By the numbers. 34,858 French communes mapped · 1,509 global GBFS feeds audited · 37 M bike share trip observations processed · 27 bike-share networks benchmarked · 322 cycling poverty deserts identified · 8-task MatBench applicability-domain panel · empirically validated across 24 international networks and a 34,858-commune multi-modal panel · one open-source Python package implementing the bound and its augmentation · one structural lower bound that connects them all.

Our central research goal is a universal spectral lower bound on the generalisation error of any graph-supervised learner. The bound depends only on three objects — the graph Laplacian, the target signal, and the learner's reachable feature subspace — and is independent of the regressor choice. Each empirical application in this organisation is, at the methodological level, a corollary or instantiation of this single bound.

flowchart TD
    P5["<b>structural-bounds-framework</b><br/>Universal spectral lower bound<br/>+ C1, C2, C3 proofs absorbed<br/><i>JMLR / FoCM · v0.4 working draft (20 pp main + 5 pp SI)</i>"]
    P1["<b>materials-applicability-bound</b><br/>Corollary C1 — encoding gap under LSO<br/><i>MLST v1.0-rc.5 · draft ready (not yet submitted)</i>"]
    P4["<b>mobility-applicability-bound</b><br/>Empirical instantiation of C1 on<br/>34,858 French commune mobility panel<br/><i>TR-B target · early draft</i>"]
    P6["<b>topological-localization-mobility</b><br/>Bare-Laplacian eigenvector localization<br/>predicts the bound on bike-share<br/><i>EPJ Data Science / Applied Network Sci · v0.1 working draft</i>"]
    TOOL["<b>spectral-mobility</b><br/>Open-source Python package (MIT)<br/>operationalising the bound + augmentation<br/><i>v0.4.0 · 72 tests · CitySpectralProfile + SpectralAugmentedRegressor</i>"]
    P2["<b>(planned) negative-transfer-corollary</b><br/>C2 empirical anchor on QM9 → MatBench<br/><i>theory done in P5; experiments TBD</i>"]
    P3["<b>(planned) active-learning-corollary</b><br/>C3 empirical anchor: leverage-score vs uniform<br/><i>theory done in P5; experiments TBD</i>"]

    P5 -->|C1| P1
    P5 -->|C2| P2
    P5 -->|C3| P3
    P5 -.->|implemented in| TOOL
    P1 -.->|empirical sibling| P4
    P1 -.->|empirical sibling| P6
    P6 -.->|productised as| TOOL

Shared theoretical signature. All bounds in the program take the form

expected loss under evaluation protocol Π ≥ (1 − R²_spec(𝒮_𝒜, y)) · Var(y) − slack(Π, 𝒮_𝒜),

where R²_spec is the projection-R² of the target signal y onto the learner's reachable feature subspace 𝒮_𝒜, computed in the eigenbasis of the graph Laplacian, and the slack term is controlled by the Pesenson sampling quality of the protocol on that subspace (Pesenson 2008; Anis–Gadde–Ortega 2016; the extension to arbitrary feature subspaces follows Chepuri–Leus 2018, Tanaka–Eldar 2020).

Minimax-tight efficiency. In the realisable case, an ERM-on-projection witness saturates the bound up to an O(M² / √(N−n)) slack via Berry–Esseen anticoncentration (Theorem 2 of structural-bounds-framework), establishing the Pesenson-ridge estimator on the restricted feature subspace as an efficient estimator in the sense of the classical Cramér–Rao bound. Sharpening the constant via a multipoint Fano refinement is open.

Why the program is organised this way. Publishing several focused corollaries alongside the universal framework yields both tactical impact (each corollary stands on its own) and strategic coherence (the program builds a recognisable theoretical lane, in the spirit of how Cramér–Rao bounds organise classical estimation theory). Cross-domain controls (cycling networks, MovieLens, materials) are an intrinsic part of the methodology, not an afterthought: every corollary is validated on at least two unrelated domains to confirm that it reflects a property of graph-supervised learning, not an artefact of any single field.

We measure cycling environments, bike share demand and the social distribution of both, at the granularity at which French transport policy is actually decided: the commune (n = 34,858) and the station (n ≈ 50,000 across France and 6 international networks). Methodologically, the same graph-signal-processing tools that we built for cycling network expansion turn out to apply far beyond that setting — to materials informatics (materials-applicability-bound, MLST submission), to urban mobility transferability (mobility-applicability-bound, TR-B target), and ultimately to a unified theoretical statement (structural-bounds-framework) of which the others are corollaries.

Three open data substrates meet here in a single research pipeline: OpenStreetMap infrastructure, GBFS station feeds, and INSEE social statistics. Plus, increasingly, MatBench DFT panels for the materials-side methodology work. The pipeline produces:

1. A reproducible audit of 1,509 GBFS feeds worldwide, exposing the semantic ambiguities of the standard and releasing a 46 column certified catalogue across 48 countries.
2. A commune level supply side composite indicator (the IMD-4) that improves on the de facto French standard (Cerema cycling infrastructure density) by +18 pts R² in predicting realised commuting share.
3. A demand prediction benchmark on 27 dock based networks across two continents, with paired bootstrap CIs and an explicit decomposition of the +0.27 headline ΔR² into transferable spatial and station fingerprint components.
4. A mobility justice diagnostic that turns the indicator into a ranked, intersectional priority list of 322 cycling poverty deserts for the 2023 to 2027 Plan Vélo.
5. A graph signal processing toolkit that develops the spectral bounds, sampling theoretic siting and empirical learning curves which underpin the prediction work.
6. A structural lower bound on the applicability-domain gap in materials property prediction, derived from the same GSP framework as the bike-share siting bounds, validated on 8 MatBench tasks with a foundation-model encoder-discrimination oracle test (CHGNet).
7. An empirical instantiation of that same bound in urban mobility, on the 34,858 French commune panel — answering the question "why do mode-choice models trained in city A fail in city B?" in the same language as the materials encoding gap.
8. A unified theoretical framework that contains all of the above as corollaries of a single regressor-independent spectral inequality.

All released as code, data and reproducible LaTeX under MIT, with Zenodo DOIs minted on every versioned release.

flowchart TD
    A[gbfs-audit-catalogue<br/><i>1,509 feeds · 46,307 stations · 48 countries</i>]
    B[imd-national-catalogue<br/><i>IMD-4 + IES on 34,858 French communes</i>]
    C[bikeshare-demand-forecasting<br/><i>Prediction + leave-station-out siting</i>]
    D[bikeshare-gsp-tools<br/><i>Spectral bounds · D-optimal siting · learning curves</i>]
    E[penality-analysis<br/><i>Triple-penalty mobility-justice diagnostic</i>]
    F[materials-applicability-bound<br/><i>Corollary C1 · 8-task MatBench · CHGNet oracle test</i>]
    M[mobility-applicability-bound<br/><i>Empirical instantiation of C1 on 34,858 communes</i>]
    U[structural-bounds-framework<br/><i>Universal spectral lower bound · contains C1–C3 as corollaries</i>]
    T[topological-localization-mobility<br/><i>Eigenvector localization predicts the bound · 9-city panel</i>]
    S[spectral-mobility<br/><i>Python package · structural bound + spectral augmentation</i>]
    G[paper-template<br/><i>Starter repo for new papers</i>]

    A --> B
    A --> C
    B --> C
    B --> D
    B --> E
    B --> M
    C -.->|nine-city panel| T
    D -.->|GSP framework transfers| F
    F -.->|methodology contributes back| D
    F -.->|sibling empirical| M
    U ==>|C1| F
    U ==>|empirical sibling of C1| M
    U ==>|empirical sibling of C1| T
    G -.->|template for| F
    G -.->|template for| M
    G -.->|template for| U
    G -.->|template for| C
    G -.->|template for| T
    U -.->|implemented in| S
    T -.->|productised in| S
    S -.->|used by| C
    S -.->|used by| T

Status note (May 2026). No manuscript from this organisation has been submitted to a journal yet. Several drafts have reached the point where submission is technically possible — materials-applicability-bound v1.0-rc.5 (MLST), gbfs-audit-catalogue v1.0.1 (data paper), structural-bounds-framework v0.4 (JMLR / FoCM), bikeshare-demand-forecasting, penality-analysis, and topological-localization-mobility v0.1 — but the program is deliberately paced (see the Submission roadmap below). The framework draft includes full proofs of Corollaries C2 (negative transfer) and C3 (active learning) absorbed inside the main paper; planned standalone follow-up repositories negative-transfer-corollary and active-learning-corollary will host the empirical-validation experiments. Working drafts are released openly during the writing process so that feedback can shape the eventual submission.

Provenance note. The topological-localization-mobility paper started life under an Anderson-localization framing that was empirically falsified by our own disorder-robustness placebo tests; the precursor repository is archived (read-only) at cycling-data-lab/anderson-localization-mobility, tag v0.1-anderson-falsified, for transparency.

Tool release. The spectral-mobility Python package operationalises the structural-bound and spectral-augmentation methodologies of the program. v0.4.0 ships SpectralAugmentedRegressor (sklearn-style, transductive + Nyström-inductive), CitySpectralProfile (self-contained spectral signature of a single network) and compare_cities / cross_city_similarity_matrix (multi-city pairwise comparison). 72 unit tests passing. Validated on real Boston Bluebikes data: baseline R² = +0.05 → augmented R² = +0.46 (inductive, strict, K=16), a × 9 improvement.

Working drafts are available openly in this organisation as they mature; formal journal submissions are being staged across Q3/Q4 2026. arXiv preprints will resolve cross-paper citations as drafts go out.

The two planned follow-ups build on topological-localization-mobility and spectral-mobility but are kept as separate manuscripts: the first is a diagnostic across modes and scales, the second is the algorithm that operationally closes the gap measured by the first. Merging them would dilute both narratives.

Every result in every repo can be reproduced from the raw open data sources:

• OpenStreetMap (OdbL): cycling infrastructure (I axis), heavy transit stops (M axis proxy).
• GBFS feeds (provider terms): station inventory and real time status for the 27 network panel.
• INSEE Filosofi (Licence Ouverte 2.0): commune level median income, poverty rate, part vélo travail outcome.
• Open Elevation SRTM 30 m (CC BY): topography (T axis).
• FUB Baromètre Vélo, EMP survey, Cerema cycling infrastructure inventory: calibration and comparison panels.
• Lyft (Bluebikes, Capital Bikeshare, Divvy, Bay Wheels), BIXI, TfL, Citi Bike trip logs: 37 M observations across the Tier 1 panel.
• MatBench v0.1 + Materials Project + CHGNet pretrained: 8-task DFT panel and foundation-model crystal embeddings (materials methodology side).

Each repo ships:

• a requirements.txt pinning the Python stack;
• random seeds (typically 42) and explicit RAM and wall time budgets per script;
• pre computed intermediate parquets to bypass long recomputations;
• a CITATION.cff for machine readable citation;
• a .zenodo.json for automatic DOI minting on each GitHub Release;
• an MIT LICENSE for the code (data products inherit upstream licenses).

New repos in this organisation should be created from paper-template, which ships all of the above plus a starter LaTeX manuscript in the IOP iopjournal.cls style.

@misc{cyclingDataLab,
  author       = {Foss\'e, Rohan and Pallares, Ga\"el},
  title        = {{cycling-data-lab}: a research program on structural lower bounds
                  for graph-supervised learning, with empirical instantiations in
                  materials informatics, urban mobility, bike share demand and
                  mobility justice},
  year         = {2026},
  howpublished = {\url{https://github.com/cycling-data-lab}}
}

Per repo BibTeX entries are in the corresponding README.md.

Rohan Fossé · Enseignant Responsable Pédagogique, CESI École d'Ingénieurs, Montpellier

Gaël Pallares · Enseignant Chercheur, CESI LINEACT (EA 7527)

Affiliated with CESI LINEACT (EA 7527), Montpellier, France.

To complete.

Issues and pull requests are welcome on any of the repos. We follow a publish then discuss model: drafts are released openly during the writing process so external feedback can shape the eventual submission.

For larger collaborations (joint papers, data sharing, code contributions), email Rohan directly.