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Quantify how the culture ranking changes with distance definition and reference-sample uncertainty, then recommend which comparison merits experimental validation for a synthetic tumour-microenvironment program.\n\n## Challenge details\nThe project aims to improve the relevance of synthetic tumour-microenvironment models. This task addresses model fidelity, not differential-expression discovery: is a proposed culture condition closer to freshly isolated tumour cells, and is that ranking robust to the small reference sample? Use the mouse processed data in GSE107063: three freshly isolated samples and four samples each grown on soft gel, intermediate gel and glass. “Freshly isolated” is not intact in-vivo tissue; isolation and culture introduce their own selection effects. No claim of tumour fidelity can be established solely by these expression distances.\n\nFor features with finite numeric measurements in all 15 samples, define each condition's centroid as its feature-wise mean. Benchmark each culture centroid against the isolate centroid using (a) mean squared difference across features; (b) mean absolute difference across features; and (c) one minus Pearson correlation across features. Also compute a noise-adjusted squared centroid distance: mean across features of [(culture_mean−isolate_mean)^2−culture_sample_variance/n_culture−isolate_sample_variance/n_isolate]. Retain negative estimates; explain why sampling variability can produce them. Use sample variances with denominator n−1. This correction assumes independent samples within and between groups and does not remove batch effects or systematic isolation bias.\n\nEvaluate robustness in two ways. First, omit each isolate sample in turn and recalculate all four measures for every culture condition. Second, perform 2,000 sample-column bootstrap resamples independently within the four groups, with a recorded random seed; preserve each sampled column as a whole to retain dependence across features. Use the same resampled reference in all three culture comparisons within a bootstrap draw. Report pairwise culture distance differences, their central 95% percentile sensitivity intervals (2.5th and 97.5th percentiles, linear interpolation equivalent to R quantile type 7 / NumPy method=\"linear\") and ranking frequencies. These are conditional resampling summaries from a very small sample, not calibrated probabilities that one model is biologically superior.\n\n## What you need to submit (Deliverables)\n- The exact compressed mouse processed input, `provenance.json` with source and checksum, and `samples.csv` mapping all 15 columns to GEO IDs and biological conditions. Record what metadata establish about independent biological replication and what remains unknown about animal pairing/batches.\n- `analysis.py` or `analysis.R`, `README.md`, and `distances.csv`: executable parsing/QC and all four full-data and leave-one-isolate-out distance results. Do not silently re-normalize or transform deposited values. Explain expression-scale evidence and limitations. Handle constant-vector correlations explicitly as undefined; do not replace undefined values with zero.\n- `bootstrap.csv.gz` and `ranking-summary.csv`: every resample's distances and the specified pairwise/ranking summaries. Define ties and undefined draws and report their counts. Ranking frequencies must not conceal ties or excluded draws.\n- `fidelity.svg` or `fidelity.png`: readable distance and sensitivity comparisons, clearly separating the four metrics and identifying the reference.\n- `decision.md`: compare metric-dependent and reference-dependent rankings; identify which feature classes or scale properties can dominate each metric; report whether a single preferred condition is defensible. Propose a concrete validation comparison that could distinguish expression-profile similarity from functional tumour-model fidelity. Address shared-reference dependence, tiny n, unverified pairing/batches, single mouse model, culture duration, isolation effects and absence of patient or drug-response prediction validation. A finding that the ranking is inconclusive is eligible.\n\nAll required artifacts must be included as file bytes. The README must provide dependencies, execution command, feature exclusion counts and a reproducible seed. No wet-lab or animal experiment is performed in this bounty.\n\n## Inputs, Materials and References\n1. GEO GSE107063: https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE107063 . Exact processed mouse input: https://www.ncbi.nlm.nih.gov/geo/download/?acc=GSE107063&file=GSE107063_All_Expression_Mouse.txt.gz&format=file . File `GSE107063_All_Expression_Mouse.txt.gz`, SHA-256 `31c8b928bf8d8e902d5622e8b5cbcdd02f616de4de6cc7a787f44d6bc93aad85`, 3,513,819 compressed bytes, verified 17 September 2026. Required samples GSM2860488–GSM2860502; all are linked from the series record.\n2. Medina et al. (2019), *Identification of a Mechanogenetic Link between Substrate Stiffness and Chemotherapeutic Response in Breast Cancer*, DOI 10.1016/j.biomaterials.2019.02.018, PMC6474249: https://pmc.ncbi.nlm.nih.gov/articles/PMC6474249/ . Methods and Figure 5 provide the model-preservation rationale and limitations. No raw CEL data, gene annotation or linked supplement is required.\n\nProject context: https://openlabs-git-codex-openlabs-elgora-adapter-bio-xyz.vercel.app/projects/da8d4ec9-aa84-45b5-9d6b-aa3f8afaecf9 . Independent research contribution, without claimed project endorsement.\n\n## Acceptance Criteria\n1. Input checksum and all sample mappings are correct. Human arrays are excluded. Wholly empty formatting fields may be removed; biological sample removal is prohibited in the primary analysis. Incomplete or invalid feature exclusions are recorded explicitly.\n2. The four distance definitions, three reference omissions and 2,000 bootstrap draws are implemented as specified. Full-data calculations reproduce within 0.000001 absolute tolerance before rounding; rerunning with the stated seed reproduces bootstrap outputs within the declared environment. Shared-reference resampling and complete-column resampling are preserved.\n3. Noise-adjusted distances retain negative values, undefined correlations remain identified, and ties/undefined bootstrap results are accounted for. Resampling summaries are not presented as independent experimental evidence or calibrated model-superiority probabilities.\n4. The decision uses computed evidence to distinguish stable versus metric-sensitive rankings and states what the dataset cannot establish. It does not equate fresh isolates with unperturbed intact tumours, infer clinical efficacy, or promise a successful new synthetic model.\n5. The validation recommendation identifies an actual comparison and independent outcome capable of challenging the profile-similarity conclusion. Missing metadata and required future resources are made explicit rather than assumed available.\n\n## How is the winner selected?\nOnly submissions satisfying all criteria are eligible. Prefer fewer material scientific/numerical errors, then stronger reasoning connecting sensitivity to a concrete model-validation decision, then clearer reproducibility and provenance. A forced preferred model does not score better than supported uncertainty. Remaining ties go to earlier on-chain submission timestamp, then lower numeric submission ID. 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