{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QBASRGN7UVGT3ZZVNWGLNMHIRH","short_pith_number":"pith:QBASRGN7","canonical_record":{"source":{"id":"1908.07584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-20T19:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"2b0642e77af2f2ed3ab7c4dc4d766dc4fdf81fdacfb42af4e1238ec6d3b698a2","abstract_canon_sha256":"df68829a41f1fff49714f361c574ee55c641da0f8fd0fcc0e1a4a061a8a1a0ba"},"schema_version":"1.0"},"canonical_sha256":"80412899bfa54d3de7356d8cb6b0e889d12cc7c1168c60e017293d4888704b24","source":{"kind":"arxiv","id":"1908.07584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07584","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07584v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07584","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"QBASRGN7UVGT","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"QBASRGN7UVGT3ZZV","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"QBASRGN7","created_at":"2026-07-04T23:58:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QBASRGN7UVGT3ZZVNWGLNMHIRH","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07584","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-20T19:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"2b0642e77af2f2ed3ab7c4dc4d766dc4fdf81fdacfb42af4e1238ec6d3b698a2","abstract_canon_sha256":"df68829a41f1fff49714f361c574ee55c641da0f8fd0fcc0e1a4a061a8a1a0ba"},"schema_version":"1.0"},"canonical_sha256":"80412899bfa54d3de7356d8cb6b0e889d12cc7c1168c60e017293d4888704b24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:59.383860Z","signature_b64":"gAjMK3GLLukMS2IWENcSVSyidTH3QseyOUHYPwUkyZV9ZlUOK3XW0e+q1y0o0bFBJouTI1yD46hQ/oJox7OZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80412899bfa54d3de7356d8cb6b0e889d12cc7c1168c60e017293d4888704b24","last_reissued_at":"2026-07-04T23:58:59.383515Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:59.383515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07584","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":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IwUvzrnOEQ55qKCqrzoOgkA0biHn0vYpN6EhHSBywzsf55HqOmdJlrPyX4aa45Bb8n1N5VN6sZMJQ6Dh3rdICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:45:46.583816Z"},"content_sha256":"c27140be52d97f42ce73207b4a098d23f599ad313e85848c9689264a94f89f31","schema_version":"1.0","event_id":"sha256:c27140be52d97f42ce73207b4a098d23f599ad313e85848c9689264a94f89f31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QBASRGN7UVGT3ZZVNWGLNMHIRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimization Bounds from the Branching Dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. G. Benade, J. N. Hooker","submitted_at":"2019-08-20T19:45:46Z","abstract_excerpt":"We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a \"worst-bound\" local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07584","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07584/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pe3b+CVm3gnwPYwi6vPQyeGuM061NB7WyiAnSbwZIdKXjjivHktRv/BG5kNtehKH7OKCrtI5eSX6yFRfq1WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:45:46.584321Z"},"content_sha256":"17131da27b6556fcfe2559473f5d12ce42cf38192bb5c5836cf451c9da9844a3","schema_version":"1.0","event_id":"sha256:17131da27b6556fcfe2559473f5d12ce42cf38192bb5c5836cf451c9da9844a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/bundle.json","state_url":"https://pith.science/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/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":"2026-08-16T07:45:46Z","links":{"resolver":"https://pith.science/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH","bundle":"https://pith.science/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/bundle.json","state":"https://pith.science/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBASRGN7UVGT3ZZVNWGLNMHIRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QBASRGN7UVGT3ZZVNWGLNMHIRH","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":"df68829a41f1fff49714f361c574ee55c641da0f8fd0fcc0e1a4a061a8a1a0ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-20T19:45:46Z","title_canon_sha256":"2b0642e77af2f2ed3ab7c4dc4d766dc4fdf81fdacfb42af4e1238ec6d3b698a2"},"schema_version":"1.0","source":{"id":"1908.07584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07584","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07584v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07584","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"QBASRGN7UVGT","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"QBASRGN7UVGT3ZZV","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"QBASRGN7","created_at":"2026-07-04T23:58:59Z"}],"graph_snapshots":[{"event_id":"sha256:17131da27b6556fcfe2559473f5d12ce42cf38192bb5c5836cf451c9da9844a3","target":"graph","created_at":"2026-07-04T23:58:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07584/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with the minimum bandwidth problem. The method strengthens a known bound for a given problem by formulating a dual problem whose feasible solutions are partial branching trees. It solves the dual problem with a \"worst-bound\" local search heuristic that explores neighboring partial trees. After proving some optimality properties of the heuristic, we show that it ","authors_text":"J. G. Benade, J. N. Hooker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-20T19:45:46Z","title":"Optimization Bounds from the Branching Dual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07584","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:c27140be52d97f42ce73207b4a098d23f599ad313e85848c9689264a94f89f31","target":"record","created_at":"2026-07-04T23:58:59Z","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":"df68829a41f1fff49714f361c574ee55c641da0f8fd0fcc0e1a4a061a8a1a0ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-08-20T19:45:46Z","title_canon_sha256":"2b0642e77af2f2ed3ab7c4dc4d766dc4fdf81fdacfb42af4e1238ec6d3b698a2"},"schema_version":"1.0","source":{"id":"1908.07584","kind":"arxiv","version":1}},"canonical_sha256":"80412899bfa54d3de7356d8cb6b0e889d12cc7c1168c60e017293d4888704b24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80412899bfa54d3de7356d8cb6b0e889d12cc7c1168c60e017293d4888704b24","first_computed_at":"2026-07-04T23:58:59.383515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:59.383515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gAjMK3GLLukMS2IWENcSVSyidTH3QseyOUHYPwUkyZV9ZlUOK3XW0e+q1y0o0bFBJouTI1yD46hQ/oJox7OZAg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:59.383860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c27140be52d97f42ce73207b4a098d23f599ad313e85848c9689264a94f89f31","sha256:17131da27b6556fcfe2559473f5d12ce42cf38192bb5c5836cf451c9da9844a3"],"state_sha256":"5d37b77eaa5528e2ad3ddfeec1cbb8c038ccb063f8b845d39452e024761ae382"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEy2uRUbaLnPT1mk5cBy6aQTTRLE5mnVOevy9EIOAs/xI13bqwydPL4JO3yB2ShNSH/2z2ZCSCVka/HuHNUXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:45:46.589011Z","bundle_sha256":"9939a7d790322aa06ec9d282815b99d708274b4f25075fedcb4d4d2e3b40f41f"}}