{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MC4UCNIRCCGZ3C642WEXAZKIAX","short_pith_number":"pith:MC4UCNIR","canonical_record":{"source":{"id":"1211.4611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-19T22:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"4c0ddfdadd84a0dd1862b417a428bf1158bd3b46540544308b97729693d14e48","abstract_canon_sha256":"ffa5afe9663dde4abcf76e355db37d5bb61c60ea8b123b7f93b541551a0c8701"},"schema_version":"1.0"},"canonical_sha256":"60b9413511108d9d8bdcd58970654805c61a95ec7de3b40351bdfb7ab99ddd2e","source":{"kind":"arxiv","id":"1211.4611","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4611","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4611v3","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4611","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"MC4UCNIRCCGZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MC4UCNIRCCGZ3C64","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MC4UCNIR","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MC4UCNIRCCGZ3C642WEXAZKIAX","target":"record","payload":{"canonical_record":{"source":{"id":"1211.4611","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-19T22:28:08Z","cross_cats_sorted":[],"title_canon_sha256":"4c0ddfdadd84a0dd1862b417a428bf1158bd3b46540544308b97729693d14e48","abstract_canon_sha256":"ffa5afe9663dde4abcf76e355db37d5bb61c60ea8b123b7f93b541551a0c8701"},"schema_version":"1.0"},"canonical_sha256":"60b9413511108d9d8bdcd58970654805c61a95ec7de3b40351bdfb7ab99ddd2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:23.749336Z","signature_b64":"2c9vNhlZGEikN81kEPYmD//1FwdSy1W7gNGoszhRQIgCxB3JJGmwPs2PxKTt4ppuEDWV2jHhrOsR+4oMie8SCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b9413511108d9d8bdcd58970654805c61a95ec7de3b40351bdfb7ab99ddd2e","last_reissued_at":"2026-05-18T01:18:23.748836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:23.748836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.4611","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IjUMgVrtUQhf8iqHS9M/CkkUMEM3yb81ORJ6D/aTh4htpiWsfo5tyzCrvFfxuDPLGmt03+vCY4yPvDjYJXqJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:06.661094Z"},"content_sha256":"a80ad34182185fa8f4257970f46cf2ef642e141cef0b3d47b1392e6e4c7d66db","schema_version":"1.0","event_id":"sha256:a80ad34182185fa8f4257970f46cf2ef642e141cef0b3d47b1392e6e4c7d66db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MC4UCNIRCCGZ3C642WEXAZKIAX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A variational approach for continuous supply chain networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Ke Han, Tao Yao, Terry L. Friesz","submitted_at":"2012-11-19T22:28:08Z","abstract_excerpt":"We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896--920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433--460] and [D. Armbruster, C. De Beer, M. Freitag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104--114]. A model was proposed for such a network by [S. G\\\"ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545--559] using a system of coupling "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4611","kind":"arxiv","version":3},"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":"2026-05-18T01:18:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5rOVzNg+3ku2Z58SnnNkJbkjPB/Z0Y/c/tJm3P+99RrmbBCp09DBCOApLJrTHmTscdz50NTojKJyxS7AWPHwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:54:06.661814Z"},"content_sha256":"aa5e20eb4e4356ccd96569da24a5dca1c892a364b3daf376b1d043e9731d30d5","schema_version":"1.0","event_id":"sha256:aa5e20eb4e4356ccd96569da24a5dca1c892a364b3daf376b1d043e9731d30d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/bundle.json","state_url":"https://pith.science/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/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":"2026-05-30T08:54:06Z","links":{"resolver":"https://pith.science/pith/MC4UCNIRCCGZ3C642WEXAZKIAX","bundle":"https://pith.science/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/bundle.json","state":"https://pith.science/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MC4UCNIRCCGZ3C642WEXAZKIAX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MC4UCNIRCCGZ3C642WEXAZKIAX","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":"ffa5afe9663dde4abcf76e355db37d5bb61c60ea8b123b7f93b541551a0c8701","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-19T22:28:08Z","title_canon_sha256":"4c0ddfdadd84a0dd1862b417a428bf1158bd3b46540544308b97729693d14e48"},"schema_version":"1.0","source":{"id":"1211.4611","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4611","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4611v3","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4611","created_at":"2026-05-18T01:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"MC4UCNIRCCGZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MC4UCNIRCCGZ3C64","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MC4UCNIR","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:aa5e20eb4e4356ccd96569da24a5dca1c892a364b3daf376b1d043e9731d30d5","target":"graph","created_at":"2026-05-18T01:18:23Z","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":"We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896--920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433--460] and [D. Armbruster, C. De Beer, M. Freitag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104--114]. A model was proposed for such a network by [S. G\\\"ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545--559] using a system of coupling ","authors_text":"Ke Han, Tao Yao, Terry L. Friesz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-19T22:28:08Z","title":"A variational approach for continuous supply chain networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4611","kind":"arxiv","version":3},"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:a80ad34182185fa8f4257970f46cf2ef642e141cef0b3d47b1392e6e4c7d66db","target":"record","created_at":"2026-05-18T01:18:23Z","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":"ffa5afe9663dde4abcf76e355db37d5bb61c60ea8b123b7f93b541551a0c8701","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-11-19T22:28:08Z","title_canon_sha256":"4c0ddfdadd84a0dd1862b417a428bf1158bd3b46540544308b97729693d14e48"},"schema_version":"1.0","source":{"id":"1211.4611","kind":"arxiv","version":3}},"canonical_sha256":"60b9413511108d9d8bdcd58970654805c61a95ec7de3b40351bdfb7ab99ddd2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60b9413511108d9d8bdcd58970654805c61a95ec7de3b40351bdfb7ab99ddd2e","first_computed_at":"2026-05-18T01:18:23.748836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:23.748836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2c9vNhlZGEikN81kEPYmD//1FwdSy1W7gNGoszhRQIgCxB3JJGmwPs2PxKTt4ppuEDWV2jHhrOsR+4oMie8SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:23.749336Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4611","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a80ad34182185fa8f4257970f46cf2ef642e141cef0b3d47b1392e6e4c7d66db","sha256:aa5e20eb4e4356ccd96569da24a5dca1c892a364b3daf376b1d043e9731d30d5"],"state_sha256":"9325f041acea2db7691740cec348775f79fd2fd53ef0a56a608ef20429a557d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vF8VeRFEs0kmLZPoxJDS0NoYxsFgaEpnEz6HXlvIIINI4P0ulQCQdtlfIu4E7iC6q6p1ukY8bgfx80F3FIraCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:54:06.666069Z","bundle_sha256":"d4274bb1b9579a137b5d06a4e333ffd1a39229a1964778981b5ab5839d07d714"}}