{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MNQNFJL2CBMV2NYU6SK7GCTGWY","short_pith_number":"pith:MNQNFJL2","canonical_record":{"source":{"id":"1702.05567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-18T03:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"f7e6c03e8c6456ea870aa68fb8df65fb91b0c916db1e0cfeb84cce07f62f1845","abstract_canon_sha256":"f3ca64be22758db72c16a2cb14639b6c89074773ce8e08cdf4ac3fbc759f73d3"},"schema_version":"1.0"},"canonical_sha256":"6360d2a57a10595d3714f495f30a66b6396a418395ada4eb99da3ef9a608aa4e","source":{"kind":"arxiv","id":"1702.05567","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05567","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05567v2","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05567","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"MNQNFJL2CBMV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MNQNFJL2CBMV2NYU","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MNQNFJL2","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MNQNFJL2CBMV2NYU6SK7GCTGWY","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05567","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-18T03:46:55Z","cross_cats_sorted":[],"title_canon_sha256":"f7e6c03e8c6456ea870aa68fb8df65fb91b0c916db1e0cfeb84cce07f62f1845","abstract_canon_sha256":"f3ca64be22758db72c16a2cb14639b6c89074773ce8e08cdf4ac3fbc759f73d3"},"schema_version":"1.0"},"canonical_sha256":"6360d2a57a10595d3714f495f30a66b6396a418395ada4eb99da3ef9a608aa4e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:03.706181Z","signature_b64":"MintH8OwxYtcRsiDQEUS/gZFjLePOS80GYJA4rlFI/ECZlE6VpFg1EZ9TFUHAtj9oBkXxIDHkVztjGsUMs/ABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6360d2a57a10595d3714f495f30a66b6396a418395ada4eb99da3ef9a608aa4e","last_reissued_at":"2026-05-18T00:50:03.705569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:03.705569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05567","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":"2026-05-18T00:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UW+A2u+M8Q7Git63hDZGEWpaUbJ5QkI1UuB+SnQp7jDLJKYKQrKK0tZyTtW383ZD+QFlzlEJqepmcdBcC+G0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T03:06:28.923384Z"},"content_sha256":"1813c7729a4639b38d21af6383ee3fb39bbfce89b809d0ff311bf6f059dd1a05","schema_version":"1.0","event_id":"sha256:1813c7729a4639b38d21af6383ee3fb39bbfce89b809d0ff311bf6f059dd1a05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MNQNFJL2CBMV2NYU6SK7GCTGWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A $\\frac{3}{2}$-Approximation Algorithm for Tree Augmentation via Chv\\'atal-Gomory Cuts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jochen K\\\"onemann, Laura Sanit\\`a, Martin Gro{\\ss}, Samuel Fiorini","submitted_at":"2017-02-18T03:46:55Z","abstract_excerpt":"The weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c \\in \\mathbb{R}^L_{\\geq 1}$. The goal is to choose a minimum cost subset $S \\subseteq L$ such that $G = (V, E \\cup S)$ is $2$-edge-connected. In the unweighted case, that is, when we have $c_\\ell = 1$ for all $\\ell \\in L$, the problem is called the tree augmentation problem (TAP).\n  Both problems are known to be APX-hard, and the best known approximation factors are $2$ for WTAP by (Frederickson and J"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05567","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":"2026-05-18T00:50:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3k3cvGp5vNP42Q2/L/Jdx38of7MCRdT3VPj2X4cWdIPFi4iEh6cy6zAAe+XnmW0pLJFHOqHrXIxHk0H02HZzCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T03:06:28.924030Z"},"content_sha256":"2d7b8989e1807f1939eb0835f4070424e18ccc62eb17813cbc48db6127b8c889","schema_version":"1.0","event_id":"sha256:2d7b8989e1807f1939eb0835f4070424e18ccc62eb17813cbc48db6127b8c889"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/bundle.json","state_url":"https://pith.science/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/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":"2026-05-24T03:06:28Z","links":{"resolver":"https://pith.science/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY","bundle":"https://pith.science/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/bundle.json","state":"https://pith.science/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNQNFJL2CBMV2NYU6SK7GCTGWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MNQNFJL2CBMV2NYU6SK7GCTGWY","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":"f3ca64be22758db72c16a2cb14639b6c89074773ce8e08cdf4ac3fbc759f73d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-18T03:46:55Z","title_canon_sha256":"f7e6c03e8c6456ea870aa68fb8df65fb91b0c916db1e0cfeb84cce07f62f1845"},"schema_version":"1.0","source":{"id":"1702.05567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05567","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05567v2","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05567","created_at":"2026-05-18T00:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"MNQNFJL2CBMV","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MNQNFJL2CBMV2NYU","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MNQNFJL2","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:2d7b8989e1807f1939eb0835f4070424e18ccc62eb17813cbc48db6127b8c889","target":"graph","created_at":"2026-05-18T00:50:03Z","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 weighted tree augmentation problem (WTAP) is a fundamental network design problem. We are given an undirected tree $G = (V,E)$, an additional set of edges $L$ called links and a cost vector $c \\in \\mathbb{R}^L_{\\geq 1}$. The goal is to choose a minimum cost subset $S \\subseteq L$ such that $G = (V, E \\cup S)$ is $2$-edge-connected. In the unweighted case, that is, when we have $c_\\ell = 1$ for all $\\ell \\in L$, the problem is called the tree augmentation problem (TAP).\n  Both problems are known to be APX-hard, and the best known approximation factors are $2$ for WTAP by (Frederickson and J","authors_text":"Jochen K\\\"onemann, Laura Sanit\\`a, Martin Gro{\\ss}, Samuel Fiorini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-18T03:46:55Z","title":"A $\\frac{3}{2}$-Approximation Algorithm for Tree Augmentation via Chv\\'atal-Gomory Cuts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05567","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":"sha256:1813c7729a4639b38d21af6383ee3fb39bbfce89b809d0ff311bf6f059dd1a05","target":"record","created_at":"2026-05-18T00:50:03Z","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":"f3ca64be22758db72c16a2cb14639b6c89074773ce8e08cdf4ac3fbc759f73d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-02-18T03:46:55Z","title_canon_sha256":"f7e6c03e8c6456ea870aa68fb8df65fb91b0c916db1e0cfeb84cce07f62f1845"},"schema_version":"1.0","source":{"id":"1702.05567","kind":"arxiv","version":2}},"canonical_sha256":"6360d2a57a10595d3714f495f30a66b6396a418395ada4eb99da3ef9a608aa4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6360d2a57a10595d3714f495f30a66b6396a418395ada4eb99da3ef9a608aa4e","first_computed_at":"2026-05-18T00:50:03.705569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:03.705569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MintH8OwxYtcRsiDQEUS/gZFjLePOS80GYJA4rlFI/ECZlE6VpFg1EZ9TFUHAtj9oBkXxIDHkVztjGsUMs/ABw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:03.706181Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1813c7729a4639b38d21af6383ee3fb39bbfce89b809d0ff311bf6f059dd1a05","sha256:2d7b8989e1807f1939eb0835f4070424e18ccc62eb17813cbc48db6127b8c889"],"state_sha256":"8c3d99ff8a4364b328742d91d1df9a023080ce54f9c682840db100a18a038958"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CVUv+H/Lk4/op6yuQgofmR55coPPquJSWpbGl3xtlfPc9wc5KYmcoJJbCeHvhAR49UXIvz371IhWxQdASVtkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T03:06:28.927626Z","bundle_sha256":"f550aa59ccca10c6d67c4688a89c7cc6d54878f1bf3a065a07d254c239d105e2"}}