{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:KNVTCIHFRJ4HYQ5X2RMULXYA6M","short_pith_number":"pith:KNVTCIHF","canonical_record":{"source":{"id":"2210.15251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-27T08:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"0c37f3a70eb12be35eb9a8d052d42a47223fca189294e8e79dd26ff8d36fa2ef","abstract_canon_sha256":"cee492d48bef49693d9bd0c7917ddf28edf04a36c0e6ce20f4dec68ee8755ace"},"schema_version":"1.0"},"canonical_sha256":"536b3120e58a787c43b7d45945df00f32770d2c6b60bf110c3bec5606aa4eba8","source":{"kind":"arxiv","id":"2210.15251","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15251","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15251v1","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15251","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"KNVTCIHFRJ4H","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_16","alias_value":"KNVTCIHFRJ4HYQ5X","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_8","alias_value":"KNVTCIHF","created_at":"2026-07-05T08:51:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:KNVTCIHFRJ4HYQ5X2RMULXYA6M","target":"record","payload":{"canonical_record":{"source":{"id":"2210.15251","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-27T08:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"0c37f3a70eb12be35eb9a8d052d42a47223fca189294e8e79dd26ff8d36fa2ef","abstract_canon_sha256":"cee492d48bef49693d9bd0c7917ddf28edf04a36c0e6ce20f4dec68ee8755ace"},"schema_version":"1.0"},"canonical_sha256":"536b3120e58a787c43b7d45945df00f32770d2c6b60bf110c3bec5606aa4eba8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:51:40.580609Z","signature_b64":"nH3QxVtlcoRVDWkGyAj5RnB9cDAHVYTiXOfGH5cDEwyRg154pWTeU1rl1XWDSROdeRm+a6lNAHEss3rGs3D9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"536b3120e58a787c43b7d45945df00f32770d2c6b60bf110c3bec5606aa4eba8","last_reissued_at":"2026-07-05T08:51:40.580239Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:51:40.580239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.15251","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":"2026-07-05T08:51:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hPkUGCqopL82JalLYjey9EAl3i/AGQd9t6lUpVhBtNjg1Hx+R3eKgd8/1k5G1J+nruYxsad+fat505buuCt+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:44:49.847795Z"},"content_sha256":"e95971c899e4eeec37a7e13459d1d283993e5723abddc747709d914bd4f094ad","schema_version":"1.0","event_id":"sha256:e95971c899e4eeec37a7e13459d1d283993e5723abddc747709d914bd4f094ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:KNVTCIHFRJ4HYQ5X2RMULXYA6M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control for production inventory system with various cost criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Abhay Sobhanan, Chandan Pal, Manikandan R., Subrata Golui","submitted_at":"2022-10-27T08:11:08Z","abstract_excerpt":"In this article, we investigate a dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customers' demand is the exponential distribution. The production manufacturers produce the items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that an item's production time follows exponential distribution and the amount of time for the produced item to reach the retail shop "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15251","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/2210.15251/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":"2026-07-05T08:51:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TpUJNmss9Tyxml56odmC/pizHcbJ3Z81tlTZ9g6LM/OegyXQ7HRWwIAuOsysA29JYwvgG7GKV6XWHCaiyzCSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T13:44:49.848610Z"},"content_sha256":"17167ab3b058e8f4f35e7807055e7d8871f7541669e5e9b9d1b2622b2be2abcb","schema_version":"1.0","event_id":"sha256:17167ab3b058e8f4f35e7807055e7d8871f7541669e5e9b9d1b2622b2be2abcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/bundle.json","state_url":"https://pith.science/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/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":"2026-08-19T13:44:49Z","links":{"resolver":"https://pith.science/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M","bundle":"https://pith.science/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/bundle.json","state":"https://pith.science/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNVTCIHFRJ4HYQ5X2RMULXYA6M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:KNVTCIHFRJ4HYQ5X2RMULXYA6M","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":"cee492d48bef49693d9bd0c7917ddf28edf04a36c0e6ce20f4dec68ee8755ace","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-27T08:11:08Z","title_canon_sha256":"0c37f3a70eb12be35eb9a8d052d42a47223fca189294e8e79dd26ff8d36fa2ef"},"schema_version":"1.0","source":{"id":"2210.15251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.15251","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"arxiv_version","alias_value":"2210.15251v1","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.15251","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_12","alias_value":"KNVTCIHFRJ4H","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_16","alias_value":"KNVTCIHFRJ4HYQ5X","created_at":"2026-07-05T08:51:40Z"},{"alias_kind":"pith_short_8","alias_value":"KNVTCIHF","created_at":"2026-07-05T08:51:40Z"}],"graph_snapshots":[{"event_id":"sha256:17167ab3b058e8f4f35e7807055e7d8871f7541669e5e9b9d1b2622b2be2abcb","target":"graph","created_at":"2026-07-05T08:51:40Z","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/2210.15251/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we investigate a dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customers' demand is the exponential distribution. The production manufacturers produce the items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that an item's production time follows exponential distribution and the amount of time for the produced item to reach the retail shop ","authors_text":"Abhay Sobhanan, Chandan Pal, Manikandan R., Subrata Golui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-27T08:11:08Z","title":"Optimal control for production inventory system with various cost criterion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.15251","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:e95971c899e4eeec37a7e13459d1d283993e5723abddc747709d914bd4f094ad","target":"record","created_at":"2026-07-05T08:51:40Z","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":"cee492d48bef49693d9bd0c7917ddf28edf04a36c0e6ce20f4dec68ee8755ace","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-10-27T08:11:08Z","title_canon_sha256":"0c37f3a70eb12be35eb9a8d052d42a47223fca189294e8e79dd26ff8d36fa2ef"},"schema_version":"1.0","source":{"id":"2210.15251","kind":"arxiv","version":1}},"canonical_sha256":"536b3120e58a787c43b7d45945df00f32770d2c6b60bf110c3bec5606aa4eba8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"536b3120e58a787c43b7d45945df00f32770d2c6b60bf110c3bec5606aa4eba8","first_computed_at":"2026-07-05T08:51:40.580239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:51:40.580239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nH3QxVtlcoRVDWkGyAj5RnB9cDAHVYTiXOfGH5cDEwyRg154pWTeU1rl1XWDSROdeRm+a6lNAHEss3rGs3D9BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:51:40.580609Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.15251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e95971c899e4eeec37a7e13459d1d283993e5723abddc747709d914bd4f094ad","sha256:17167ab3b058e8f4f35e7807055e7d8871f7541669e5e9b9d1b2622b2be2abcb"],"state_sha256":"c60b436288c4385833994e6c6c1fb819dba5b643e1d98dc5c90aa77d3a48bff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yx67vrlP32BzVHhYUzuJueWFwsJfTT2eoROAhbtMaKKTCH7JlqohFqwVtPwvg8pYfOIcQGnBx+mGnhTB9ZdQCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T13:44:49.856636Z","bundle_sha256":"80a9e0c9c5858f03614377c73cc1ec688f93580effa887425557fd883b4a4e97"}}