{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JSIAMCEX6NDIO4LVSMX7BAMING","short_pith_number":"pith:JSIAMCEX","canonical_record":{"source":{"id":"1501.00343","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2015-01-02T04:11:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bf1ca4359e81168845e5ff9077a8a46bbcd3660e74f7c2eb9a56adef52d9fb8a","abstract_canon_sha256":"5f4f7f6fe59c8f1b1fccdd59d696b8ac6aa4386d8013a192fb281a8ff5e0d482"},"schema_version":"1.0"},"canonical_sha256":"4c90060897f346877175932ff0818869b0f7c461586dee64d57ceee3fbc93e00","source":{"kind":"arxiv","id":"1501.00343","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00343","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00343v4","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00343","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"JSIAMCEX6NDI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSIAMCEX6NDIO4LV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSIAMCEX","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JSIAMCEX6NDIO4LVSMX7BAMING","target":"record","payload":{"canonical_record":{"source":{"id":"1501.00343","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2015-01-02T04:11:11Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bf1ca4359e81168845e5ff9077a8a46bbcd3660e74f7c2eb9a56adef52d9fb8a","abstract_canon_sha256":"5f4f7f6fe59c8f1b1fccdd59d696b8ac6aa4386d8013a192fb281a8ff5e0d482"},"schema_version":"1.0"},"canonical_sha256":"4c90060897f346877175932ff0818869b0f7c461586dee64d57ceee3fbc93e00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:35.436854Z","signature_b64":"4fznLTncaW6x8Bpoxu3+zEpX0bXgKaAFmfK/DmuXblEjnYm4/T6IEbNag4daBWSqYMcDFN46Gn3YO8+W2HH5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c90060897f346877175932ff0818869b0f7c461586dee64d57ceee3fbc93e00","last_reissued_at":"2026-05-18T01:19:35.436480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:35.436480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.00343","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rA1ons99LlgG4xwJL+oqwoqHz+3SHefeCPLwnHmHiEN1KcSOXDhV6Y3JRbBNpSjGRtP8ZPgHaVge9n/ASC03BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:40:46.147548Z"},"content_sha256":"bf1939cad85ab73720da768318cfc3f9dd87152ab06e1f0dc6fc731b851c8e11","schema_version":"1.0","event_id":"sha256:bf1939cad85ab73720da768318cfc3f9dd87152ab06e1f0dc6fc731b851c8e11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JSIAMCEX6NDIO4LVSMX7BAMING","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bicoloring covers for graphs and hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","submitted_at":"2015-01-02T04:11:11Z","abstract_excerpt":"Let the {\\it bicoloring cover number $\\chi^c(G)$} for a hypergraph $G(V,E)$ be the minimum number of bicolorings of vertices of $G$ such that every hyperedge $e\\in E$ of $G$ is properly bicolored in at least one of the $\\chi^c(G)$ bicolorings. We investigate the relationship between $\\chi^c(G)$, matchings, hitting sets, $\\alpha(G)$(independence number) and $\\chi(G)$ (chromatic number). We design a factor $O(\\frac{\\log n}{\\log \\log n-\\log \\log \\log n})$ approximation algorithm for computing a bicoloring cover. We define a new parameter for hypergraphs - \"cover independence number $\\gamma(G)$\" a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00343","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQ8jBZKgwPfq3qHGG8P9XTDhXh9ctKaooY33k4vCA5N7O9EDvN8Tbv36picoJt84DTwIUVN7ngI4qg3ko1wWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T20:40:46.147889Z"},"content_sha256":"ee17141b8b8b3980dd0d0bc20993c7e096748b1102d987b144bd96cd4d1ccf76","schema_version":"1.0","event_id":"sha256:ee17141b8b8b3980dd0d0bc20993c7e096748b1102d987b144bd96cd4d1ccf76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSIAMCEX6NDIO4LVSMX7BAMING/bundle.json","state_url":"https://pith.science/pith/JSIAMCEX6NDIO4LVSMX7BAMING/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSIAMCEX6NDIO4LVSMX7BAMING/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":"2026-06-29T20:40:46Z","links":{"resolver":"https://pith.science/pith/JSIAMCEX6NDIO4LVSMX7BAMING","bundle":"https://pith.science/pith/JSIAMCEX6NDIO4LVSMX7BAMING/bundle.json","state":"https://pith.science/pith/JSIAMCEX6NDIO4LVSMX7BAMING/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSIAMCEX6NDIO4LVSMX7BAMING/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JSIAMCEX6NDIO4LVSMX7BAMING","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":"5f4f7f6fe59c8f1b1fccdd59d696b8ac6aa4386d8013a192fb281a8ff5e0d482","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2015-01-02T04:11:11Z","title_canon_sha256":"bf1ca4359e81168845e5ff9077a8a46bbcd3660e74f7c2eb9a56adef52d9fb8a"},"schema_version":"1.0","source":{"id":"1501.00343","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00343","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00343v4","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00343","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"JSIAMCEX6NDI","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JSIAMCEX6NDIO4LV","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JSIAMCEX","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:ee17141b8b8b3980dd0d0bc20993c7e096748b1102d987b144bd96cd4d1ccf76","target":"graph","created_at":"2026-05-18T01:19:35Z","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"},"paper":{"abstract_excerpt":"Let the {\\it bicoloring cover number $\\chi^c(G)$} for a hypergraph $G(V,E)$ be the minimum number of bicolorings of vertices of $G$ such that every hyperedge $e\\in E$ of $G$ is properly bicolored in at least one of the $\\chi^c(G)$ bicolorings. We investigate the relationship between $\\chi^c(G)$, matchings, hitting sets, $\\alpha(G)$(independence number) and $\\chi(G)$ (chromatic number). We design a factor $O(\\frac{\\log n}{\\log \\log n-\\log \\log \\log n})$ approximation algorithm for computing a bicoloring cover. We define a new parameter for hypergraphs - \"cover independence number $\\gamma(G)$\" a","authors_text":"Sudebkumar Prasant Pal, Tapas Kumar Mishra","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2015-01-02T04:11:11Z","title":"Bicoloring covers for graphs and hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00343","kind":"arxiv","version":4},"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:bf1939cad85ab73720da768318cfc3f9dd87152ab06e1f0dc6fc731b851c8e11","target":"record","created_at":"2026-05-18T01:19:35Z","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":"5f4f7f6fe59c8f1b1fccdd59d696b8ac6aa4386d8013a192fb281a8ff5e0d482","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2015-01-02T04:11:11Z","title_canon_sha256":"bf1ca4359e81168845e5ff9077a8a46bbcd3660e74f7c2eb9a56adef52d9fb8a"},"schema_version":"1.0","source":{"id":"1501.00343","kind":"arxiv","version":4}},"canonical_sha256":"4c90060897f346877175932ff0818869b0f7c461586dee64d57ceee3fbc93e00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c90060897f346877175932ff0818869b0f7c461586dee64d57ceee3fbc93e00","first_computed_at":"2026-05-18T01:19:35.436480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:35.436480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4fznLTncaW6x8Bpoxu3+zEpX0bXgKaAFmfK/DmuXblEjnYm4/T6IEbNag4daBWSqYMcDFN46Gn3YO8+W2HH5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:35.436854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00343","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf1939cad85ab73720da768318cfc3f9dd87152ab06e1f0dc6fc731b851c8e11","sha256:ee17141b8b8b3980dd0d0bc20993c7e096748b1102d987b144bd96cd4d1ccf76"],"state_sha256":"b520f263d49af92f0939ef7bb24b4eef641365e956a344e25ae9ca31b6eaeb91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HgwhH6Usbk3lrVE+K4JyVBMUIpjG+pFGIPAO8Tf4ftr+hYR+JyS1OzgLcqO6yp2ueRYSlUlWKVrtfCNXYRTFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T20:40:46.149800Z","bundle_sha256":"aab8b9614979beb5e6780efb285261d4ac5928eb9182eb851b71ee7f9b9c7139"}}