{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NN4BJCV3NIAYIRTPRCSHV25YWT","short_pith_number":"pith:NN4BJCV3","canonical_record":{"source":{"id":"1908.08208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2019-08-22T05:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"51ca63f81be1046a7a9d96c2937489256180c484d20a20f27ee4ed98e0ab6022","abstract_canon_sha256":"c89a65912a8ceed7e1a6fc6bce5ca78a01b7fd907f4de3fb14e14dd9a4fd9035"},"schema_version":"1.0"},"canonical_sha256":"6b78148abb6a0184466f88a47aebb8b4ea29ad3c57d1b4392700e77e0586a508","source":{"kind":"arxiv","id":"1908.08208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08208","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08208v1","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08208","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"NN4BJCV3NIAY","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"NN4BJCV3NIAYIRTP","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"NN4BJCV3","created_at":"2026-07-04T23:59:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NN4BJCV3NIAYIRTPRCSHV25YWT","target":"record","payload":{"canonical_record":{"source":{"id":"1908.08208","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2019-08-22T05:35:46Z","cross_cats_sorted":[],"title_canon_sha256":"51ca63f81be1046a7a9d96c2937489256180c484d20a20f27ee4ed98e0ab6022","abstract_canon_sha256":"c89a65912a8ceed7e1a6fc6bce5ca78a01b7fd907f4de3fb14e14dd9a4fd9035"},"schema_version":"1.0"},"canonical_sha256":"6b78148abb6a0184466f88a47aebb8b4ea29ad3c57d1b4392700e77e0586a508","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:59:10.590779Z","signature_b64":"0BFy/yg6G/O7REqDcDG2YKBoig4FP2k2xPkFrYz0Ad27Ne5xgct/6d3Ku+d9h7oSsBgwDnLcMxeNK5P1bBUgBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b78148abb6a0184466f88a47aebb8b4ea29ad3c57d1b4392700e77e0586a508","last_reissued_at":"2026-07-04T23:59:10.590399Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:59:10.590399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.08208","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":"2026-07-04T23:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZDzd5PNtJmo7rQzwSfZlcombyEjQRZLxzeazylz63a4pKgp2NvNxhg0Pv1xNRVcs09RlhvbHKqEny95O4ZeWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:05:15.484451Z"},"content_sha256":"394618023c2526d489df7c330d7d73b81ec15eaa8d345694483768c5452636f5","schema_version":"1.0","event_id":"sha256:394618023c2526d489df7c330d7d73b81ec15eaa8d345694483768c5452636f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NN4BJCV3NIAYIRTPRCSHV25YWT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium in Production Chains with Multiple Upstream Partners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"econ.TH","authors_text":"Junnan Zhang, Meng Yu","submitted_at":"2019-08-22T05:35:46Z","abstract_excerpt":"In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08208","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/1908.08208/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":"2026-07-04T23:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5c1d+Lf1SyKPoJcMh+Mn8LQ8MHeip1xgZ9ATikojyJP7ft3GONmB5skv8lzPoMWOhmgiCBmWnn/0hict20DCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T08:05:15.484953Z"},"content_sha256":"c24b7fc9f68b26c69cd130af57a8d6a55c4f0b3a1e10008cea2a6d2cc0388d2a","schema_version":"1.0","event_id":"sha256:c24b7fc9f68b26c69cd130af57a8d6a55c4f0b3a1e10008cea2a6d2cc0388d2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/bundle.json","state_url":"https://pith.science/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/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":"2026-08-15T08:05:15Z","links":{"resolver":"https://pith.science/pith/NN4BJCV3NIAYIRTPRCSHV25YWT","bundle":"https://pith.science/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/bundle.json","state":"https://pith.science/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NN4BJCV3NIAYIRTPRCSHV25YWT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NN4BJCV3NIAYIRTPRCSHV25YWT","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":"c89a65912a8ceed7e1a6fc6bce5ca78a01b7fd907f4de3fb14e14dd9a4fd9035","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2019-08-22T05:35:46Z","title_canon_sha256":"51ca63f81be1046a7a9d96c2937489256180c484d20a20f27ee4ed98e0ab6022"},"schema_version":"1.0","source":{"id":"1908.08208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.08208","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"1908.08208v1","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08208","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"NN4BJCV3NIAY","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"NN4BJCV3NIAYIRTP","created_at":"2026-07-04T23:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"NN4BJCV3","created_at":"2026-07-04T23:59:10Z"}],"graph_snapshots":[{"event_id":"sha256:c24b7fc9f68b26c69cd130af57a8d6a55c4f0b3a1e10008cea2a6d2cc0388d2a","target":"graph","created_at":"2026-07-04T23:59:10Z","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/1908.08208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence improving their results on production networks with multiple upstream partners. We propose an algorithm for computing the equilibrium price function that is more than ten times faster than successive evaluations of the operator. The model is then generalized to a stochastic setting that offers richer implications for the distribution of firms in a production n","authors_text":"Junnan Zhang, Meng Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2019-08-22T05:35:46Z","title":"Equilibrium in Production Chains with Multiple Upstream Partners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08208","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":"sha256:394618023c2526d489df7c330d7d73b81ec15eaa8d345694483768c5452636f5","target":"record","created_at":"2026-07-04T23:59:10Z","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":"c89a65912a8ceed7e1a6fc6bce5ca78a01b7fd907f4de3fb14e14dd9a4fd9035","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"econ.TH","submitted_at":"2019-08-22T05:35:46Z","title_canon_sha256":"51ca63f81be1046a7a9d96c2937489256180c484d20a20f27ee4ed98e0ab6022"},"schema_version":"1.0","source":{"id":"1908.08208","kind":"arxiv","version":1}},"canonical_sha256":"6b78148abb6a0184466f88a47aebb8b4ea29ad3c57d1b4392700e77e0586a508","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b78148abb6a0184466f88a47aebb8b4ea29ad3c57d1b4392700e77e0586a508","first_computed_at":"2026-07-04T23:59:10.590399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:59:10.590399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0BFy/yg6G/O7REqDcDG2YKBoig4FP2k2xPkFrYz0Ad27Ne5xgct/6d3Ku+d9h7oSsBgwDnLcMxeNK5P1bBUgBg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:59:10.590779Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.08208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:394618023c2526d489df7c330d7d73b81ec15eaa8d345694483768c5452636f5","sha256:c24b7fc9f68b26c69cd130af57a8d6a55c4f0b3a1e10008cea2a6d2cc0388d2a"],"state_sha256":"fbe2af122e5c8a116855fa9a5e2ac8421078bca9b7dff562f9bb5cef72f7ddd3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bONXRKLJMZCjWDXVLU6uocqWB74UCSI9+Ns5qNnBRb6Zkdy1x6QNiDlnzwtZjMlKJ0AYI8627sSOxBUYtpJNDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T08:05:15.490444Z","bundle_sha256":"d66874446522cd0fb9a758888f6f682e9e1d0829f22378248f9c3cf461b3004c"}}