{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5GL3XRHA6E3CS62R7N37C2J4CS","short_pith_number":"pith:5GL3XRHA","canonical_record":{"source":{"id":"1501.07460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-29T14:37:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"92ba95c181cd9d83bf311d3b60a6ef3dce6f9afa23f3f876d1622ffa955966d7","abstract_canon_sha256":"d8f5822a580e3add4dbe659b097811b76485aa82a96758c96dc3b263b2b2d18c"},"schema_version":"1.0"},"canonical_sha256":"e997bbc4e0f136297b51fb77f1693c149045f3aa3085252d8d1f0b58301fecf6","source":{"kind":"arxiv","id":"1501.07460","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07460","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07460v1","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07460","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"5GL3XRHA6E3C","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GL3XRHA6E3CS62R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GL3XRHA","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5GL3XRHA6E3CS62R7N37C2J4CS","target":"record","payload":{"canonical_record":{"source":{"id":"1501.07460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-29T14:37:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"92ba95c181cd9d83bf311d3b60a6ef3dce6f9afa23f3f876d1622ffa955966d7","abstract_canon_sha256":"d8f5822a580e3add4dbe659b097811b76485aa82a96758c96dc3b263b2b2d18c"},"schema_version":"1.0"},"canonical_sha256":"e997bbc4e0f136297b51fb77f1693c149045f3aa3085252d8d1f0b58301fecf6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:21.882445Z","signature_b64":"KQPzawnfaNrmDsxcUY2jBeap4to/UkhqbvMvui/Ep9Wgeuox/37MasI54wJ8fh5BkKvmve2tEJ7PkYoXCib+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e997bbc4e0f136297b51fb77f1693c149045f3aa3085252d8d1f0b58301fecf6","last_reissued_at":"2026-05-18T02:28:21.881947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:21.881947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.07460","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHZEDGVMQPLZGJFKL8q/xkK8ig6xEhAO+KWNJ1T1/XiBIdcbDzXoj0YJLWSxSf9rSVrRf5oAsMv0sXcj6skgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:19:21.108761Z"},"content_sha256":"2d01c4c89bd2ab2761d3d40a4aee372c7c2ff1725b672c5f2fdacf283de877ae","schema_version":"1.0","event_id":"sha256:2d01c4c89bd2ab2761d3d40a4aee372c7c2ff1725b672c5f2fdacf283de877ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5GL3XRHA6E3CS62R7N37C2J4CS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simple greedy 2-approximation algorithm for the maximum genus of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Martin Skoviera, Michal Kotrbcik","submitted_at":"2015-01-29T14:37:12Z","abstract_excerpt":"The maximum genus $\\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal results in a connected spanning subgraph of G. In this paper we prove that removing pairs of adjacent edges from G arbitrarily while retaining connectedness leads to at least $\\gamma_M(G)/2$ pairs of edges removed. This allows us to describe a greedy algorithm for the maximum genus of a graph; our algorithm returns an integer k such that $\\gamma_M(G)/2\\le k \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07460","kind":"arxiv","version":1},"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":"2026-05-18T02:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWjGVeTNYJkL9G+/44ODeqD9urkuceLCYdUhzhUmJG6oORF2eX7efisMoGxrm8lDyWDhX1EVGlXKQQ+aebUnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:19:21.109101Z"},"content_sha256":"29042828def5887b6c63c167bdda7946a40e4f9f9e4f380c261f9c4c20a416b8","schema_version":"1.0","event_id":"sha256:29042828def5887b6c63c167bdda7946a40e4f9f9e4f380c261f9c4c20a416b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5GL3XRHA6E3CS62R7N37C2J4CS/bundle.json","state_url":"https://pith.science/pith/5GL3XRHA6E3CS62R7N37C2J4CS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5GL3XRHA6E3CS62R7N37C2J4CS/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":"2026-06-23T15:19:21Z","links":{"resolver":"https://pith.science/pith/5GL3XRHA6E3CS62R7N37C2J4CS","bundle":"https://pith.science/pith/5GL3XRHA6E3CS62R7N37C2J4CS/bundle.json","state":"https://pith.science/pith/5GL3XRHA6E3CS62R7N37C2J4CS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5GL3XRHA6E3CS62R7N37C2J4CS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5GL3XRHA6E3CS62R7N37C2J4CS","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":"d8f5822a580e3add4dbe659b097811b76485aa82a96758c96dc3b263b2b2d18c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-29T14:37:12Z","title_canon_sha256":"92ba95c181cd9d83bf311d3b60a6ef3dce6f9afa23f3f876d1622ffa955966d7"},"schema_version":"1.0","source":{"id":"1501.07460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07460","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07460v1","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07460","created_at":"2026-05-18T02:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"5GL3XRHA6E3C","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5GL3XRHA6E3CS62R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5GL3XRHA","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:29042828def5887b6c63c167bdda7946a40e4f9f9e4f380c261f9c4c20a416b8","target":"graph","created_at":"2026-05-18T02:28:21Z","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":"The maximum genus $\\gamma_M(G)$ of a graph G is the largest genus of an orientable surface into which G has a cellular embedding. Combinatorially, it coincides with the maximum number of disjoint pairs of adjacent edges of G whose removal results in a connected spanning subgraph of G. In this paper we prove that removing pairs of adjacent edges from G arbitrarily while retaining connectedness leads to at least $\\gamma_M(G)/2$ pairs of edges removed. This allows us to describe a greedy algorithm for the maximum genus of a graph; our algorithm returns an integer k such that $\\gamma_M(G)/2\\le k \\","authors_text":"Martin Skoviera, Michal Kotrbcik","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-29T14:37:12Z","title":"Simple greedy 2-approximation algorithm for the maximum genus of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07460","kind":"arxiv","version":1},"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":"sha256:2d01c4c89bd2ab2761d3d40a4aee372c7c2ff1725b672c5f2fdacf283de877ae","target":"record","created_at":"2026-05-18T02:28:21Z","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":"d8f5822a580e3add4dbe659b097811b76485aa82a96758c96dc3b263b2b2d18c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-29T14:37:12Z","title_canon_sha256":"92ba95c181cd9d83bf311d3b60a6ef3dce6f9afa23f3f876d1622ffa955966d7"},"schema_version":"1.0","source":{"id":"1501.07460","kind":"arxiv","version":1}},"canonical_sha256":"e997bbc4e0f136297b51fb77f1693c149045f3aa3085252d8d1f0b58301fecf6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e997bbc4e0f136297b51fb77f1693c149045f3aa3085252d8d1f0b58301fecf6","first_computed_at":"2026-05-18T02:28:21.881947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:21.881947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQPzawnfaNrmDsxcUY2jBeap4to/UkhqbvMvui/Ep9Wgeuox/37MasI54wJ8fh5BkKvmve2tEJ7PkYoXCib+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:21.882445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d01c4c89bd2ab2761d3d40a4aee372c7c2ff1725b672c5f2fdacf283de877ae","sha256:29042828def5887b6c63c167bdda7946a40e4f9f9e4f380c261f9c4c20a416b8"],"state_sha256":"d897d86350df0abd21ce383776e23ba024570303355c7f09431128dc3ca63023"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qqjEnLaiWaOKejotPIiD/c+8WnCCAKs+thsWNxs0XD5n/hfGPfeKguFDWuTB6fznO4k1QOF3lultjHlOI8UpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:19:21.111102Z","bundle_sha256":"ef03a2d942af4be1ce43e71ccc6ff742c446973ce2e36af96994d1d46d15042f"}}