{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:H2IDIJAHXK6OPMF5UK3IATXRBB","short_pith_number":"pith:H2IDIJAH","canonical_record":{"source":{"id":"2503.05882","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-16T10:00:50Z","cross_cats_sorted":["cs.AI","cs.NA","math.OC"],"title_canon_sha256":"f8d32b5277277926ee07ffc91387e1968db0676c2b4290a16c0ca73d3f0784c3","abstract_canon_sha256":"21edaa598d5dc01123f1318ab4cef1741e0983c78d46f8384aad51dc4604cff4"},"schema_version":"1.0"},"canonical_sha256":"3e90342407babce7b0bda2b6804ef1084351702534b567635faa60317f4ded6e","source":{"kind":"arxiv","id":"2503.05882","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05882","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05882v1","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05882","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"H2IDIJAHXK6O","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_16","alias_value":"H2IDIJAHXK6OPMF5","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_8","alias_value":"H2IDIJAH","created_at":"2026-07-05T10:26:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:H2IDIJAHXK6OPMF5UK3IATXRBB","target":"record","payload":{"canonical_record":{"source":{"id":"2503.05882","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-16T10:00:50Z","cross_cats_sorted":["cs.AI","cs.NA","math.OC"],"title_canon_sha256":"f8d32b5277277926ee07ffc91387e1968db0676c2b4290a16c0ca73d3f0784c3","abstract_canon_sha256":"21edaa598d5dc01123f1318ab4cef1741e0983c78d46f8384aad51dc4604cff4"},"schema_version":"1.0"},"canonical_sha256":"3e90342407babce7b0bda2b6804ef1084351702534b567635faa60317f4ded6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:26:48.430265Z","signature_b64":"xC1Ro09irzuxjYoC+yIyyCfmYmpDvhMOq7x/SPCjbAzPmlcB2S2Anh5m03lamE6NChfO2N8JiSHIhJIDRkFMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e90342407babce7b0bda2b6804ef1084351702534b567635faa60317f4ded6e","last_reissued_at":"2026-07-05T10:26:48.429786Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:26:48.429786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.05882","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":"2026-07-05T10:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ETCgf5V2LgVuKfO7rDV0ld64zoTQ9l+6I+Ks/kcRGLBqjmFDeazBYN/D5Fal4vIklI2WpBQckFCTPg2q4OxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:35:13.828832Z"},"content_sha256":"61e2bd11ad6e036cd589491cbdf4b798f4fda2336b545cf0ab7d9c779a85333a","schema_version":"1.0","event_id":"sha256:61e2bd11ad6e036cd589491cbdf4b798f4fda2336b545cf0ab7d9c779a85333a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:H2IDIJAHXK6OPMF5UK3IATXRBB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Practical Topics in Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Jun Lu","submitted_at":"2025-02-16T10:00:50Z","abstract_excerpt":"In an era where data-driven decision-making and computational efficiency are paramount, optimization plays a foundational role in advancing fields such as mathematics, computer science, operations research, machine learning, and beyond. From refining machine learning models to improving resource allocation and designing efficient algorithms, optimization techniques serve as essential tools for tackling complex problems. This book aims to provide both an introductory guide and a comprehensive reference, equipping readers with the necessary knowledge to understand and apply optimization methods "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05882","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/2503.05882/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":"2026-07-05T10:26:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PznNcXjuTinv1rpe0nKoycRxYiypKmsuGMwlHqqCtsunE7spv/6o5Kbi0pDKwkJZlW9XPYLEGiPqV6+Ai00fDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:35:13.829364Z"},"content_sha256":"be7b9079519c4c78eb1f1a6cd2c57ac90625821b5c3b4943c6707b12f0127709","schema_version":"1.0","event_id":"sha256:be7b9079519c4c78eb1f1a6cd2c57ac90625821b5c3b4943c6707b12f0127709"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/bundle.json","state_url":"https://pith.science/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/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":"2026-08-20T10:35:13Z","links":{"resolver":"https://pith.science/pith/H2IDIJAHXK6OPMF5UK3IATXRBB","bundle":"https://pith.science/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/bundle.json","state":"https://pith.science/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2IDIJAHXK6OPMF5UK3IATXRBB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:H2IDIJAHXK6OPMF5UK3IATXRBB","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":"21edaa598d5dc01123f1318ab4cef1741e0983c78d46f8384aad51dc4604cff4","cross_cats_sorted":["cs.AI","cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-16T10:00:50Z","title_canon_sha256":"f8d32b5277277926ee07ffc91387e1968db0676c2b4290a16c0ca73d3f0784c3"},"schema_version":"1.0","source":{"id":"2503.05882","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05882","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05882v1","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05882","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_12","alias_value":"H2IDIJAHXK6O","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_16","alias_value":"H2IDIJAHXK6OPMF5","created_at":"2026-07-05T10:26:48Z"},{"alias_kind":"pith_short_8","alias_value":"H2IDIJAH","created_at":"2026-07-05T10:26:48Z"}],"graph_snapshots":[{"event_id":"sha256:be7b9079519c4c78eb1f1a6cd2c57ac90625821b5c3b4943c6707b12f0127709","target":"graph","created_at":"2026-07-05T10:26:48Z","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/2503.05882/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In an era where data-driven decision-making and computational efficiency are paramount, optimization plays a foundational role in advancing fields such as mathematics, computer science, operations research, machine learning, and beyond. From refining machine learning models to improving resource allocation and designing efficient algorithms, optimization techniques serve as essential tools for tackling complex problems. This book aims to provide both an introductory guide and a comprehensive reference, equipping readers with the necessary knowledge to understand and apply optimization methods ","authors_text":"Jun Lu","cross_cats":["cs.AI","cs.NA","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-16T10:00:50Z","title":"Practical Topics in Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05882","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":"sha256:61e2bd11ad6e036cd589491cbdf4b798f4fda2336b545cf0ab7d9c779a85333a","target":"record","created_at":"2026-07-05T10:26:48Z","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":"21edaa598d5dc01123f1318ab4cef1741e0983c78d46f8384aad51dc4604cff4","cross_cats_sorted":["cs.AI","cs.NA","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-02-16T10:00:50Z","title_canon_sha256":"f8d32b5277277926ee07ffc91387e1968db0676c2b4290a16c0ca73d3f0784c3"},"schema_version":"1.0","source":{"id":"2503.05882","kind":"arxiv","version":1}},"canonical_sha256":"3e90342407babce7b0bda2b6804ef1084351702534b567635faa60317f4ded6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e90342407babce7b0bda2b6804ef1084351702534b567635faa60317f4ded6e","first_computed_at":"2026-07-05T10:26:48.429786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:26:48.429786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xC1Ro09irzuxjYoC+yIyyCfmYmpDvhMOq7x/SPCjbAzPmlcB2S2Anh5m03lamE6NChfO2N8JiSHIhJIDRkFMAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:26:48.430265Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.05882","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61e2bd11ad6e036cd589491cbdf4b798f4fda2336b545cf0ab7d9c779a85333a","sha256:be7b9079519c4c78eb1f1a6cd2c57ac90625821b5c3b4943c6707b12f0127709"],"state_sha256":"5fbc0cdd882f931ff86fc958eba9a7db84dd96edceb91f9fc9ac125c359f013a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G6v7tNej4wUPL0E4L7ln8hQTW1c3R7A3KJ0jHLar8VhGoU9HPh0b3O93aQJeb6lc/b5STsB0HKNKAG/nZuNiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T10:35:13.834268Z","bundle_sha256":"7dedc947807230e0acbe4195f504251736d65025ecce2ace4a3097b30b40bf69"}}