{"paper":{"title":"A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"PLACE builds classifiers for point clouds and graphs from persistent-homology signatures using only training labels and closed-form rules.","cross_cats":["math.AT"],"primary_cat":"cs.LG","authors_text":"Atish Mitra, Pramita Bagchi, Sushovan Majhi, \\v{Z}iga Virk","submitted_at":"2026-05-04T17:15:01Z","abstract_excerpt":"We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration. The embedding sums Mitra-Virk single-point coordinate functions over a sparse landmark grid; the closed-form weight rule $w_k^2 \\propto (d_{k+1}^2 - d_k^2)/R_k^2$ maximizes the distorti"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"PLACE is a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derivations rely on a non-interference condition when summing Mitra-Virk coordinate functions over the landmark grid and on the existence of a structural distortion constant λ(ν) that can be maximized in closed form to produce the embedding weights.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"PLACE delivers a closed-form persistent-homology classifier for point clouds and graphs with explicit margin bounds, descriptor selection, and training-time certificates derived solely from labels.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"PLACE builds classifiers for point clouds and graphs from persistent-homology signatures using only training labels and closed-form rules.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d946f3e2c56d73601d5b150756617c32d85e0ea7d42772fb920a418ddface521"},"source":{"id":"2605.02836","kind":"arxiv","version":2},"verdict":{"id":"9b7dc267-eb32-43ee-baa0-2c7dc8af97da","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T15:37:40.498841Z","strongest_claim":"PLACE is a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration.","one_line_summary":"PLACE delivers a closed-form persistent-homology classifier for point clouds and graphs with explicit margin bounds, descriptor selection, and training-time certificates derived solely from labels.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derivations rely on a non-interference condition when summing Mitra-Virk coordinate functions over the landmark grid and on the existence of a structural distortion constant λ(ν) that can be maximized in closed form to produce the embedding weights.","pith_extraction_headline":"PLACE builds classifiers for point clouds and graphs from persistent-homology signatures using only training labels and closed-form rules."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.02836/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T14:40:58.652546Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T02:31:21.987917Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:56:30.076606Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7f47c1e8c6f87d06a1829c0b7ddce4fc4f39e7941520d0d52a3db1ec34948e8e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}