{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AQFQDIVKZS3MSVMZ2E2TNCTEI5","short_pith_number":"pith:AQFQDIVK","canonical_record":{"source":{"id":"1706.06565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-20T17:41:43Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"abeaabbecaa08b997a3790bdaff2a1dc03a5c3b27fa3b46fc993afe8db4059e9","abstract_canon_sha256":"395165fe353307e010733264df6eef76b9cd43b1a54d52f04739e0b652c03c5f"},"schema_version":"1.0"},"canonical_sha256":"040b01a2aaccb6c95599d135368a644754e0a4bddc815897186b9473ef850bcc","source":{"kind":"arxiv","id":"1706.06565","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06565","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06565v1","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06565","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"AQFQDIVKZS3M","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQFQDIVKZS3MSVMZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQFQDIVK","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AQFQDIVKZS3MSVMZ2E2TNCTEI5","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-20T17:41:43Z","cross_cats_sorted":["cs.DS","math.OC"],"title_canon_sha256":"abeaabbecaa08b997a3790bdaff2a1dc03a5c3b27fa3b46fc993afe8db4059e9","abstract_canon_sha256":"395165fe353307e010733264df6eef76b9cd43b1a54d52f04739e0b652c03c5f"},"schema_version":"1.0"},"canonical_sha256":"040b01a2aaccb6c95599d135368a644754e0a4bddc815897186b9473ef850bcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:02.910165Z","signature_b64":"iyL71YvW6BluI0Jyn5GGOw9L2sGQhpegu+0BtHvULJu0Gmi1JRYjtSxNlMyQiUN/S6+SzljkiqckYyu5OFU6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"040b01a2aaccb6c95599d135368a644754e0a4bddc815897186b9473ef850bcc","last_reissued_at":"2026-05-18T00:42:02.909626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:02.909626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06565","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":"2026-05-18T00:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Su/dIvW/q4eN9af0a+A/w5weODJ0GEFKPwgtaN/NcV9mtBsOl5aA51rOuJaYZ79VqFpV04KKI1q9j28Ckh6BCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:42:45.173895Z"},"content_sha256":"dc5dd8d6d0581914e61ef4a1707366bf4cbf0cd1a46842a772cb643167196c98","schema_version":"1.0","event_id":"sha256:dc5dd8d6d0581914e61ef4a1707366bf4cbf0cd1a46842a772cb643167196c98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AQFQDIVKZS3MSVMZ2E2TNCTEI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Integrality Gap of the Prize-Collecting Steiner Forest LP","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.DM","authors_text":"Chaitanya Swamy, Jens Vygen, Jochen K\\\"onemann, Kanstantsin Pashkovich, Neil Olver, R. Ravi","submitted_at":"2017-06-20T17:41:43Z","abstract_excerpt":"In the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\\{c_e\\geq 0\\}_{e\\in E}$, terminal pairs $\\{(s_i,t_i)\\}_{i=1}^k$, and penalties $\\{\\pi_i\\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\\sum_{i: (s_i,t_i)\\text{ not connected in }F}\\pi_i$. The Steiner forest problem can be viewed as the special case where $\\pi_i=\\infty$ for all $i$. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF is at most 2. We dispel this belief by sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06565","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":"2026-05-18T00:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdJo845+Rwlkt4dzaw+lgrgMiDKcdKRjGMQzpqGVwc510ss6Z9ibyMtn7es6t/0MUVSvODHHEWGPU5UUrz0gDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T15:42:45.174249Z"},"content_sha256":"95bba6d3bf9246485a7c0c7f7280e4d726ec3cc8e8675eedc0ef55a9c4a9f9c3","schema_version":"1.0","event_id":"sha256:95bba6d3bf9246485a7c0c7f7280e4d726ec3cc8e8675eedc0ef55a9c4a9f9c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/bundle.json","state_url":"https://pith.science/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/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":"2026-05-29T15:42:45Z","links":{"resolver":"https://pith.science/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5","bundle":"https://pith.science/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/bundle.json","state":"https://pith.science/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AQFQDIVKZS3MSVMZ2E2TNCTEI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AQFQDIVKZS3MSVMZ2E2TNCTEI5","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":"395165fe353307e010733264df6eef76b9cd43b1a54d52f04739e0b652c03c5f","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-20T17:41:43Z","title_canon_sha256":"abeaabbecaa08b997a3790bdaff2a1dc03a5c3b27fa3b46fc993afe8db4059e9"},"schema_version":"1.0","source":{"id":"1706.06565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06565","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06565v1","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06565","created_at":"2026-05-18T00:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"AQFQDIVKZS3M","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AQFQDIVKZS3MSVMZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AQFQDIVK","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:95bba6d3bf9246485a7c0c7f7280e4d726ec3cc8e8675eedc0ef55a9c4a9f9c3","target":"graph","created_at":"2026-05-18T00:42:02Z","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 the prize-collecting Steiner forest (PCSF) problem, we are given an undirected graph $G=(V,E)$, edge costs $\\{c_e\\geq 0\\}_{e\\in E}$, terminal pairs $\\{(s_i,t_i)\\}_{i=1}^k$, and penalties $\\{\\pi_i\\}_{i=1}^k$ for each terminal pair; the goal is to find a forest $F$ to minimize $c(F)+\\sum_{i: (s_i,t_i)\\text{ not connected in }F}\\pi_i$. The Steiner forest problem can be viewed as the special case where $\\pi_i=\\infty$ for all $i$. It was widely believed that the integrality gap of the natural (and well-studied) linear-programming (LP) relaxation for PCSF is at most 2. We dispel this belief by sh","authors_text":"Chaitanya Swamy, Jens Vygen, Jochen K\\\"onemann, Kanstantsin Pashkovich, Neil Olver, R. Ravi","cross_cats":["cs.DS","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-20T17:41:43Z","title":"On the Integrality Gap of the Prize-Collecting Steiner Forest LP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06565","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:dc5dd8d6d0581914e61ef4a1707366bf4cbf0cd1a46842a772cb643167196c98","target":"record","created_at":"2026-05-18T00:42:02Z","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":"395165fe353307e010733264df6eef76b9cd43b1a54d52f04739e0b652c03c5f","cross_cats_sorted":["cs.DS","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-20T17:41:43Z","title_canon_sha256":"abeaabbecaa08b997a3790bdaff2a1dc03a5c3b27fa3b46fc993afe8db4059e9"},"schema_version":"1.0","source":{"id":"1706.06565","kind":"arxiv","version":1}},"canonical_sha256":"040b01a2aaccb6c95599d135368a644754e0a4bddc815897186b9473ef850bcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"040b01a2aaccb6c95599d135368a644754e0a4bddc815897186b9473ef850bcc","first_computed_at":"2026-05-18T00:42:02.909626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:02.909626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iyL71YvW6BluI0Jyn5GGOw9L2sGQhpegu+0BtHvULJu0Gmi1JRYjtSxNlMyQiUN/S6+SzljkiqckYyu5OFU6BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:02.910165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc5dd8d6d0581914e61ef4a1707366bf4cbf0cd1a46842a772cb643167196c98","sha256:95bba6d3bf9246485a7c0c7f7280e4d726ec3cc8e8675eedc0ef55a9c4a9f9c3"],"state_sha256":"5403725f6d6a9c84bf7ebaeb5782df2f3f6e60607751700afcfbb1c285cea300"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c6vEzzNwjLYkvJZAj8MXH+iTB6/ZWW1XKdozNdwrGP5oxe6bebQdjwbOdPkTNiFNukLLwVKDS2XR2GipgMcACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T15:42:45.176406Z","bundle_sha256":"c20dc214b46ea039acbabf81fcf2d78759acdccd12e59371400e7cc25c4efb63"}}