{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MPSPV675P5CKWMUMTL77WAZDFB","short_pith_number":"pith:MPSPV675","canonical_record":{"source":{"id":"1511.08152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-25T19:01:05Z","cross_cats_sorted":[],"title_canon_sha256":"6f6a47e83a1d6bd7aafb79094831d03f1bfb36495f59419e46348011a83c9ed2","abstract_canon_sha256":"0003a557202d4f8bece26bf85b4e563836a32e03552738830d93cb0cbe30aa43"},"schema_version":"1.0"},"canonical_sha256":"63e4fafbfd7f44ab328c9afffb03232853a3e5dd021c57be87df542355472480","source":{"kind":"arxiv","id":"1511.08152","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08152","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08152v1","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08152","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"MPSPV675P5CK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPSPV675P5CKWMUM","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPSPV675","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MPSPV675P5CKWMUMTL77WAZDFB","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08152","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-25T19:01:05Z","cross_cats_sorted":[],"title_canon_sha256":"6f6a47e83a1d6bd7aafb79094831d03f1bfb36495f59419e46348011a83c9ed2","abstract_canon_sha256":"0003a557202d4f8bece26bf85b4e563836a32e03552738830d93cb0cbe30aa43"},"schema_version":"1.0"},"canonical_sha256":"63e4fafbfd7f44ab328c9afffb03232853a3e5dd021c57be87df542355472480","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:00.622356Z","signature_b64":"+39u0EsmgzBk9h900VjrkHrGJQsKGkCY4wKL1IgaF40ON4FtP8zO8yd17QIoV/kQaiRDeA1EXdU7frSIYNofAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63e4fafbfd7f44ab328c9afffb03232853a3e5dd021c57be87df542355472480","last_reissued_at":"2026-05-18T00:03:00.621741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:00.621741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08152","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":"2026-05-18T00:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14q/Ftivo2x3pENoTmEXAxWWjMx+OH4PLCFKJpQohf+5QWI2+SEmqgp61CIBixEZW2o2mnQzksQPWTGdEux+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:35:58.896602Z"},"content_sha256":"b6b5b8c84063e7b8443852564b3667d1ccc9fc0559a8abead0ea496e2b0411af","schema_version":"1.0","event_id":"sha256:b6b5b8c84063e7b8443852564b3667d1ccc9fc0559a8abead0ea496e2b0411af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MPSPV675P5CKWMUMTL77WAZDFB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Max-Cut under Graph Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jon Lee, Viswanath Nagarajan, Xiangkun Shen","submitted_at":"2015-11-25T19:01:05Z","abstract_excerpt":"An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some graph-based constraint in G that maximizes the total weight of edges in the cut. The types of graph constraints we can handle include independent set, vertex cover, dominating set and connectivity. Our main results are for the case when G is a graph with bounded treewidth, where we obtain a 0.5-approximation algorithm. Our algorithm uses an LP relaxation based "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08152","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":"2026-05-18T00:03:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yYBGYYyVcUBmN9doCKnN6YMxm3SeRgiGLFkp50CfAbNE5qkNqVmeKzFDSYRohUJiMOlycmBGDySBNubZMTGVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:35:58.897378Z"},"content_sha256":"a2d49728bc2f4e510bddcbd096cfe437c902468628f3cea39836d46f058e92c2","schema_version":"1.0","event_id":"sha256:a2d49728bc2f4e510bddcbd096cfe437c902468628f3cea39836d46f058e92c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MPSPV675P5CKWMUMTL77WAZDFB/bundle.json","state_url":"https://pith.science/pith/MPSPV675P5CKWMUMTL77WAZDFB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MPSPV675P5CKWMUMTL77WAZDFB/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":"2026-06-07T01:35:58Z","links":{"resolver":"https://pith.science/pith/MPSPV675P5CKWMUMTL77WAZDFB","bundle":"https://pith.science/pith/MPSPV675P5CKWMUMTL77WAZDFB/bundle.json","state":"https://pith.science/pith/MPSPV675P5CKWMUMTL77WAZDFB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MPSPV675P5CKWMUMTL77WAZDFB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MPSPV675P5CKWMUMTL77WAZDFB","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":"0003a557202d4f8bece26bf85b4e563836a32e03552738830d93cb0cbe30aa43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-25T19:01:05Z","title_canon_sha256":"6f6a47e83a1d6bd7aafb79094831d03f1bfb36495f59419e46348011a83c9ed2"},"schema_version":"1.0","source":{"id":"1511.08152","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08152","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08152v1","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08152","created_at":"2026-05-18T00:03:00Z"},{"alias_kind":"pith_short_12","alias_value":"MPSPV675P5CK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MPSPV675P5CKWMUM","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MPSPV675","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:a2d49728bc2f4e510bddcbd096cfe437c902468628f3cea39836d46f058e92c2","target":"graph","created_at":"2026-05-18T00:03:00Z","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":"An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some graph-based constraint in G that maximizes the total weight of edges in the cut. The types of graph constraints we can handle include independent set, vertex cover, dominating set and connectivity. Our main results are for the case when G is a graph with bounded treewidth, where we obtain a 0.5-approximation algorithm. Our algorithm uses an LP relaxation based ","authors_text":"Jon Lee, Viswanath Nagarajan, Xiangkun Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-25T19:01:05Z","title":"Max-Cut under Graph Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08152","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:b6b5b8c84063e7b8443852564b3667d1ccc9fc0559a8abead0ea496e2b0411af","target":"record","created_at":"2026-05-18T00:03:00Z","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":"0003a557202d4f8bece26bf85b4e563836a32e03552738830d93cb0cbe30aa43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-11-25T19:01:05Z","title_canon_sha256":"6f6a47e83a1d6bd7aafb79094831d03f1bfb36495f59419e46348011a83c9ed2"},"schema_version":"1.0","source":{"id":"1511.08152","kind":"arxiv","version":1}},"canonical_sha256":"63e4fafbfd7f44ab328c9afffb03232853a3e5dd021c57be87df542355472480","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63e4fafbfd7f44ab328c9afffb03232853a3e5dd021c57be87df542355472480","first_computed_at":"2026-05-18T00:03:00.621741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:00.621741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+39u0EsmgzBk9h900VjrkHrGJQsKGkCY4wKL1IgaF40ON4FtP8zO8yd17QIoV/kQaiRDeA1EXdU7frSIYNofAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:00.622356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08152","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6b5b8c84063e7b8443852564b3667d1ccc9fc0559a8abead0ea496e2b0411af","sha256:a2d49728bc2f4e510bddcbd096cfe437c902468628f3cea39836d46f058e92c2"],"state_sha256":"d6797d3a6329d6f38db8f3fbc7bcf1b656deb700fbfd52be0eb2d49e8bfa4b30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUz545eCMnbaUF5jUrt8yXIk664XkXP585lowKAYiZ+Pn/d+j6W+AHrNqUXVZII6HHi05iLjurJXvxTzyg7MDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:35:58.901571Z","bundle_sha256":"9915d71dd3de7029d50ffccf46bb53a031f33cae73d586d167086999cde6efb6"}}