{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZOROMZSNP33SAY4V337CRDTDFA","short_pith_number":"pith:ZOROMZSN","canonical_record":{"source":{"id":"1306.2740","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2013-06-12T08:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"2b32aec9676a846ca00d4615bf20329b3ddbb02a2fabb7623417da48147eac3a","abstract_canon_sha256":"4429713582d0797bccb94c9589091cb71d15e7cb78cdb9f3ee6381bcaba1fa4e"},"schema_version":"1.0"},"canonical_sha256":"cba2e6664d7ef7206395defe288e6328240b1b4692246b865e5b2e95e1c435e5","source":{"kind":"arxiv","id":"1306.2740","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2740","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2740v1","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2740","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZOROMZSNP33S","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZOROMZSNP33SAY4V","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZOROMZSN","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZOROMZSNP33SAY4V337CRDTDFA","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2740","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2013-06-12T08:07:44Z","cross_cats_sorted":[],"title_canon_sha256":"2b32aec9676a846ca00d4615bf20329b3ddbb02a2fabb7623417da48147eac3a","abstract_canon_sha256":"4429713582d0797bccb94c9589091cb71d15e7cb78cdb9f3ee6381bcaba1fa4e"},"schema_version":"1.0"},"canonical_sha256":"cba2e6664d7ef7206395defe288e6328240b1b4692246b865e5b2e95e1c435e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:56.965073Z","signature_b64":"7tYWUxrCUspqwoG0D6y9JGqW57rQhqefJSqclwwc2aqi42uub1Lp5uc68bUvKcjpe6NHV5JV+oGBS1wQxT5wBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cba2e6664d7ef7206395defe288e6328240b1b4692246b865e5b2e95e1c435e5","last_reissued_at":"2026-05-18T02:44:56.964668Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:56.964668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2740","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":"2026-05-18T02:44:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BnLRzqet/oukGujyTm/vcdUKC9ikExPoVqagX8zGSNifdMLnXIo1AxdEz+u31YL/LmGD+1oU0/iPQ5R60Wc1CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:27:11.363741Z"},"content_sha256":"6c0b59ea6766321d2c8cb2dcbcfde4032da98a7ac384840c46f94c0b45f0bf06","schema_version":"1.0","event_id":"sha256:6c0b59ea6766321d2c8cb2dcbcfde4032da98a7ac384840c46f94c0b45f0bf06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZOROMZSNP33SAY4V337CRDTDFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Partial Hamiltonian Approach for Current Value Hamiltonian Systems","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Azam Chaudhry, F. M. Mahomed, R. Naz","submitted_at":"2013-06-12T08:07:44Z","abstract_excerpt":"We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs).\n  The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2740","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":"2026-05-18T02:44:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/Oye2wQjv7vAV+6dPbyo/VbUeRyx+tSg4FWFVQnBm1+1GQA938GqEZo/QEq6yENFaQ/6ov70/vLsckFdMlkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T21:27:11.364300Z"},"content_sha256":"f5aaaf4216088eac1c411cc12c11ce85016fd1aba28a6c93d32b3909da8822f6","schema_version":"1.0","event_id":"sha256:f5aaaf4216088eac1c411cc12c11ce85016fd1aba28a6c93d32b3909da8822f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOROMZSNP33SAY4V337CRDTDFA/bundle.json","state_url":"https://pith.science/pith/ZOROMZSNP33SAY4V337CRDTDFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOROMZSNP33SAY4V337CRDTDFA/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":"2026-05-21T21:27:11Z","links":{"resolver":"https://pith.science/pith/ZOROMZSNP33SAY4V337CRDTDFA","bundle":"https://pith.science/pith/ZOROMZSNP33SAY4V337CRDTDFA/bundle.json","state":"https://pith.science/pith/ZOROMZSNP33SAY4V337CRDTDFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOROMZSNP33SAY4V337CRDTDFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZOROMZSNP33SAY4V337CRDTDFA","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":"4429713582d0797bccb94c9589091cb71d15e7cb78cdb9f3ee6381bcaba1fa4e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2013-06-12T08:07:44Z","title_canon_sha256":"2b32aec9676a846ca00d4615bf20329b3ddbb02a2fabb7623417da48147eac3a"},"schema_version":"1.0","source":{"id":"1306.2740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2740","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2740v1","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2740","created_at":"2026-05-18T02:44:56Z"},{"alias_kind":"pith_short_12","alias_value":"ZOROMZSNP33S","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZOROMZSNP33SAY4V","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZOROMZSN","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:f5aaaf4216088eac1c411cc12c11ce85016fd1aba28a6c93d32b3909da8822f6","target":"graph","created_at":"2026-05-18T02:44:56Z","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":"We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs).\n  The approach is algorithmic and applies to many state and costate variables of the current value Hamiltonian. However, we apply the method to models with one control, one state and one costate variable to illustrate its effectiveness. The current value Hamiltonian systems arise in economic growth theory and other economic models. We explain our approach with the help of a simple illustrative example and t","authors_text":"Azam Chaudhry, F. M. Mahomed, R. Naz","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2013-06-12T08:07:44Z","title":"A Partial Hamiltonian Approach for Current Value Hamiltonian Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2740","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":"sha256:6c0b59ea6766321d2c8cb2dcbcfde4032da98a7ac384840c46f94c0b45f0bf06","target":"record","created_at":"2026-05-18T02:44:56Z","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":"4429713582d0797bccb94c9589091cb71d15e7cb78cdb9f3ee6381bcaba1fa4e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.OC","submitted_at":"2013-06-12T08:07:44Z","title_canon_sha256":"2b32aec9676a846ca00d4615bf20329b3ddbb02a2fabb7623417da48147eac3a"},"schema_version":"1.0","source":{"id":"1306.2740","kind":"arxiv","version":1}},"canonical_sha256":"cba2e6664d7ef7206395defe288e6328240b1b4692246b865e5b2e95e1c435e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cba2e6664d7ef7206395defe288e6328240b1b4692246b865e5b2e95e1c435e5","first_computed_at":"2026-05-18T02:44:56.964668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:56.964668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7tYWUxrCUspqwoG0D6y9JGqW57rQhqefJSqclwwc2aqi42uub1Lp5uc68bUvKcjpe6NHV5JV+oGBS1wQxT5wBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:56.965073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c0b59ea6766321d2c8cb2dcbcfde4032da98a7ac384840c46f94c0b45f0bf06","sha256:f5aaaf4216088eac1c411cc12c11ce85016fd1aba28a6c93d32b3909da8822f6"],"state_sha256":"44520768796807edeb388485d6ac69cae2e2d875da74d12206dccca627278c9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zryE3oC8wt8d7qJmkYhJe8yLNMF/WKprO0h7QqQFeHYgupf/TdWvkzj5OmO6Y+8hWwsjEIF8I+3oLxiYuP9wDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T21:27:11.366741Z","bundle_sha256":"548f8de6a3881c2c72e33151ca6c20d0b7f5dd7609a22095c9c8f4a359b77ef3"}}