{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:TBI3M3X7D3NPGI4VQCTSHBZAD3","short_pith_number":"pith:TBI3M3X7","canonical_record":{"source":{"id":"1412.0791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-02T06:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"5c3e6311d48916b5bd39576b10424db355151884272267258b15057541ccda2c","abstract_canon_sha256":"aa64a9759c30d6b3de7fa080b387641b711b74805ae070c899229fe1a64559f8"},"schema_version":"1.0"},"canonical_sha256":"9851b66eff1edaf3239580a72387201ec21c2230ce6b383b00d6901bf175e48a","source":{"kind":"arxiv","id":"1412.0791","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0791","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0791v1","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0791","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"TBI3M3X7D3NP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TBI3M3X7D3NPGI4V","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TBI3M3X7","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:TBI3M3X7D3NPGI4VQCTSHBZAD3","target":"record","payload":{"canonical_record":{"source":{"id":"1412.0791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-02T06:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"5c3e6311d48916b5bd39576b10424db355151884272267258b15057541ccda2c","abstract_canon_sha256":"aa64a9759c30d6b3de7fa080b387641b711b74805ae070c899229fe1a64559f8"},"schema_version":"1.0"},"canonical_sha256":"9851b66eff1edaf3239580a72387201ec21c2230ce6b383b00d6901bf175e48a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:21.201904Z","signature_b64":"ewRGzRNVzxdElPBqZeDEp7aSFiRUHqiyF7bc4JuJaZ1pqNcU+h9S7CY/WfB8fRIz9xnjpv0onkIsYGdH7XIzCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9851b66eff1edaf3239580a72387201ec21c2230ce6b383b00d6901bf175e48a","last_reissued_at":"2026-05-18T02:32:21.201542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:21.201542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.0791","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":"2026-05-18T02:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZYrsp0XfOSyaBOyHXFgtP6JIhKtEAGnTsxKSphUS1QUUSmW2CSd2rvVLAIEnxslO4lvVJskuDc8Ww6lzbzfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:58:41.598108Z"},"content_sha256":"bb6395a75d6c62d0a40210cf3e3b921ca7ae1834398d1f465ccbcdf0df31277c","schema_version":"1.0","event_id":"sha256:bb6395a75d6c62d0a40210cf3e3b921ca7ae1834398d1f465ccbcdf0df31277c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:TBI3M3X7D3NPGI4VQCTSHBZAD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Simple Convergence Time Analysis of Drift-Plus-Penalty for Stochastic Optimization and Convex Programs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Michael J. Neely","submitted_at":"2014-12-02T06:29:13Z","abstract_excerpt":"This paper considers the problem of minimizing the time average of a stochastic process subject to time average constraints on other processes. A canonical example is minimizing average power in a data network subject to multi-user throughput constraints. Another example is a (static) convex program. Under a Slater condition, the drift-plus-penalty algorithm is known to provide an $O(\\epsilon)$ approximation to optimality with a convergence time of $O(1/\\epsilon^2)$. This paper proves the same result with a simpler technique and in a more general context that does not require the Slater condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0791","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":"2026-05-18T02:32:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AmUNEpusBflwD5TogDzMzgfQPe5q+UMFfa98Iq4yJDpMis5oWnJR4Yx7eydQ9/UDbJG42pLar5i3DhJjs5cJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:58:41.598466Z"},"content_sha256":"fe8925ef022e404eee3efd3390c12cc500bd04889d3e51f79e3359c7c1c3a8f6","schema_version":"1.0","event_id":"sha256:fe8925ef022e404eee3efd3390c12cc500bd04889d3e51f79e3359c7c1c3a8f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/bundle.json","state_url":"https://pith.science/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/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":"2026-05-30T10:58:41Z","links":{"resolver":"https://pith.science/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3","bundle":"https://pith.science/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/bundle.json","state":"https://pith.science/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TBI3M3X7D3NPGI4VQCTSHBZAD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TBI3M3X7D3NPGI4VQCTSHBZAD3","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":"aa64a9759c30d6b3de7fa080b387641b711b74805ae070c899229fe1a64559f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-02T06:29:13Z","title_canon_sha256":"5c3e6311d48916b5bd39576b10424db355151884272267258b15057541ccda2c"},"schema_version":"1.0","source":{"id":"1412.0791","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0791","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0791v1","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0791","created_at":"2026-05-18T02:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"TBI3M3X7D3NP","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TBI3M3X7D3NPGI4V","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TBI3M3X7","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:fe8925ef022e404eee3efd3390c12cc500bd04889d3e51f79e3359c7c1c3a8f6","target":"graph","created_at":"2026-05-18T02:32:21Z","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":"This paper considers the problem of minimizing the time average of a stochastic process subject to time average constraints on other processes. A canonical example is minimizing average power in a data network subject to multi-user throughput constraints. Another example is a (static) convex program. Under a Slater condition, the drift-plus-penalty algorithm is known to provide an $O(\\epsilon)$ approximation to optimality with a convergence time of $O(1/\\epsilon^2)$. This paper proves the same result with a simpler technique and in a more general context that does not require the Slater condit","authors_text":"Michael J. Neely","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-02T06:29:13Z","title":"A Simple Convergence Time Analysis of Drift-Plus-Penalty for Stochastic Optimization and Convex Programs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0791","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:bb6395a75d6c62d0a40210cf3e3b921ca7ae1834398d1f465ccbcdf0df31277c","target":"record","created_at":"2026-05-18T02:32:21Z","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":"aa64a9759c30d6b3de7fa080b387641b711b74805ae070c899229fe1a64559f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-12-02T06:29:13Z","title_canon_sha256":"5c3e6311d48916b5bd39576b10424db355151884272267258b15057541ccda2c"},"schema_version":"1.0","source":{"id":"1412.0791","kind":"arxiv","version":1}},"canonical_sha256":"9851b66eff1edaf3239580a72387201ec21c2230ce6b383b00d6901bf175e48a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9851b66eff1edaf3239580a72387201ec21c2230ce6b383b00d6901bf175e48a","first_computed_at":"2026-05-18T02:32:21.201542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:21.201542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewRGzRNVzxdElPBqZeDEp7aSFiRUHqiyF7bc4JuJaZ1pqNcU+h9S7CY/WfB8fRIz9xnjpv0onkIsYGdH7XIzCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:21.201904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0791","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb6395a75d6c62d0a40210cf3e3b921ca7ae1834398d1f465ccbcdf0df31277c","sha256:fe8925ef022e404eee3efd3390c12cc500bd04889d3e51f79e3359c7c1c3a8f6"],"state_sha256":"de1aa3304e15f2f4e9377f1c8054bd1a9d00f492d2c54f4dc82cdab0d45e9eff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EihViW3e0hehBO17r0OxZi6slscBApsQNm0ptJbcXvPeJmkO6FQfw46iLWKfYjUUOirvbKYha4ZCJlsQfL+fCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:58:41.600479Z","bundle_sha256":"6cb5684517ab829a66633de727327d8ab3f4354e7e95f32b06ba19e67efacea5"}}