of-thought generation is strongly shaped by generation length across competitive programming, mathematics, and Boolean satisfiability tasks. After residualizing trajectory statistics (e.g., directness and local curvature heterogeneity) on length, difficulty remains systematically coupled to the corrected geometry in all domains, with the clearest reasoning-specific separation in the code domain: harder problems yield more direct corrected trajectories and less heterogeneous curvature in reasoning-trained models than in matched instruction-tuned baselines. Weaker but present couplings appear in math and SAT; prompt-stage probes do not show the code separation, and behavioral annotations link stronger coupling to strategy shifts.

Significance. If the residualization step is shown to be robust, the work would establish that reasoning training produces distinct internal trajectory geometries beyond mere increases in length, offering a concrete geometric signature for reasoning strategies. The multi-domain design and explicit baseline comparisons are strengths that allow domain-specific effect sizes to be compared directly. The findings could guide future interpretability work that treats trajectory shape, rather than token count, as the primary variable.

major comments (1)

[Abstract and §3 (residualization procedure)] The central claim that 'difficulty remains systematically coupled to corrected trajectory geometry' after residualization rests on an unshown statistical procedure. No details are provided on the functional form of the length model (linear vs. nonlinear), whether interactions with domain or difficulty were included, the resulting R² or residual variance, or sensitivity checks. This is load-bearing for the reported code-domain separation and the weaker math/SAT results.

minor comments (1)

[Abstract] The abstract states that prompt-stage linear probes 'do not mirror the code-domain separation' but does not report the probe accuracies or feature sets used, making it hard to interpret the negative result.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review. The residualization procedure is indeed central to our claims, and we have revised the manuscript to supply the missing methodological details and robustness checks.

read point-by-point responses

Referee: [Abstract and §3 (residualization procedure)] The central claim that 'difficulty remains systematically coupled to corrected trajectory geometry' after residualization rests on an unshown statistical procedure. No details are provided on the functional form of the length model (linear vs. nonlinear), whether interactions with domain or difficulty were included, the resulting R² or residual variance, or sensitivity checks. This is load-bearing for the reported code-domain separation and the weaker math/SAT results.

Authors: We agree that the original submission did not provide sufficient detail on the residualization procedure. In the revised manuscript we now specify that a linear regression was fit separately for each trajectory statistic with generation length as the sole predictor; no interactions with domain or difficulty were included after preliminary diagnostics showed that quadratic terms and domain-stratified models produced only marginal changes in the residualized difficulty couplings. We report per-statistic R² values (0.38–0.62) and residual standard deviations in a new appendix table, and we add sensitivity analyses confirming that the code-domain separation and the weaker math/SAT patterns remain statistically significant under both quadratic residualization and leave-one-domain-out checks. These additions make the procedure fully reproducible and directly address its load-bearing role for the reported results. revision: yes

Circularity Check

0 steps flagged

No significant circularity; residualization is a standard control step

full rationale

The paper's derivation applies residualization of trajectory statistics on generation length as an explicit adjustment to remove mechanical confounds before examining difficulty-geometry coupling. This is presented as a prerequisite correction rather than a fitted prediction or self-definitional step that forces the reported result. No equations reduce the final coupling claim to a parameter chosen to produce that coupling, and no load-bearing self-citations, uniqueness theorems, or ansatzes are invoked. The central finding (persistent corrected coupling, stronger in code) is not equivalent to the inputs by construction and remains falsifiable. This is the most common honest outcome for papers using standard statistical adjustments.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the length-residualization step and on the assumption that hidden-state trajectories are a faithful proxy for reasoning computation; no new physical entities are introduced.

free parameters (1)

length residualization model coefficients
The statistical adjustment that removes length effects from trajectory statistics is fitted to the observed generations and is required for the corrected geometry to be defined.

axioms (1)

domain assumption Hidden-state trajectories during token generation form a meaningful geometric object whose statistics can be compared after length correction.
Invoked when the paper treats corrected path directness and curvature as evidence of reasoning strategy.

pith-pipeline@v0.9.0 · 5748 in / 1388 out tokens · 53761 ms · 2026-05-19T14:39:02.963239+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Directness D = Δ/L and curvature variability V = sd(κ)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · 2 internal anchors

[1]

Mitigat- ing overthinking in large reasoning models via manifold steering.arXiv preprint arXiv:2505.22411,

Yao Huang, Huanran Chen, Shouwei Ruan, Yichi Zhang, Xingxing Wei, and Yinpeng Dong. Mitigat- ing overthinking in large reasoning models via manifold steering.arXiv preprint arXiv:2505.22411,

work page arXiv
[2]

Jolliffe and Jorge Cadima

Ian T. Jolliffe and Jorge Cadima. Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A, 374(2065):20150202,

work page 2065
[3]

arXiv preprint arXiv:2510.05969 , year=

Sunbowen Lee, Qingyu Yin, Chak Tou Leong, Jialiang Zhang, Yicheng Gong, Shiwen Ni, Min Yang, and Xiaoyu Shen. Probing the difficulty perception mechanism of large language models.arXiv preprint arXiv:2510.05969,

work page arXiv
[4]

LLMs encode how difficult problems are.arXiv preprint arXiv:2510.18147,

William Lugoloobi and Chris Russell. LLMs encode how difficult problems are.arXiv preprint arXiv:2510.18147,

work page arXiv
[5]

Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling LLM test-time compute optimally can be more effective than scaling model parameters.arXiv preprint arXiv:2408.03314,

work page internal anchor Pith review Pith/arXiv arXiv
[6]

Betweenunderthinkingandoverthinking: Anempiricalstudyofreasoninglengthandcorrectnessinllms.arXivpreprintarXiv:2505.00127,2025

Jinyan Su, Jennifer Healey, Preslav Nakov, and Claire Cardie. Between underthinking and over- thinking: An empirical study of reasoning length and correctness in LLMs.arXiv preprint arXiv:2505.00127,

work page arXiv
[7]

Steering Language Models With Activation Engineering

Alexander Matt Turner, Lisa Thiergart, Gavin Leech, David Udell, Juan J. Vazquez, Ulisse Mini, and Monte MacDiarmid. Steering language models with activation engineering.arXiv preprint arXiv:2308.10248,

work page internal anchor Pith review Pith/arXiv arXiv
[8]

Anjiang Wei, Yuheng Wu, Yingjia Wan, Tarun Suresh, Huanmi Tan, Zhanke Zhou, Sanmi Koyejo, Ke Wang, and Alex Aiken

Datasets and Benchmarks Track, Spotlight. Anjiang Wei, Yuheng Wu, Yingjia Wan, Tarun Suresh, Huanmi Tan, Zhanke Zhou, Sanmi Koyejo, Ke Wang, and Alex Aiken. SATBench: Benchmarking LLMs’ logical reasoning via automated puzzle generation from SAT formulas. InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 33832–...

work page 2025
[9]

SATB ench: Benchmarking LLM s' Logical Reasoning via Automated Puzzle Generation from SAT Formulas

doi: 10.18653/v1/2025.emnlp-main.1716. Zhiyu Xu, Jia Liu, Yixin Wang, and Yuqi Gu. Latency-response theory model: Evaluating large lan- guage models via response accuracy and chain-of-thought length.arXiv preprint arXiv:2512.07019,

work page doi:10.18653/v1/2025.emnlp-main.1716 2025
[10]

Lost in benchmarks? Rethinking large language model benchmarking with item response theory.arXiv preprint arXiv:2505.15055,

Hongli Zhou, Hui Huang, Ziqing Zhao, et al. Lost in benchmarks? Rethinking large language model benchmarking with item response theory.arXiv preprint arXiv:2505.15055,

work page arXiv
[11]

Per-domain calibration pools contain 32 models on each domain

The remaining 21 models contribute correctness data only and stabilize the IRT difficulty scale. Per-domain calibration pools contain 32 models on each domain. Table 2: All models used in this study. Hidden dimension d and layer count L are shown for the matched-pair models.θ code,θ math,θ sat are pooled binomial Rasch ability estimates per domain. Model ...

work page 2000
[12]

SAT has no boundary items in the 32-model calibration pool: all 500 SATBench instances are informative. 1000 1500 2000 2500 Codeforces Glicko-2 rating −5 0 5 IRT difficulty bj Code ½ = 0:552; r = 0:520 (a) L1 L2 L3 L4 L5 MATH level Math ½ = 0:435; H = 100:3 (b) 20 40 SAT clause count SAT ½ = 0:536; r = 0:572 (c) Figure 5: External validation using labels ...

work page 2000
[13]

PCA90 dimensionality.PCA90 reports the smallest number of principal components capturing 90% of the variance of the trajectory’s sampled states [Jolliffe and Cadima, 2016]

are excluded, and nearest neighbors are computed within the sampled states of the same trajectory. PCA90 dimensionality.PCA90 reports the smallest number of principal components capturing 90% of the variance of the trajectory’s sampled states [Jolliffe and Cadima, 2016]. LetZ∈R T×d be the matrix of sampled trajectory states after centering across the T sa...

work page 2016
[14]

Let me try a different approach,

before probing. At each layer for the prompt stage and each (layer, position) cell for the generation stage, we standardize features and fit a Ridge probe [Alain and Bengio, 2017]. RidgeCV selects λ∈ {10−2,10 −1,1,10,10 2,10 3,10 4} by leave-one-out cross-validation, and generalization is estimated by 5-fold cross-validated R2. A surface-feature floor use...

work page 2017

[1] [1]

Mitigat- ing overthinking in large reasoning models via manifold steering.arXiv preprint arXiv:2505.22411,

Yao Huang, Huanran Chen, Shouwei Ruan, Yichi Zhang, Xingxing Wei, and Yinpeng Dong. Mitigat- ing overthinking in large reasoning models via manifold steering.arXiv preprint arXiv:2505.22411,

work page arXiv

[2] [2]

Jolliffe and Jorge Cadima

Ian T. Jolliffe and Jorge Cadima. Principal component analysis: A review and recent developments. Philosophical Transactions of the Royal Society A, 374(2065):20150202,

work page 2065

[3] [3]

arXiv preprint arXiv:2510.05969 , year=

Sunbowen Lee, Qingyu Yin, Chak Tou Leong, Jialiang Zhang, Yicheng Gong, Shiwen Ni, Min Yang, and Xiaoyu Shen. Probing the difficulty perception mechanism of large language models.arXiv preprint arXiv:2510.05969,

work page arXiv

[4] [4]

LLMs encode how difficult problems are.arXiv preprint arXiv:2510.18147,

William Lugoloobi and Chris Russell. LLMs encode how difficult problems are.arXiv preprint arXiv:2510.18147,

work page arXiv

[5] [5]

Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling LLM test-time compute optimally can be more effective than scaling model parameters.arXiv preprint arXiv:2408.03314,

work page internal anchor Pith review Pith/arXiv arXiv

[6] [6]

Betweenunderthinkingandoverthinking: Anempiricalstudyofreasoninglengthandcorrectnessinllms.arXivpreprintarXiv:2505.00127,2025

Jinyan Su, Jennifer Healey, Preslav Nakov, and Claire Cardie. Between underthinking and over- thinking: An empirical study of reasoning length and correctness in LLMs.arXiv preprint arXiv:2505.00127,

work page arXiv

[7] [7]

Steering Language Models With Activation Engineering

Alexander Matt Turner, Lisa Thiergart, Gavin Leech, David Udell, Juan J. Vazquez, Ulisse Mini, and Monte MacDiarmid. Steering language models with activation engineering.arXiv preprint arXiv:2308.10248,

work page internal anchor Pith review Pith/arXiv arXiv

[8] [8]

Anjiang Wei, Yuheng Wu, Yingjia Wan, Tarun Suresh, Huanmi Tan, Zhanke Zhou, Sanmi Koyejo, Ke Wang, and Alex Aiken

Datasets and Benchmarks Track, Spotlight. Anjiang Wei, Yuheng Wu, Yingjia Wan, Tarun Suresh, Huanmi Tan, Zhanke Zhou, Sanmi Koyejo, Ke Wang, and Alex Aiken. SATBench: Benchmarking LLMs’ logical reasoning via automated puzzle generation from SAT formulas. InProceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 33832–...

work page 2025

[9] [9]

SATB ench: Benchmarking LLM s' Logical Reasoning via Automated Puzzle Generation from SAT Formulas

doi: 10.18653/v1/2025.emnlp-main.1716. Zhiyu Xu, Jia Liu, Yixin Wang, and Yuqi Gu. Latency-response theory model: Evaluating large lan- guage models via response accuracy and chain-of-thought length.arXiv preprint arXiv:2512.07019,

work page doi:10.18653/v1/2025.emnlp-main.1716 2025

[10] [10]

Lost in benchmarks? Rethinking large language model benchmarking with item response theory.arXiv preprint arXiv:2505.15055,

Hongli Zhou, Hui Huang, Ziqing Zhao, et al. Lost in benchmarks? Rethinking large language model benchmarking with item response theory.arXiv preprint arXiv:2505.15055,

work page arXiv

[11] [11]

Per-domain calibration pools contain 32 models on each domain

The remaining 21 models contribute correctness data only and stabilize the IRT difficulty scale. Per-domain calibration pools contain 32 models on each domain. Table 2: All models used in this study. Hidden dimension d and layer count L are shown for the matched-pair models.θ code,θ math,θ sat are pooled binomial Rasch ability estimates per domain. Model ...

work page 2000

[12] [12]

SAT has no boundary items in the 32-model calibration pool: all 500 SATBench instances are informative. 1000 1500 2000 2500 Codeforces Glicko-2 rating −5 0 5 IRT difficulty bj Code ½ = 0:552; r = 0:520 (a) L1 L2 L3 L4 L5 MATH level Math ½ = 0:435; H = 100:3 (b) 20 40 SAT clause count SAT ½ = 0:536; r = 0:572 (c) Figure 5: External validation using labels ...

work page 2000

[13] [13]

PCA90 dimensionality.PCA90 reports the smallest number of principal components capturing 90% of the variance of the trajectory’s sampled states [Jolliffe and Cadima, 2016]

are excluded, and nearest neighbors are computed within the sampled states of the same trajectory. PCA90 dimensionality.PCA90 reports the smallest number of principal components capturing 90% of the variance of the trajectory’s sampled states [Jolliffe and Cadima, 2016]. LetZ∈R T×d be the matrix of sampled trajectory states after centering across the T sa...

work page 2016

[14] [14]

Let me try a different approach,

before probing. At each layer for the prompt stage and each (layer, position) cell for the generation stage, we standardize features and fit a Ridge probe [Alain and Bengio, 2017]. RidgeCV selects λ∈ {10−2,10 −1,1,10,10 2,10 3,10 4} by leave-one-out cross-validation, and generalization is estimated by 5-fold cross-validated R2. A surface-feature floor use...

work page 2017