{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YKRM54E4PY5SEOVI55EZJ5Z5O2","short_pith_number":"pith:YKRM54E4","canonical_record":{"source":{"id":"2103.13940","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2021-03-25T16:01:13Z","cross_cats_sorted":[],"title_canon_sha256":"f73abbda47e7cc854ac52568b9d6081145105bc9e703146fa61d1376b5ecea11","abstract_canon_sha256":"24821a455e9e73d9c526a484075f2330bc4b1a7505f93513e2f133ca04801eaf"},"schema_version":"1.0"},"canonical_sha256":"c2a2cef09c7e3b223aa8ef4994f73d769f21b524d483845d69c22d82b4535cf7","source":{"kind":"arxiv","id":"2103.13940","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YKRM54E4PY5SEOVI55EZJ5Z5O2","target":"record","payload":{"canonical_record":{"source":{"id":"2103.13940","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CC","submitted_at":"2021-03-25T16:01:13Z","cross_cats_sorted":[],"title_canon_sha256":"f73abbda47e7cc854ac52568b9d6081145105bc9e703146fa61d1376b5ecea11","abstract_canon_sha256":"24821a455e9e73d9c526a484075f2330bc4b1a7505f93513e2f133ca04801eaf"},"schema_version":"1.0"},"canonical_sha256":"c2a2cef09c7e3b223aa8ef4994f73d769f21b524d483845d69c22d82b4535cf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:11:28.693955Z","signature_b64":"03w17xjiGhuwdw2mvs/ceJD3XatUtFps2Zgm9j6U6do3eQrkI/+hEwdK67L2GaijkPsx2vAkxnXLOHG2xLJHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2a2cef09c7e3b223aa8ef4994f73d769f21b524d483845d69c22d82b4535cf7","last_reissued_at":"2026-07-05T03:11:28.693601Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:11:28.693601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2103.13940","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oKp0iXXBeylPEe0JHLl0i4zcY0r/6jkffUrZb9leUL3zemvRcu88Iuulw1PvkLIDZBUyF9YsWFwVmEE/SUbtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:38:18.591436Z"},"content_sha256":"3073164c5c40169c7d0c88ba15a3ec4b85994d96366d7ef57d85a855f477188c","schema_version":"1.0","event_id":"sha256:3073164c5c40169c7d0c88ba15a3ec4b85994d96366d7ef57d85a855f477188c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YKRM54E4PY5SEOVI55EZJ5Z5O2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reachability and Matching in Single Crossing Minor Free Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Anish Mukherjee, Chetan Gupta, Raghunath Tewari, Rahul Jain, Samir Datta, Vimal Raj Sharma","submitted_at":"2021-03-25T16:01:13Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.13940","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.13940/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pkRmcktnffZ+k4JCvTZ2vi+m42sqi0MZHt+ipgeCzWR0aA2GW6grN3lYjvkuqbfyrVwmkUqmWC4viv0hYEGGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:38:18.591939Z"},"content_sha256":"e6f3e6c07b49ceeb291dcde2f31539e05abf76780e13a54453ff659932130ec1","schema_version":"1.0","event_id":"sha256:e6f3e6c07b49ceeb291dcde2f31539e05abf76780e13a54453ff659932130ec1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/bundle.json","state_url":"https://pith.science/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T23:38:18Z","links":{"resolver":"https://pith.science/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2","bundle":"https://pith.science/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/bundle.json","state":"https://pith.science/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKRM54E4PY5SEOVI55EZJ5Z5O2/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVZ0gfCUdz4o800GRvxgIMh+EKqFS/ssfmTqUDYPu/6DBaHBlEHN8gbtl+uNUvOemTuiqF/bQy4UsxMfD8tGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:38:18.597102Z","bundle_sha256":"71821588d26fd896c172b69e82153d7776acab315a254fe5dabae3a49d8a0ece"}}