{
  "abstract": "Motivation: Single-cell fate mapping at atlas scale is constrained by memory: in the tested CellRank 2.3.2 pip environment without the optional PETSc/SLEPc stack, the GPCCA estimator fell back--after a warning--to a dense Brandts Schur routine. Across three measured sizes, its peak memory was consistent with ~72 n^2 bytes, a model that back-calculates to ~405 GB [BACK-CALCULATED] for the 74,984-cell dataset studied here--beyond any consumer workstation. Results: We present scalable-fate (sfate), which computes absorption probabilities to annotation-defined target states--where 'fate probability' denotes absorption probability toward user-defined target states on a latent-space transition graph, conceptually related to Palantir-style diffusion-based Markov-chain fate modeling rather than a velocity-derived lineage probability--from latent-space kNN graphs via column-wise GMRES solves, without any Schur decomposition. Memory scaled linearly with cell number over four measured graph-construction tiers (R^2 = 0.9985; 4.03 GiB at 500,000 synthetic cells in 66.2 s); the 500k absorption solve did not converge under the default configuration, so the largest measured full-pipeline scale is the 75k real-data run (1.76 GiB). Solutions agree with float64 direct references within the prespecified 1e-5 tolerance at every tested configuration (production default L-inf = 1.74e-06; best tested configuration 3.21e-07, 31x below the threshold), and reproduce CellRank's fate probabilities when the transition kernel and terminal representative cells are held identical. On 75k mouse 5xFAD/Cd28-cKO microglia (Ayata et al., 2025; GEO: GSE296768), the full analysis ran at 1.76 GiB peak memory, returning a six-state annotation-defined absorption landscape where the archived CellRank analysis returned three comparable arms; a controlled 2x2 comparison identifies terminal-state selection as an important contributor to the cross-tool discrepancy. Availability: sfate is available at https://github.com/Ericleo-zeng/sfate (release v1.0.0, commit 5472f62; MIT license) and is archived at Zenodo (DOI: 10.5281/zenodo.22851715). The repository includes the source code, the validation suite (32 unit tests, deterministic under fixed seed), all benchmark and figure-generation scripts, the synthetic fixtures, and the records underlying every figure and table. Contact: Wei Zeng (ericleo_zeng@hotmail.com)",
  "abstract_shown": true,
  "affiliations": [
    "The Third School of Clinical Medicine, Southern Medical University"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "W. Zeng"
    },
    {
      "name": "L. Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/37q0eawy43dm6.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.09.19.752930",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.09.19.752930v1.full",
  "id": "37q0eawy43dm6",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.09.19.752930v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "bioinformatics"
    ],
    [
      "openalex",
      "1312|Single-cell and spatial transcriptomics"
    ]
  ],
  "openalex": "W7214394586",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.09.19.752930v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/37q0eawy43dm6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:34Z",
      "native_id": "10.64898/2026.09.19.752930",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.09.19.752930v1"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:bioinformatics",
      "subfield": "bioinformatics"
    }
  ],
  "title": "sfate: Schur-free, target-conditioned absorption probabilities for scalable single-cell fate analysis",
  "title_text": "sfate: Schur-free, target-conditioned absorption probabilities for scalable single-cell fate analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:34Z",
  "url": "https://research.draconitic.com/paper/37q0eawy43dm6",
  "venue": "bioRxiv",
  "versions": []
}