{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:W7HIAMXHQ5AKJJ3RNS2NFPMRSV","short_pith_number":"pith:W7HIAMXH","canonical_record":{"source":{"id":"1608.01526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-04T13:33:44Z","cross_cats_sorted":[],"title_canon_sha256":"bdecccefffe6f40918c135c5a4c2c94dde314321c480c782407433996a220fb8","abstract_canon_sha256":"d40343c720fc6794b2f0a8c663851cb701291077d4d4553b74b0fbc55090bff6"},"schema_version":"1.0"},"canonical_sha256":"b7ce8032e78740a4a7716cb4d2bd91956d25790739d5b419e0e56d8d3374ae56","source":{"kind":"arxiv","id":"1608.01526","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01526","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01526v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01526","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"W7HIAMXHQ5AK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7HIAMXHQ5AKJJ3R","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7HIAMXH","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:W7HIAMXHQ5AKJJ3RNS2NFPMRSV","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-04T13:33:44Z","cross_cats_sorted":[],"title_canon_sha256":"bdecccefffe6f40918c135c5a4c2c94dde314321c480c782407433996a220fb8","abstract_canon_sha256":"d40343c720fc6794b2f0a8c663851cb701291077d4d4553b74b0fbc55090bff6"},"schema_version":"1.0"},"canonical_sha256":"b7ce8032e78740a4a7716cb4d2bd91956d25790739d5b419e0e56d8d3374ae56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:52.215624Z","signature_b64":"ZUkcvKsQQXbtqUTy2UojUP952bYeCrUlMG2w73Dzrg9/v7C1tq47xfTSVqFu2dapeuXJsmIBiP8MtT4LgOzgCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7ce8032e78740a4a7716cb4d2bd91956d25790739d5b419e0e56d8d3374ae56","last_reissued_at":"2026-05-18T01:09:52.214963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:52.214963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01526","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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a0txzDg58JKSiZ9JSFN1XOCgd3I++S1XJeB7MEoFdt5tDTLG2yVKOXDd8pFf/K6BsyviC99Q6iM0ycyHwm8tAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:14:04.656834Z"},"content_sha256":"eb8e7ac13571aac196f9ed5c891960fd1319b8caaa7c1a907f60a3199da16315","schema_version":"1.0","event_id":"sha256:eb8e7ac13571aac196f9ed5c891960fd1319b8caaa7c1a907f60a3199da16315"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:W7HIAMXHQ5AKJJ3RNS2NFPMRSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Instantaneous Control of Brownian Motion with a Positive Lead Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jiheng Zhang, Rachel Q. Zhang, Zhen Xu","submitted_at":"2016-08-04T13:33:44Z","abstract_excerpt":"Consider a storage system where the content is driven by a Brownian motion absent control. At any time, one may increase or decrease the content at a cost proportional to the amount of adjustment. A decrease of the content takes effect immediately, while an increase is realized after a fixed lead time $\\lt$. Holding costs are incurred continuously over time and are a convex function of the content. The objective is to find a control policy that minimizes the expected present value of the total costs. Due to the positive lead time for upward adjustments, one needs to keep track of all the outst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01526","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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/X8Aw8g4dfcqep26G11vCeZlM+X+87K1tiQPURsxwImazpTxUZ3x8+gWdA1HOldBuj9A6b8rLncLOmHim7MuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:14:04.657594Z"},"content_sha256":"46604208a387ad07c8bffe0e47ea27888a9b18993a3ab52b6b4d2eb6fd55c6d2","schema_version":"1.0","event_id":"sha256:46604208a387ad07c8bffe0e47ea27888a9b18993a3ab52b6b4d2eb6fd55c6d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/bundle.json","state_url":"https://pith.science/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/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":"2026-06-10T13:14:04Z","links":{"resolver":"https://pith.science/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV","bundle":"https://pith.science/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/bundle.json","state":"https://pith.science/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7HIAMXHQ5AKJJ3RNS2NFPMRSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:W7HIAMXHQ5AKJJ3RNS2NFPMRSV","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":"d40343c720fc6794b2f0a8c663851cb701291077d4d4553b74b0fbc55090bff6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-04T13:33:44Z","title_canon_sha256":"bdecccefffe6f40918c135c5a4c2c94dde314321c480c782407433996a220fb8"},"schema_version":"1.0","source":{"id":"1608.01526","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01526","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01526v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01526","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"W7HIAMXHQ5AK","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"W7HIAMXHQ5AKJJ3R","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"W7HIAMXH","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:46604208a387ad07c8bffe0e47ea27888a9b18993a3ab52b6b4d2eb6fd55c6d2","target":"graph","created_at":"2026-05-18T01:09:52Z","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":"Consider a storage system where the content is driven by a Brownian motion absent control. At any time, one may increase or decrease the content at a cost proportional to the amount of adjustment. A decrease of the content takes effect immediately, while an increase is realized after a fixed lead time $\\lt$. Holding costs are incurred continuously over time and are a convex function of the content. The objective is to find a control policy that minimizes the expected present value of the total costs. Due to the positive lead time for upward adjustments, one needs to keep track of all the outst","authors_text":"Jiheng Zhang, Rachel Q. Zhang, Zhen Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-04T13:33:44Z","title":"Instantaneous Control of Brownian Motion with a Positive Lead Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01526","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:eb8e7ac13571aac196f9ed5c891960fd1319b8caaa7c1a907f60a3199da16315","target":"record","created_at":"2026-05-18T01:09:52Z","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":"d40343c720fc6794b2f0a8c663851cb701291077d4d4553b74b0fbc55090bff6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-04T13:33:44Z","title_canon_sha256":"bdecccefffe6f40918c135c5a4c2c94dde314321c480c782407433996a220fb8"},"schema_version":"1.0","source":{"id":"1608.01526","kind":"arxiv","version":1}},"canonical_sha256":"b7ce8032e78740a4a7716cb4d2bd91956d25790739d5b419e0e56d8d3374ae56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7ce8032e78740a4a7716cb4d2bd91956d25790739d5b419e0e56d8d3374ae56","first_computed_at":"2026-05-18T01:09:52.214963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:52.214963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZUkcvKsQQXbtqUTy2UojUP952bYeCrUlMG2w73Dzrg9/v7C1tq47xfTSVqFu2dapeuXJsmIBiP8MtT4LgOzgCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:52.215624Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01526","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb8e7ac13571aac196f9ed5c891960fd1319b8caaa7c1a907f60a3199da16315","sha256:46604208a387ad07c8bffe0e47ea27888a9b18993a3ab52b6b4d2eb6fd55c6d2"],"state_sha256":"83ec3dd7924ae0c8879b05cda9fff09be07ec91368fe078b94a9edb2b8b4308a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XPFnGtDtcCP8IkcX5T1k0sXGfHom4AJDavIinPP0ZQGxZPWxi01JYNuUfXYHtX6GtG5e+PHlguWbO7RiEb1KAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:14:04.660593Z","bundle_sha256":"47d8a53333fefbb2af37a529296c94b0ba911bdc2f81d23c0c05ca7f1c211fd7"}}