Our Work

Let R_m = C[t]/(t^m), 1 ≤ d ≤ m. Dualizing the universal degree-d finite flat algebra and applying truncated polynomial remainder, we construct a locally closed family in the framed Quot scheme …

Let R_m = C[t]/(t^m), 1 ≤ d ≤ m. Dualizing the universal degree-d finite flat algebra and applying truncated polynomial remainder, we construct a locally closed family in the framed Quot scheme of a weighted R_m-module. In coordinates its embedded submodule is the weighted staircase graph, compatibly with arbitrary base change. The represented étale-sheaf image of d pairwise distinct evaluation rows is the finite étale locus, whose complement is the trace-discriminant effective Cartier divisor. Along each exact multiplicity stratum, the socle identifies the tangent bundle, lower confluent jets form the conormal bundle, and a Quot differential transports the tangent-normal sequence to the canonical family. After forgetting the frame, a graph shear identifies the normal directions with tangent directions to the ambient automorphism orbit. Finite-length Quot strata are constructed recursively as affine torsors; the universal transcript attains rank and collision-jet bounds in a target-independent linear category.

Editorial Revista OWL – v. 4, n. 8 (2026) É com satisfação que apresentamos aos nossos leitores a Revista OWL, Volume 4, Número 8, reafirmando nosso compromisso com …

Editorial Revista OWL – v. 4, n. 8 (2026) É com satisfação que apresentamos aos nossos leitores a Revista OWL, Volume 4, Número 8, reafirmando nosso compromisso com a difusão de pesquisas científicas que promovem o diálogo entre diferentes áreas do conhecimento. Em um cenário marcado pela rápida circulação da informação e pelos constantes desafios sociais, científicos e tecnológicos, a produção acadêmica permanece como um dos principais instrumentos para compreender a realidade e propor soluções inovadoras para problemas contemporâneos. Nesta edição, reunimos artigos que refletem a diversidade temática característica da Revista OWL Journal. As contribuições publicadas evidenciam o potencial transformador da ciência ao abordar questões relevantes nas áreas da educação, saúde, ciências sociais, tecnologia, gestão, meio ambiente e demais campos interdisciplinares. Essa pluralidade reafirma nossa convicção de que o avanço do conhecimento depende da integração de diferentes perspectivas, metodologias e experiências. A publicação científica desempenha um papel essencial na consolidação da pesquisa, ampliando a visibilidade dos estudos, fortalecendo a cooperação entre pesquisadores e promovendo o acesso ao conhecimento produzido em diferentes contextos. Nesse sentido, a revista mantém seu compromisso com a qualidade editorial, a ética em pesquisa, a avaliação por pares e a disseminação responsável da ciência em acesso aberto, contribuindo para que os resultados das investigações alcancem a comunidade acadêmica e a sociedade. Agradecemos aos autores pela confiança depositada em nosso periódico, aos avaliadores pelo rigor e dedicação no processo de revisão e a toda a equipe editorial pelo empenho contínuo na construção de uma revista comprometida com a excelência científica. O trabalho colaborativo de cada um é fundamental para fortalecer um ambiente acadêmico pautado pela integridade, pela inovação e pelo compartilhamento do conhecimento. Esperamos que os estudos apresentados nesta edição inspirem novas pesquisas, estimulem reflexões críticas e contribuam para o desenvolvimento científico em âmbito nacional e internacional. Que cada artigo publicado seja um convite ao diálogo, à descoberta e à construção coletiva de novos saberes. Boa leitura! Conselho EditorialRevista OWL JournalVolume 4, Número 8 – 2026

This dataset contains microsatellite genotypes data for 32 Chinese goral (Naemorhedus griseus) individuals collected from Xuebaoshan National Nature Reserve (XB), Chongqing, and Hupingshan N…

This dataset contains microsatellite genotypes data for 32 Chinese goral (Naemorhedus griseus) individuals collected from Xuebaoshan National Nature Reserve (XB), Chongqing, and Hupingshan National Nature Reserve (HP), Hunan, China, between 2022 and 2024. All samples were collected non-invasively from fresh feces and species origin was confirmed via mitochondrial DNA sequencing.

Reproducibility software for the all-time ruin asymptotics of a Sparre–Andersen process with Mittag–Leffler interarrival times and claim sizes. The package contains the numerical…

Reproducibility software for the all-time ruin asymptotics of a Sparre–Andersen process with Mittag–Leffler interarrival times and claim sizes. The package contains the numerical functions, parameter grid, formula checks, sampler validation, near-critical experiments, saved machine-readable results, tests, and environment requirements used to generate and verify the paper's figures and asymptotic comparisons. Version 1.1.0 adds the all-horizon relative-deviation heatmap, a direct finite-reserve first-passage experiment for the conditional ruin-time and deficit laws, simultaneous 95% DKW envelopes for the conditional-law diagnostics, and an explicit CC BY 4.0 licence notice.

The purpose of this work was to explore what a community of user-centred subject matter experts could look like. It involved a desk study and two workshops.  The report includes information about…

The purpose of this work was to explore what a community of user-centred subject matter experts could look like. It involved a desk study and two workshops.  The report includes information about internal and international community building explored by experts at the Environmental Data Service.  This work was undertaken as part of the UNITED project: https://eds.ukri.org/projects/united  Please contact data@nerc.ukri.org referencing the UNITED project if you would like to discuss this further.     

AbstractModern AI systems invest heavily in generation but lack a reusable computational substrate for deterministic consequence evaluation. This paper synthesizes the Identity–Persistence Progr…

AbstractModern AI systems invest heavily in generation but lack a reusable computational substrate for deterministic consequence evaluation. This paper synthesizes the Identity–Persistence Program into a single runtime architecture that evaluates proposed consequential actions under declared regimes before commitment. It introduces Runtime Regime Infrastructure as a systems category and specifies its layered architecture, typed semantics, runtime laws, ownership boundaries, and verification contracts. The paper makes no new mathematical claims; every load-bearing result is imported from prior work and assembled into an explicit computational architecture. Runtime Regime Infrastructure is presented as the engineering realization of the forcing corpus, separating prediction from evaluation, evaluation from execution, and verification from reconstruction while preserving claim-status discipline throughout.

What this paper does. It builds a tower of Kochen–Specker circles: continuous one-parameter families of KS sets in even dimensions 4, 6, 8, 10 and 12, all carried by the unimodular cancellation …

What this paper does. It builds a tower of Kochen–Specker circles: continuous one-parameter families of KS sets in even dimensions 4, 6, 8, 10 and 12, all carried by the unimodular cancellation mechanism |x|2 = 1 over two-symbol coordinate alphabets. For each rung it computes the Wilczek–Zee holonomy of the KS loop and determines the Galois group of the holonomy's characteristic polynomial, which is the full symmetric group Sd at all five even rungs for cores with irreducible coupling. It also proves a trace law — |Tr S| = d/2 identically on the working stratum, hence det W(2π) = 1 — and assembles a p-cycle certificate route whose required prime exists at every even dimension. Attribution. The three-dimensional Peres/Penrose family originates with Gould and Aravind; this program's contribution there is the gauge reduction showing the moduli space is a circle rather than a 3-torus, which corrects their pairwise-inequivalence claim. The Kochen–Specker uncolorability of the integer {0,±1} ray pools is due to Pavičić and collaborators, not to this program; the paper records only an independent re-derivation and a mechanism-independence observation downstream of their result. The dimension-three two-symbol classification is Kernaghan's (arXiv:2603.16988). The Galois machinery is classical and is not claimed as new: Jordan's 1873 theorem, the block argument of Wielandt (Finite Permutation Groups, Thm. 13.9), the standard practice recorded by Isaacs and Zieschang, and Nagura's 1952 prime-interval theorem. Only the application of that machinery to these holonomy polynomials is this program's. Status and scope. This is a preprint, not a peer-reviewed article. Every claim in the paper carries an explicit evidence label (proved, exact, numerical, conjecture, literature, open), and the scope limits are stated rather than implied. In particular: the Sd law is established only at the rungs actually built, and the general even-dimensional statement is a conjecture; the hypothesis of irreducible coupling is necessary, and the paper exhibits the counterexamples that show it; existence of cores beyond d = 12 is not claimed constructively; and flex certificates have been run at d = 10 only, not at d = 8 or d = 12. All arithmetic is exact; no claim rests on floating-point evidence. Relation to arXiv:2603.16988. An earlier version of that survey reported the Peres/Penrose flex as infinitesimal only. In v8 its author retracts that statement in a labelled correction note and publishes the cause, a constraint-ordering error. The present paper describes the matter as settled, and does not treat v8 as independent confirmation of finiteness: v8's own continuation is double precision and its modular rank computation bounds flex only from above, as its author states. The finite-flexibility verdict rests on the exact certificates of the companion paper. Use of AI assistance. This work was produced with substantial assistance from AI language models, used for exact symbolic and combinatorial computation, for drafting, for literature search, and for adversarial review of the arguments. Every mathematical claim was independently recomputed, and an adversarial pre-publication audit was run against the manuscript. The author is responsible for the content. This disclosure is made unconditionally. Verification code. https://github.com/manuflog/contextuality-obstructions

# Granule cells reorient cortical trajectories to separate contexts   Two codebases Garcia-Garcia et al. (in press, 2026): (1) Python simulations (Fig. 5) [expansion_layer_geom-main.zip]   …

# Granule cells reorient cortical trajectories to separate contexts   Two codebases Garcia-Garcia et al. (in press, 2026): (1) Python simulations (Fig. 5) [expansion_layer_geom-main.zip]   (2) MATLAB data analysis [garciagarcia-2026-main.zip] with documentation for the associated processed behavioral and dual-site two-photon imaging data. ## Data availability The processed data are archived on Dryad and are not stored in this GitHub repository. - **Dryad record:** [url pending] - Download `data1.mat` through `data4.mat` and `optodata.mat`. - Place the downloaded files in a `data/` directory beside the analysis scripts, or select their location when prompted by the setup section. ## Repository contents - `GarciaGarcia2026.m` - principal imaging and behavioral analysis. - `GarciaGarcia2026_gtacr1.m` - GtACR1 optogenetic analysis. - `dependencies/` - helper functions required by the analysis. The study follows the same mice while they learn two skills in parallel: - **Reach:** the mouse pushes a robotic handle with its left forepaw. A successful reach is followed by a 1 s delay and water reward. - **VR:** the mouse runs along a 60 mm virtual linear track. Arrival at the target is followed by the same 1 s delay and water reward. Although the tasks use different movements, sensory environments, and apparatuses, both share the temporal structure **Action -> 1 s Delay -> Reward + ITI**. Premotor layer 5 pyramidal tract neurons (L5PTs) and cerebellar granule cells (GrCs) were imaged simultaneously and tracked across sessions. Most of the paper, including the principal analyses in Figures 1-4, concerns animals after dual-task training. The Novice recordings are used later, primarily in Figure 5 and Extended Data Figure 5, to examine how context separation develops with learning. The workspace is organized as follows: - `crossTask` (`27 x 1` struct) contains paired VR and Reach sessions:   - **18 Trained pairs**, represented in the workspace by the `mid` and `expert` learning-stage labels. These are the primary data used to compare cortical generalization with cerebellar context separation.   - **9 Novice pairs**, labeled `novice`. These were recorded on consecutive VR and Reach training days immediately after pre-training, before animals had learned predictive timing in both tasks. - `sameTask` (`9 x 1` struct) contains Trained VR-VR or Reach-Reach session pairs. These are cross-day controls used to distinguish genuine context-dependent remapping from tracking noise or ordinary day-to-day variability. - `xlstbl` (`70 x 16` table) is the session manifest and matching table. In the manuscript, **Trained** is the group-level term encompassing the `mid` and `expert` acquisition stages. The public analysis script consistently combines `mid` and `expert` for group-level Trained analyses: Example stage selection: ```matlab stage = lower([crossTask.learningstage]); trainedIdx = ismember(stage, ["mid", "expert"]); noviceIdx  = stage == "novice"; trainedCrossTask = crossTask(trainedIdx);  % 18 VR-Reach pairs noviceCrossTask  = crossTask(noviceIdx);   % 9 VR-Reach pairs trainedControls  = sameTask;               % 9 same-task pairs ``` ## Files in this dataset | File | Approximate size | Saved variables | Contents | |---|---:|---|---| | `data1.mat` | 1.488 GB | `xlstbl1` | First fragment of the session manifest and its nested processed single-session data. | | `data2.mat` | 2.294 GB | `xlstbl2` | Second fragment of the session manifest and its nested processed single-session data. | | `data3.mat` | 3.092 GB | `xlstbl3` | Third fragment of the session manifest and its nested processed single-session data. | | `data4.mat` | 3.760 GB | `crossTask`, `sameTask` | Analysis-ready paired-session imaging and behavioral structures. | | `optodata.mat` | 0.027 GB | `laser_stack`, `lickratestack`, `lickstack`, `tplt_s_tsk` | Processed GtACR1 optogenetic licking data for Extended Data Figure 2. | The five files total approximately 10.662 GB. The MAT-files contain processed data; raw two-photon movies are not included. ## Software and hardware requirements The associated analysis was tested with MATLAB R2025a. Required MathWorks products are: - MATLAB; - Statistics and Machine Learning Toolbox; - Signal Processing Toolbox; and - Image Processing Toolbox. The analysis uses MATLAB R2025a functions including `kde` and `violinplot`. Earlier MATLAB releases are not supported. Because loading the complete manifest and paired structures requires substantially more memory than the compressed files occupy on disk, a computer with at least 32 GB RAM is recommended. The analysis scripts add the bundled `dependencies/` directory automatically during setup. ## Loading the public data The scripts look for the required MAT-files first in a `data` subdirectory beside the scripts and then beside the scripts themselves. If the files are not found, the setup section asks the user to select the Dryad download directory. A recommended local arrangement is: ```text GarciaGarcia2026.m GarciaGarcia2026_gtacr1.m dependencies/ data/     data1.mat     data2.mat     data3.mat     data4.mat     optodata.mat ``` Run the first setup section of `GarciaGarcia2026.m` before running later sections. It loads the four imaging files and constructs the combined manifest as: ```matlab xlstbl = vertcat(xlstbl1,xlstbl2,xlstbl3); clear xlstbl1 xlstbl2 xlstbl3 ``` Run the setup section of `GarciaGarcia2026_gtacr1.m` to load `optodata.mat`. Both scripts add the bundled `dependencies` directory using the saved script location, so they remain compatible with section-by-section execution in the MATLAB Editor. The main analysis is implemented as ordered MATLAB sections. Many later figure sections use intermediate variables created by the joint-PCA section, so running isolated later sections in a fresh workspace may fail. ## Optogenetic licking dataset `optodata.mat` contains the processed trial-level data for the GtACR1 experiment in Extended Data Figure 2. The manuscript describes four sessions from four mice. The file contains four saved variables: - `tplt_s_tsk` — `1 x 2` cell array of reward-centered time vectors. Element 1 is Reach (801 samples, `dt = 0.005 s`, -2 to 2 s); element 2 is VR (20,001 samples, `dt = 0.0002 s`, -2 to 2 s). - `lickstack` — `2 x 1` cell array. Each task element contains four binary trial-by-time lick-contact matrices. - `lickratestack` — `2 x 1` cell array with the same organization, containing normalized lick-rate traces. Values were normalized to the peak lick rate in rewarded laser-off trials; filtering/normalization can produce small values below zero. - `laser_stack` — `2 x 1` cell array with the same organization, containing binary laser-state matrices. Within each task, the four groups are ordered: 1. Rewarded, laser-off. 2. Rewarded, laser-on. 3. Reward omitted, laser-off. 4. Reward omitted, laser-on. The trial counts are `[263, 34, 48, 43]` for Reach and `[243, 35, 39, 34]` for VR. The analysis summarizes normalized lick rate from -0.7 to -0.2 s relative to reward. The detected laser epochs are -0.745 to -0.200 s for Reach and -0.7978 to -0.1058 s for VR. The processed file pools trials and does not store mouse or session identifiers aligned to individual rows. The GtACR1 plots andcomparisons use trials as observations. ## Experimental and processing summary - L5PTs in premotor cortex expressed jRGECO1a and were imaged through the cortical arm of a custom dual-site microscope. - GrCs expressed GCaMP6f and were imaged simultaneously in contralateral cerebellar Crus I, Crus II, or simplex. - Imaging frames were acquired at 30 Hz. - Movies were motion-corrected with NoRMCorre, slow fluorescence drift was removed, and sources were extracted with constrained non-negative matrix factorization followed by manual curation. - Extracted fluorescence traces were z-scored. - Cells were registered across the paired imaging sessions. The analysis retained cells with validated activity in both sessions. - Unless a particular analysis states otherwise, paired neural comparisons use cells that were jointly task-locked in both sessions. Reliability was calculated from odd-versus-even trial averages, corrected with the Spearman-Brown formulas, and thresholded at adjusted reliability greater than 0.4 (except Extended Data Fig. 7 which reproduced main results with no threshold). - Stored behavioral and neural trials span `[-3, 2]` s relative to reward. Reward is at `t = 0`, and the end of the reach/run is represented at approximately `t = -1` s. - The principal paired neural analyses generally crop the stored data to `[-2, 2]` s. The movement-stereotypy calculations use task-specific pre-reward windows: `[-2, -1]` s for Reach and `[-3, -1]` s for VR. - Reward omission trials comprised approximately 20% of trials and were randomly interleaved. ## MATLAB structure conventions Call one paired-session structure `curd`: ```matlab curd = crossTask(i); % or curd = sameTask(i); ``` Each `curd` contains two sessions from one mouse. Unless noted otherwise, elements of a `1 x 2` field follow the same ordering as: ```matlab curd.dates curd.task curd.trials curd.rawsigs ``` For `crossTask`, the public script assumes session order `[Reach, VR]`. For `sameTask`, the two sessions are addressed as `[Day1, Day2]`; the task itself is either Reach on both days or VR on both days. Dimension symbols used below are: - `Ntrial`: number of retained trials in one session. - `NGrC`: number of GrCs retained for the paired-session analysis. - `NL5PT`: number of L5PTs retained for the paired-session analysis. - `Nt_beh = 5001`: samples in the `[-3, 2]` s behavioral window, approximately 1 kHz. - `Nt_neural = 151`: samples in the `[-3, 2]` s neural window, approximately 30 Hz. - `Nt_raw`: samples in a session's continuous imaging trace, typically approximately 32,000 in this release. Cell and trial counts vary across mice and session pairs. ## Units and value conventions - All time values and time axes are in seconds unless stated otherwise. - Behavioral position is stored in millimeters along the task-relevant trajectory: robotic-handle displacement for Reach and virtual-track position for VR. - `lick` is a binary contact signal (`0` = no contact, `1` = contact). - `lickrate` is expressed in licks per second. - L5PT and GrC fluorescence values are z-scored and therefore dimensionless. - Cell-centroid coordinates are in image pixels. - Reliability values and licking fractions are dimensionless. - Trial labels use the strings `rewarded` and `omitted`. - MATLAB missing strings are represented by `<missing>`, missing numeric manifest values by `NaN`, and unavailable nested data by empty cells or empty arrays. NaN and empty values in the manifest indicate unavailable or inapplicable metadata, not zero. ## Paired-session fields ### Identification and session metadata - `mouse` - scalar string identifying the mouse. - `learningstage` - scalar stage label. Use `mid` and `expert` for the manuscript's Trained dataset and `novice` for the Novice dataset. - `dates` - `1 x 2` string array containing the paired recording dates. - `task` - `1 x 2` string array containing `VR` or `Reach` for each session. - `ntrials` - `1 x 2` vector containing the retained trial count for each session. ### Trial-aligned behavioral and neural data `curd.trials` is a `1 x 2` structure array, with one element per session: ```matlab td = curd.trials(sessionIndex); ``` Its fields are: - `pos` - `Ntrial x 5001` single-precision matrix of reward-aligned position. It contains robotic handle position in Reach and virtual-track/running-sphere position in VR. The public script refers to this generically as "track or handle" position. - `lick` - `Ntrial x 5001` matrix of reward-aligned lick-sensor samples. - `lickrate` - `Ntrial x 5001` matrix of reward-aligned lick rate. In the paper, lick events were binned at 1 kHz and smoothed with a Gaussian kernel (`sigma = 20 ms`). - `trialTypes` - `Ntrial x 1` string array containing trial labels, including rewarded and reward-omission trials. - `trialNums` - `Ntrial x 1` vector containing the original trial number of each retained trial. - `L5PT` - `Ntrial x NL5PT x 151` single-precision array of reward-aligned, z-scored L5PT fluorescence, organized as trials by cells by time points. - `GrCs` - `Ntrial x NGrC x 151` single-precision array of reward-aligned, z-scored GrC fluorescence, organized as trials by cells by time points. The paired sessions can contain different numbers of trials. Within one `curd`, the neural arrays share the registered cell population needed for cross-session comparison. ### Continuous fluorescence `curd.rawsigs` is a `1 x 2` structure array containing continuous z-scored fluorescence traces: - `rawsigs(sessionIndex).L5PT` - `NL5PT x Nt_raw` single-precision L5PT signal matrix. - `rawsigs(sessionIndex).GrCs` - `NGrC x Nt_raw` single-precision GrC signal matrix. These continuous traces support analyses that use the entire recording rather than reward-aligned trial excerpts. The Figure 3 canonical-correlation/communicating-subspace analysis crops the two sessions to their common duration before concatenation. ### Cell tables, counts, and retained summaries - `GrCs` - `NGrC x 10` table of GrC identifiers, registration/QC information, per-session trial averages, and cell-level analysis summaries. - `L5PT` - `NL5PT x 10` table of L5PT identifiers, registration/QC information, per-session trial averages, and cell-level analysis summaries. - `GrCs_cellcount` and `L5PT_cellcount` - `1 x 2` vectors containing the detected cell count for each session. - `GrCs_trackedCells` and `L5PT_trackedCells` - `1 x 2` stored cross-session tracking counts. The public script uses the first element as the number of VR/Reach-matched or Day1/Day2-matched cells for Figure 1W and Extended Data Figure 1C. - `auc` - `1 x NGrC` per-GrC fraction of analyzed samples whose z-scored fluorescence exceeded 1. This field is retained from processing but is not used by `GarciaGarcia2026.m`. - `relCntB` - `1 x 2` count of L5PTs and GrCs, respectively, whose adjusted reliability exceeded 0.4 in both paired sessions. This field is retained for reference and is not used by `GarciaGarcia2026.m`. For a cross-task pair, each L5PT or GrC table has these ten variables: - `cellnums` - `Ncell x 2` registered cell indices for Reach and VR. - `Reach_cents` and `VR_cents` - `Ncell x 2` cell-centroid coordinates in image pixels. - `Reach_rewarded` and `VR_rewarded` - `Ncell x 151` rewarded-trial mean z-scored fluorescence. - `Reach_omitted` and `VR_omitted` - `Ncell x 151` reward-omission-trial mean z-scored fluorescence. - `Reach_reliab` and `VR_reliab` - `Ncell x 1` adjusted split-half reliability. - `rel` - `Ncell x 2` matrix containing the two session-specific reliability values. For a same-task pair, the table has the corresponding ten variables `cellnums`, `Day1_cents`, `Day1_rewarded`, `Day1_omitted`, `Day1_reliab`, `Day2_cents`, `Day2_rewarded`, `Day2_omitted`, `Day2_reliab`, and `rel`. Most paired analyses select cells whose reliability exceeds `0.4` in both sessions and then z-score the rewarded trial averages across time before PCA or correlation analysis. ### Licking summaries and dual-task proficiency - `lickPre` - `1 x 2` vector containing the stored pre-reward licking summary. The manuscript defines the pre-reward window as `[-0.5, 0]` s relative to reward. - `lickPost` - `1 x 2` vector containing the stored post-reward licking summary. The manuscript defines the post-reward window as `[1.0, 1.5]` s. - `lickFC2` - `1 x 2` vector containing the predictive licking fraction used for Figure 5 and Extended Data Figure 5. - `lickFC` - `1 x 2` additional derived licking summary retained by the analysis workspace. It is loaded into the general behavioral-results array but is not used as the paper's dual-task proficiency score. The predictive licking fraction stored in `lickFC2` is: ```text Lick_pre / (Lick_pre + Lick_post) ``` The **dual-task score** is the smaller of the predictive licking fractions from VR and Reach. This conservative definition requires predictive behavior in both tasks. One Trained pair was excluded from licking-based analyses because the VR lick sensor was stuck high; therefore those analyses use 17 Trained pairs rather than 18. ### Average images - `avIms` - `2 x 2` cell array containing mean imaging fields for registration and quality control. Rows follow cell-type order `[L5PT, GrCs]`; columns follow the two-session order (`[Reach, VR]` or `[Day1, Day2]`). Thus `curd.avIms{1,1}` is the first-session L5PT mean image and `curd.avIms{2,2}` is the second-session GrC mean image. ## Cell-registration fields Registration structures contain: - `dayNamesOthers` - scalar string identifying the companion session used for registration. - `cellnums` - `Nmatched x 1` `uint16` vector of registered cell indices. The field names depend on the comparison type. ### Cross-task VR-Reach pairs Elements of `crossTask` contain: - `GrCs_Reach` and `L5PT_Reach` - registration information associated with the Reach session. - `GrCs_VR` and `L5PT_VR` - registration information associated with the VR session. These fields are present for both Trained and Novice cross-task pairs. ### Trained same-task controls Elements of `sameTask` contain: - `GrCs_Day1` and `L5PT_Day1` - registration information associated with the first session. - `GrCs_Day2` and `L5PT_Day2` - registration information associated with the second session. Same-task pairs are controls from Trained mice and contain either VR-VR or Reach-Reach comparisons. ## Session manifest: `xlstbl` `xlstbl` is a `70 x 16` table recording session identity, acquisition metadata, learning stage, and matching relationships. Its columns are: - `Mouse` - mouse identifier. - `Date` - recording date. - `Task` - `VR` or `Reach` task label. - `CrossTaskMatch` - identifier of the matched session in the other task. - `CrossTaskMatchDir` - direction/location information for the cross-task match. - `LearnMatches` - legacy learning-session matching information retained from the acquisition manifest; it is not used by the released analysis. - `LearnMatchDir` - legacy numeric field that is `NaN` in all 70 released rows and is not used by the released analysis. - `SameTaskMatch` - identifier of the same-task control session. - `SameTaskDir` - direction/location information for the same-task match. - `TrainingDay` - legacy numeric field that is `NaN` in all 70 released rows and is not used by the released analysis. - `LearningStage` - acquisition-stage label used to distinguish Novice, mid-training, and expert recordings. - `Lobule` - imaged cerebellar lobule. - `x40xMag` - metadata for the cerebellar 40x acquisition. - `x16xMag` - metadata for the cortical 16x acquisition. - `Microscope` - microscope identifier. - `crosstaskDat` - cell containing the fuller processed single-session structure. It provides the original time axes (`tmpx_left`, `tmpx_right`, and `tmpxx`) and reward-aligned signals used when an analysis must include cells outside the longitudinally matched population. In particular, Figure 2L-N and Extended Data Figure 3A use `rewAlgn.sigFilt_left_red` for L5PTs and `rewAlgn.sigFilt_right_green` for GrCs so dimensionality can be estimated from all reliable cells in each session. ### Intentional missing manifest values - `CrossTaskMatch`, `CrossTaskMatchDir`, and `crosstaskDat` are missing or empty for 16 sessions without an available cross-task comparison. - `SameTaskMatch` and `SameTaskDir` are missing for 52 sessions without a same-task comparison. - `LearnMatchDir` and `TrainingDay` are `NaN` in every row and are retained only to preserve the source manifest schema. ### Nested `crosstaskDat` fields Nonempty `crosstaskDat` cells contain the fuller processed single-session structure used to construct the paired data. Its fields are grouped below. - Acquisition dimensions and sampling: `pixh_left`, `pixw_left`, `pixh_right`, `pixw_right`, `dtb_NI`, `dtb_VR`, `dtimleft`, `dtimright`, `ntb_NI`, `ntb_VR`, `ntim_left`, `ntim_right`, and `nf`. - Cell counts and locations: `nc_left_red`, `nc_right_green`, `centroids_left_red`, and `centroids_right_green`. - Continuous signals: `sigFilt_left_red` and `sigFilt_right_green` are cell-by-time z-scored fluorescence matrices; `f0_left_red` and `f0_right_green` contain the corresponding fluorescence baselines. - Acquisition synchronization: `frame_left`, `frame_right`, `timesharefac_left`, and `timesharefac_right`. - Behavior and trial detection: `lick`, `lickrate`, `compMvmts`, `goodMvmt`, `goodMvmts`, `rewarded`, `startPos`, `truestart`, `midpt`, `trueend`, `endTimes`, `rewtimes`, `rewdel`, `mvlen`, and `n_mv`. - Time axes: `tmpx_left`, `tmpx_right`, and `tmpxx` are reward-centered time vectors for cortical imaging, cerebellar imaging, and behavioral acquisition, respectively. - Configuration: `p` stores acquisition and processing parameters. - `rewAlgn` contains reward-aligned `sigFilt_left_red`, `sigFilt_right_green`, `lick`, `lickrate`, and `pos`. Neural arrays are organized as trials by cells by time points; lick and lick-rate arrays are trials by time points; position is trials by coordinates by time points. ## Relationship to the paper - **Figure 1:** Trained cross-task behavior, simultaneous L5PT/GrC imaging, longitudinal tracking, and same-task controls. - **Figure 2:** Trained VR and Reach activity profiles and low-dimensional population structure. Panels A-J use the paired structures. Panels L-N deliberately use `xlstbl.crosstaskDat` and all reliable cells in each individual session rather than restricting dimensionality estimates to longitudinally matched cells. - **Figure 3:** Trained cross-context generalization in L5PTs versus temporal remapping in GrCs, including continuous-recording communicating-subspace analyses. - **Figure 4:** Trained population geometry, trajectory reorientation, cross-task prediction, and behavioral-state decoding. - **Figure 5 and Extended Data Figure 5:** comparison of Novice with Trained pairs and the relationship between GrC cross-context decorrelation and dual-task predictive licking. The modeling panels do not come directly from the imaging structures described here. - **Same-task controls:** used throughout to establish that L5PT/GrC differences in cross-task remapping are not explained by ordinary cross-day variability or unequal registration quality. ## How the main script uses the released fields - **Tracking and counts:** `*_cellcount`, `*_trackedCells`, and `trials.trialNums` generate Figure 1S, V, W and Extended Data Figure 1C. - **Behavior:** `trials.pos`, `trials.lick`, `trials.lickrate`, and `trials.trialTypes` generate the behavioral panels. Stuck-high lick trials are detected at analysis time from `lick`; there is no separate stored validity vector in these public structures. - **Single-cell response analyses:** the cell-table `*_rewarded` and `*_reliab` variables generate peak-time, peak-width, reliability, and cross-session correlation analyses. - **Single-trial population analyses:** `trials.L5PT` and `trials.GrCs` provide the rewarded single trials used for PCA, representational-similarity analysis, L5PT-to-GrC prediction, and delay-versus-reward decoding. - **Whole-recording coupling:** `rawsigs.L5PT` and `rawsigs.GrCs` provide continuous traces for canonical correlation analysis. - **Learning analysis:** `learningstage` selects Novice versus combined mid/expert recordings, while `lickFC2` supplies the per-task predictive licking fraction. ## Basic example ```matlab % Select one primary Trained VR-Reach pair. stage = lower([crossTask.learningstage]); trainedIdx = find(ismember(stage, ["mid", "expert"])); curd = crossTask(trainedIdx(1)); % Inspect session order and trial counts. disp(table(curd.dates(:), curd.task(:), curd.ntrials(:), ...     'VariableNames', {'Date','Task','NTrials'})) % Select one session. td = curd.trials(1); % trials x registered cells x reward-aligned time points size(td.GrCs) size(td.L5PT) % registered cells x continuous recording samples size(curd.rawsigs(1).GrCs) size(curd.rawsigs(1).L5PT) % Inspect cell-table variables. curd.GrCs.Properties.VariableNames curd.L5PT.Properties.VariableNames ``` For exact analysis windows, normalization, reliability corrections, dimensionality reduction, decoding, and statistical procedures, refer to the Methods and the code associated with the corresponding figure. ## Citation When using the code or data, cite: > Garcia-Garcia, M. G., et al. (2026). Granule cells reorient cortical trajectories to separate contexts. [doi pending] Dryad link/doi pending ## License Code is distributed under the license provided in the repository's `LICENSE` file. Data archived on Dryad are released under Dryad's CC0 waiver. Third-party software, if any, remains subject to its original license and attribution requirements.