{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:M65BXSBBETR4KMVHYIWAN6D2KW","short_pith_number":"pith:M65BXSBB","canonical_record":{"source":{"id":"1512.08070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-26T04:12:11Z","cross_cats_sorted":[],"title_canon_sha256":"ef61d3dde7409870812f3e41bdbc4cf7a108cdec90c953b3cd4f07003ad15245","abstract_canon_sha256":"5f36ee8be6b466f91651ba629594a79d2431030a165e42a80d4a46d38e430731"},"schema_version":"1.0"},"canonical_sha256":"67ba1bc82124e3c532a7c22c06f87a558d9a2c3fe3de2ab5cc6652db40c9a2cb","source":{"kind":"arxiv","id":"1512.08070","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08070","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08070v2","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08070","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"M65BXSBBETR4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M65BXSBBETR4KMVH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M65BXSBB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:M65BXSBBETR4KMVHYIWAN6D2KW","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08070","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-26T04:12:11Z","cross_cats_sorted":[],"title_canon_sha256":"ef61d3dde7409870812f3e41bdbc4cf7a108cdec90c953b3cd4f07003ad15245","abstract_canon_sha256":"5f36ee8be6b466f91651ba629594a79d2431030a165e42a80d4a46d38e430731"},"schema_version":"1.0"},"canonical_sha256":"67ba1bc82124e3c532a7c22c06f87a558d9a2c3fe3de2ab5cc6652db40c9a2cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:36.653069Z","signature_b64":"DJgkagga0KP9QkDKRqqqQUrI1FxsclcsXQpi++q3KNTMd9QecETwe9q+Rt/mDjfoGmwugDs8IFIiIRyXB7xGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ba1bc82124e3c532a7c22c06f87a558d9a2c3fe3de2ab5cc6652db40c9a2cb","last_reissued_at":"2026-05-18T01:21:36.652548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:36.652548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08070","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VWVotw7UCGRcFG8B+W5naw0au6ELwaVxOa63MVyde57Fsap+UYeAuMjJmB7jHz3wSpmewOXHJHNR7gTExQULDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:51:17.565540Z"},"content_sha256":"674ab043095088ad961cfff27de0dfd0bfee67288d19675f29c2a9c0916021f8","schema_version":"1.0","event_id":"sha256:674ab043095088ad961cfff27de0dfd0bfee67288d19675f29c2a9c0916021f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:M65BXSBBETR4KMVHYIWAN6D2KW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward a 6/5 Bound for the Minimum Cost 2-Edge Connected Spanning Subgraph Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Philippe Legault, Sylvia Boyd","submitted_at":"2015-12-26T04:12:11Z","abstract_excerpt":"Given a complete graph $K_{n}=(V, E)$ with non-negative edge costs $c\\in {\\mathbb R}^{E}$, the problem $2EC$ is that of finding a 2-edge connected spanning multi-subgraph of $K_{n}$ of minimum cost. The integrality gap $\\alpha\\text{2EC}$ of the linear programming relaxation $\\text{2EC}^{\\text{LP}}$ for $2EC$ has been conjectured to be $\\frac{6}{5}$, although currently we only know that $\\frac{6}{5}\\leq\\alpha\\text{2EC}\\leq\\frac{3}{2}$. In this paper, we explore the idea of using the structure of solutions for $\\text{2EC}^{\\text{LP}}$ and the concept of convex combination to obtain improved boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08070","kind":"arxiv","version":2},"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":"2026-05-18T01:21:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xTVzC6Jl55xDx1dkXzm89Gm2DxyKrSm/bXzlgKUYWT6QGnwV8JIRQS0BSUpGrR/L0+6WV7cRDBG5SjESbwVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T07:51:17.565897Z"},"content_sha256":"cd69d0e209a8669d9f62d83d1562a41e696a7616b01c2e85d8104f03bd1014dd","schema_version":"1.0","event_id":"sha256:cd69d0e209a8669d9f62d83d1562a41e696a7616b01c2e85d8104f03bd1014dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M65BXSBBETR4KMVHYIWAN6D2KW/bundle.json","state_url":"https://pith.science/pith/M65BXSBBETR4KMVHYIWAN6D2KW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M65BXSBBETR4KMVHYIWAN6D2KW/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":"2026-06-24T07:51:17Z","links":{"resolver":"https://pith.science/pith/M65BXSBBETR4KMVHYIWAN6D2KW","bundle":"https://pith.science/pith/M65BXSBBETR4KMVHYIWAN6D2KW/bundle.json","state":"https://pith.science/pith/M65BXSBBETR4KMVHYIWAN6D2KW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M65BXSBBETR4KMVHYIWAN6D2KW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:M65BXSBBETR4KMVHYIWAN6D2KW","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":"5f36ee8be6b466f91651ba629594a79d2431030a165e42a80d4a46d38e430731","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-26T04:12:11Z","title_canon_sha256":"ef61d3dde7409870812f3e41bdbc4cf7a108cdec90c953b3cd4f07003ad15245"},"schema_version":"1.0","source":{"id":"1512.08070","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08070","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08070v2","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08070","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"M65BXSBBETR4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"M65BXSBBETR4KMVH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"M65BXSBB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:cd69d0e209a8669d9f62d83d1562a41e696a7616b01c2e85d8104f03bd1014dd","target":"graph","created_at":"2026-05-18T01:21:36Z","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":"Given a complete graph $K_{n}=(V, E)$ with non-negative edge costs $c\\in {\\mathbb R}^{E}$, the problem $2EC$ is that of finding a 2-edge connected spanning multi-subgraph of $K_{n}$ of minimum cost. The integrality gap $\\alpha\\text{2EC}$ of the linear programming relaxation $\\text{2EC}^{\\text{LP}}$ for $2EC$ has been conjectured to be $\\frac{6}{5}$, although currently we only know that $\\frac{6}{5}\\leq\\alpha\\text{2EC}\\leq\\frac{3}{2}$. In this paper, we explore the idea of using the structure of solutions for $\\text{2EC}^{\\text{LP}}$ and the concept of convex combination to obtain improved boun","authors_text":"Philippe Legault, Sylvia Boyd","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-26T04:12:11Z","title":"Toward a 6/5 Bound for the Minimum Cost 2-Edge Connected Spanning Subgraph Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08070","kind":"arxiv","version":2},"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":"sha256:674ab043095088ad961cfff27de0dfd0bfee67288d19675f29c2a9c0916021f8","target":"record","created_at":"2026-05-18T01:21:36Z","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":"5f36ee8be6b466f91651ba629594a79d2431030a165e42a80d4a46d38e430731","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-26T04:12:11Z","title_canon_sha256":"ef61d3dde7409870812f3e41bdbc4cf7a108cdec90c953b3cd4f07003ad15245"},"schema_version":"1.0","source":{"id":"1512.08070","kind":"arxiv","version":2}},"canonical_sha256":"67ba1bc82124e3c532a7c22c06f87a558d9a2c3fe3de2ab5cc6652db40c9a2cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ba1bc82124e3c532a7c22c06f87a558d9a2c3fe3de2ab5cc6652db40c9a2cb","first_computed_at":"2026-05-18T01:21:36.652548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:36.652548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DJgkagga0KP9QkDKRqqqQUrI1FxsclcsXQpi++q3KNTMd9QecETwe9q+Rt/mDjfoGmwugDs8IFIiIRyXB7xGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:36.653069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08070","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:674ab043095088ad961cfff27de0dfd0bfee67288d19675f29c2a9c0916021f8","sha256:cd69d0e209a8669d9f62d83d1562a41e696a7616b01c2e85d8104f03bd1014dd"],"state_sha256":"f36494138b896a42ff9b15881fceabad7a593a1d792b33e6fe8a1b1debd5137a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GAoQ0SwSN2PqPCPakn9iHGnXw9eUUEvhxyDSF+04G4/dA4vMCV9qEhsoJdfN88Gv+G9Et3V3p4eVAxMvSUBpBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T07:51:17.567897Z","bundle_sha256":"4bd327bb471856b1ba7130faee7feb1eb431fdd5c1be5b7fe042bb53d5c49239"}}