{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:UZ4MCOMED6IW5AZT24OXYX5OFU","short_pith_number":"pith:UZ4MCOME","canonical_record":{"source":{"id":"1702.01046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-03T15:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"dfca5278fa789b05db414fd22caeb1fdffabb1fdc63186a2ae06b2395f02358d","abstract_canon_sha256":"88c7bc9cc70d09ae53cb3d4589c2118da8db9befd0a711881f949dee73878e60"},"schema_version":"1.0"},"canonical_sha256":"a678c139841f916e8333d71d7c5fae2d1271c196e68b7b90572d3a0f2718d5fe","source":{"kind":"arxiv","id":"1702.01046","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01046","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01046v1","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01046","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"UZ4MCOMED6IW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UZ4MCOMED6IW5AZT","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UZ4MCOME","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:UZ4MCOMED6IW5AZT24OXYX5OFU","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01046","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-03T15:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"dfca5278fa789b05db414fd22caeb1fdffabb1fdc63186a2ae06b2395f02358d","abstract_canon_sha256":"88c7bc9cc70d09ae53cb3d4589c2118da8db9befd0a711881f949dee73878e60"},"schema_version":"1.0"},"canonical_sha256":"a678c139841f916e8333d71d7c5fae2d1271c196e68b7b90572d3a0f2718d5fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:29.121222Z","signature_b64":"zirzpkT/0okwkjPRTiHrK069BZsvK/YfHC/HQSZ5OaU+jHS0JunyM+22ZLPaWSAyPKmQLnVMvQuJDr8O6vmHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a678c139841f916e8333d71d7c5fae2d1271c196e68b7b90572d3a0f2718d5fe","last_reissued_at":"2026-05-18T00:51:29.120692Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:29.120692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01046","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":"2026-05-18T00:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oCRFv510QggvQ1L48XHQVwEZrDJ0fBobu48ZZFQHooQYnElE7Bl8uBRkP2bVTdgI/1/bdOnH2Mjoof22gDg0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T01:12:08.927415Z"},"content_sha256":"aec83c62f456c4e19bc4f776833cb62f7bca942cab3550a730eef584ac9f86b2","schema_version":"1.0","event_id":"sha256:aec83c62f456c4e19bc4f776833cb62f7bca942cab3550a730eef584ac9f86b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:UZ4MCOMED6IW5AZT24OXYX5OFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Counterintuitive Example in Inventory Management","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Chao Zhu, Kurt L. Helmes, Richard H. Stockbridge","submitted_at":"2017-02-03T15:16:50Z","abstract_excerpt":"The paper \\cite{helm:17} studies an inventory management problem under a long-term average cost criterion using weak convergence methods applied to average expected occupation and average expected ordering measures. Under the natural condition of inf-compactness of the holding cost rate function, the average expected occupation measures are seen to be tight and hence have weak limits. However inf-compactness is not a natural assumption to impose on the ordering cost function. For example, the cost function composed of a fixed cost plus proportional (to the size of the order) cost is not inf-co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01046","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":"2026-05-18T00:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SddavtmfVQhDa0aw/kJbyfHHJ9G3int6xg1On6V6ur0TQbthstOvS0d2D+1Xlkqysv2RsrGQb0QYlwZrsLC1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T01:12:08.927753Z"},"content_sha256":"34779c332168a0c5aa8d73ecc837c062f149524f0ff4d4f807c61e1b2066c099","schema_version":"1.0","event_id":"sha256:34779c332168a0c5aa8d73ecc837c062f149524f0ff4d4f807c61e1b2066c099"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/bundle.json","state_url":"https://pith.science/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/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":"2026-07-02T01:12:08Z","links":{"resolver":"https://pith.science/pith/UZ4MCOMED6IW5AZT24OXYX5OFU","bundle":"https://pith.science/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/bundle.json","state":"https://pith.science/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZ4MCOMED6IW5AZT24OXYX5OFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:UZ4MCOMED6IW5AZT24OXYX5OFU","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":"88c7bc9cc70d09ae53cb3d4589c2118da8db9befd0a711881f949dee73878e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-03T15:16:50Z","title_canon_sha256":"dfca5278fa789b05db414fd22caeb1fdffabb1fdc63186a2ae06b2395f02358d"},"schema_version":"1.0","source":{"id":"1702.01046","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01046","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01046v1","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01046","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"UZ4MCOMED6IW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"UZ4MCOMED6IW5AZT","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"UZ4MCOME","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:34779c332168a0c5aa8d73ecc837c062f149524f0ff4d4f807c61e1b2066c099","target":"graph","created_at":"2026-05-18T00:51:29Z","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":"The paper \\cite{helm:17} studies an inventory management problem under a long-term average cost criterion using weak convergence methods applied to average expected occupation and average expected ordering measures. Under the natural condition of inf-compactness of the holding cost rate function, the average expected occupation measures are seen to be tight and hence have weak limits. However inf-compactness is not a natural assumption to impose on the ordering cost function. For example, the cost function composed of a fixed cost plus proportional (to the size of the order) cost is not inf-co","authors_text":"Chao Zhu, Kurt L. Helmes, Richard H. Stockbridge","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-03T15:16:50Z","title":"A Counterintuitive Example in Inventory Management"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01046","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:aec83c62f456c4e19bc4f776833cb62f7bca942cab3550a730eef584ac9f86b2","target":"record","created_at":"2026-05-18T00:51:29Z","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":"88c7bc9cc70d09ae53cb3d4589c2118da8db9befd0a711881f949dee73878e60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-03T15:16:50Z","title_canon_sha256":"dfca5278fa789b05db414fd22caeb1fdffabb1fdc63186a2ae06b2395f02358d"},"schema_version":"1.0","source":{"id":"1702.01046","kind":"arxiv","version":1}},"canonical_sha256":"a678c139841f916e8333d71d7c5fae2d1271c196e68b7b90572d3a0f2718d5fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a678c139841f916e8333d71d7c5fae2d1271c196e68b7b90572d3a0f2718d5fe","first_computed_at":"2026-05-18T00:51:29.120692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:29.120692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zirzpkT/0okwkjPRTiHrK069BZsvK/YfHC/HQSZ5OaU+jHS0JunyM+22ZLPaWSAyPKmQLnVMvQuJDr8O6vmHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:29.121222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01046","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aec83c62f456c4e19bc4f776833cb62f7bca942cab3550a730eef584ac9f86b2","sha256:34779c332168a0c5aa8d73ecc837c062f149524f0ff4d4f807c61e1b2066c099"],"state_sha256":"cf6ba684eabe027fa0a394cd409503e43d71ed2a459a08447c660eb3691fae99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a/oTL9X4yT4c+C+RDMH8zW2V8uKGfv2MpGFN4yXPig6Ddfr/B+mN91RQ+idCH5MvJHQBMCy3dx42P4rJCCRlAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T01:12:08.929592Z","bundle_sha256":"d25e8ace8ff305977ce2177e59c00d4c6c24304c6c7ff0daaef84151dc29bc65"}}