{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RKXZSB6ZKV2MF365NYQ5GIBQ2S","short_pith_number":"pith:RKXZSB6Z","canonical_record":{"source":{"id":"1706.01609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-06T05:22:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c7c118391bab0c2718b697078fe43f05ab67bb8731aa0b885a69a967c192857f","abstract_canon_sha256":"3096beeabfb1ad132f51ca26db0ff9833ac96d0a8a027f8cfaee3f5415be5588"},"schema_version":"1.0"},"canonical_sha256":"8aaf9907d95574c2efdd6e21d32030d4bb3c380e260219c7cac493213c96892f","source":{"kind":"arxiv","id":"1706.01609","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01609","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01609v1","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01609","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"RKXZSB6ZKV2M","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKXZSB6ZKV2MF365","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKXZSB6Z","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RKXZSB6ZKV2MF365NYQ5GIBQ2S","target":"record","payload":{"canonical_record":{"source":{"id":"1706.01609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-06T05:22:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c7c118391bab0c2718b697078fe43f05ab67bb8731aa0b885a69a967c192857f","abstract_canon_sha256":"3096beeabfb1ad132f51ca26db0ff9833ac96d0a8a027f8cfaee3f5415be5588"},"schema_version":"1.0"},"canonical_sha256":"8aaf9907d95574c2efdd6e21d32030d4bb3c380e260219c7cac493213c96892f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:56.543916Z","signature_b64":"k+dBMphFk+KQQcGPecIGMPWFU5z+VFsmtpLsAH6xHgmUPb9GFCKjIHA024o7EnKfbHMSr0MfprwlTqPvdVy4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8aaf9907d95574c2efdd6e21d32030d4bb3c380e260219c7cac493213c96892f","last_reissued_at":"2026-05-18T00:42:56.543224Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:56.543224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.01609","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":"2026-05-18T00:42:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKRt31luy2dth7uqzdIRQuRxXS4GEXARPjFS/LteGw+qIOm1oztj3l+Hx5qpimTUsV8FZ6tlB13kcsmZraqVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:10:32.551696Z"},"content_sha256":"8e72fcdf83e7166cbd7e366a89f62a3321401325408564611753b3a353db217a","schema_version":"1.0","event_id":"sha256:8e72fcdf83e7166cbd7e366a89f62a3321401325408564611753b3a353db217a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RKXZSB6ZKV2MF365NYQ5GIBQ2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Upper Bound of 7n/6 for the Minimum Size 2EC on Cubic 3-Edge Connected Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Philippe Legault","submitted_at":"2017-06-06T05:22:35Z","abstract_excerpt":"In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graph G=(V, E), with n=|V| allows a 2EC solution for G of size at most 7n/6, which improves upon Boyd, Iwata and Takazawa's guarantee of 6n/5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01609","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":"2026-05-18T00:42:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7E0eHeVRs30dkjOecTWiUlBc0Rc4c3FI4C0VZ+rBnhqN7qB6liwQkHUZqk6mOjfEnubTbpgR8rHC8gd0oAzwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T12:10:32.552039Z"},"content_sha256":"0e4384f3101ca229d215b0c7cc9cef9d04dec03c8cdd17a9125a2289f596b2af","schema_version":"1.0","event_id":"sha256:0e4384f3101ca229d215b0c7cc9cef9d04dec03c8cdd17a9125a2289f596b2af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/bundle.json","state_url":"https://pith.science/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/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":"2026-06-24T12:10:32Z","links":{"resolver":"https://pith.science/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S","bundle":"https://pith.science/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/bundle.json","state":"https://pith.science/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RKXZSB6ZKV2MF365NYQ5GIBQ2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RKXZSB6ZKV2MF365NYQ5GIBQ2S","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":"3096beeabfb1ad132f51ca26db0ff9833ac96d0a8a027f8cfaee3f5415be5588","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-06T05:22:35Z","title_canon_sha256":"c7c118391bab0c2718b697078fe43f05ab67bb8731aa0b885a69a967c192857f"},"schema_version":"1.0","source":{"id":"1706.01609","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01609","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01609v1","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01609","created_at":"2026-05-18T00:42:56Z"},{"alias_kind":"pith_short_12","alias_value":"RKXZSB6ZKV2M","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RKXZSB6ZKV2MF365","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RKXZSB6Z","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:0e4384f3101ca229d215b0c7cc9cef9d04dec03c8cdd17a9125a2289f596b2af","target":"graph","created_at":"2026-05-18T00:42:56Z","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":"In this paper, we study the minimum size 2-edge connected spanning subgraph problem (henceforth 2EC) and show that every 3-edge connected cubic graph G=(V, E), with n=|V| allows a 2EC solution for G of size at most 7n/6, which improves upon Boyd, Iwata and Takazawa's guarantee of 6n/5.","authors_text":"Philippe Legault","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-06T05:22:35Z","title":"An Upper Bound of 7n/6 for the Minimum Size 2EC on Cubic 3-Edge Connected Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01609","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":"sha256:8e72fcdf83e7166cbd7e366a89f62a3321401325408564611753b3a353db217a","target":"record","created_at":"2026-05-18T00:42:56Z","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":"3096beeabfb1ad132f51ca26db0ff9833ac96d0a8a027f8cfaee3f5415be5588","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-06T05:22:35Z","title_canon_sha256":"c7c118391bab0c2718b697078fe43f05ab67bb8731aa0b885a69a967c192857f"},"schema_version":"1.0","source":{"id":"1706.01609","kind":"arxiv","version":1}},"canonical_sha256":"8aaf9907d95574c2efdd6e21d32030d4bb3c380e260219c7cac493213c96892f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aaf9907d95574c2efdd6e21d32030d4bb3c380e260219c7cac493213c96892f","first_computed_at":"2026-05-18T00:42:56.543224Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:56.543224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k+dBMphFk+KQQcGPecIGMPWFU5z+VFsmtpLsAH6xHgmUPb9GFCKjIHA024o7EnKfbHMSr0MfprwlTqPvdVy4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:56.543916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01609","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e72fcdf83e7166cbd7e366a89f62a3321401325408564611753b3a353db217a","sha256:0e4384f3101ca229d215b0c7cc9cef9d04dec03c8cdd17a9125a2289f596b2af"],"state_sha256":"7d904887cc95540ea094482e06f78792e06934cd6b8228f0aac8919806942ffe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"51kRKg4+CTBk0EJ4ik8xPDzOerRKWjGxnGk/Q//R+cyv8Zo47PBB4CW3nZFMaSNlnam2etcsvNvXgbw/z0XxDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T12:10:32.553980Z","bundle_sha256":"63b2218413b423fda4f00a95abd8e0d3ad8c641b0e462e6ef4bb81f1f7fa3220"}}