{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YKRM54E4PY5SEOVI55EZJ5Z5O2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"24821a455e9e73d9c526a484075f2330bc4b1a7505f93513e2f133ca04801eaf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2021-03-25T16:01:13Z","title_canon_sha256":"f73abbda47e7cc854ac52568b9d6081145105bc9e703146fa61d1376b5ecea11"},"schema_version":"1.0","source":{"id":"2103.13940","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.13940","created_at":"2026-07-05T03:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"2103.13940v3","created_at":"2026-07-05T03:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.13940","created_at":"2026-07-05T03:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"YKRM54E4PY5S","created_at":"2026-07-05T03:11:28Z"},{"alias_kind":"pith_short_16","alias_value":"YKRM54E4PY5SEOVI","created_at":"2026-07-05T03:11:28Z"},{"alias_kind":"pith_short_8","alias_value":"YKRM54E4","created_at":"2026-07-05T03:11:28Z"}],"graph_snapshots":[{"event_id":"sha256:e6f3e6c07b49ceeb291dcde2f31539e05abf76780e13a54453ff659932130ec1","target":"graph","created_at":"2026-07-05T03:11:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2103.13940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for each single crossing graph $H$, a polynomially bounded weight function for all $H$-minor free graphs $G$ can be constructed in Logspace such that it gives nonzero weights to all the cycles in $G$. This class of graphs subsumes almost all classes of graphs for which such a weight function is known to be constructed in Logspace. As a consequence, we obtain that for the class of $H$-minor free graphs where $H$ is a single crossing graph, reachability can be solved in UL, and bipartite maximum matching can be solved in SPL, which are small subclasses of the parallel complexity cla","authors_text":"Anish Mukherjee, Chetan Gupta, Raghunath Tewari, Rahul Jain, Samir Datta, Vimal Raj Sharma","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2021-03-25T16:01:13Z","title":"Reachability and Matching in Single Crossing Minor Free Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.13940","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3073164c5c40169c7d0c88ba15a3ec4b85994d96366d7ef57d85a855f477188c","target":"record","created_at":"2026-07-05T03:11:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"24821a455e9e73d9c526a484075f2330bc4b1a7505f93513e2f133ca04801eaf","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2021-03-25T16:01:13Z","title_canon_sha256":"f73abbda47e7cc854ac52568b9d6081145105bc9e703146fa61d1376b5ecea11"},"schema_version":"1.0","source":{"id":"2103.13940","kind":"arxiv","version":3}},"canonical_sha256":"c2a2cef09c7e3b223aa8ef4994f73d769f21b524d483845d69c22d82b4535cf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2a2cef09c7e3b223aa8ef4994f73d769f21b524d483845d69c22d82b4535cf7","first_computed_at":"2026-07-05T03:11:28.693601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:11:28.693601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"03w17xjiGhuwdw2mvs/ceJD3XatUtFps2Zgm9j6U6do3eQrkI/+hEwdK67L2GaijkPsx2vAkxnXLOHG2xLJHCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:11:28.693955Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.13940","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3073164c5c40169c7d0c88ba15a3ec4b85994d96366d7ef57d85a855f477188c","sha256:e6f3e6c07b49ceeb291dcde2f31539e05abf76780e13a54453ff659932130ec1"],"state_sha256":"f18c07c2d5c8195a2b2bb08619e5803ebd190d6609c2a8707ae2034b22d129db"}