{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:ZA6MTOSJGHAV4KXYC3VFXNDOXV","short_pith_number":"pith:ZA6MTOSJ","canonical_record":{"source":{"id":"0804.2239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-14T18:27:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"236926ba30dcf168132d70aeddfca607177cd29e27350da44b394ee116124690","abstract_canon_sha256":"23f9b78a3dced0265b2109938b953d4d25712eeaab159777bd6ed9a21274a6c8"},"schema_version":"1.0"},"canonical_sha256":"c83cc9ba4931c15e2af816ea5bb46ebd74ba39b61750ba47b5bc7efdbef1283e","source":{"kind":"arxiv","id":"0804.2239","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.2239","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"0804.2239v3","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.2239","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZA6MTOSJGHAV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZA6MTOSJGHAV4KXY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZA6MTOSJ","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:ZA6MTOSJGHAV4KXYC3VFXNDOXV","target":"record","payload":{"canonical_record":{"source":{"id":"0804.2239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-14T18:27:21Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"236926ba30dcf168132d70aeddfca607177cd29e27350da44b394ee116124690","abstract_canon_sha256":"23f9b78a3dced0265b2109938b953d4d25712eeaab159777bd6ed9a21274a6c8"},"schema_version":"1.0"},"canonical_sha256":"c83cc9ba4931c15e2af816ea5bb46ebd74ba39b61750ba47b5bc7efdbef1283e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.964469Z","signature_b64":"ZN6QYobltpushM0UXrB7PJSeXuExNIdvyDPCIpldKcLMXzS+fHZalSuR3fgl9qjavILEQ+Wfa+7y74VKhpjCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c83cc9ba4931c15e2af816ea5bb46ebd74ba39b61750ba47b5bc7efdbef1283e","last_reissued_at":"2026-05-18T04:41:54.963846Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.963846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0804.2239","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"diCwHQJr7rcQOGayDoiQtB6SherPUmlDOZiplywumzb1cF1WaS7OV83tPR/UTi/kh/XsDQBgDADjN0dA/er7Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T00:05:44.121764Z"},"content_sha256":"5e6ddb176564f7fbbc5784acffb28212b13ad77cd020e8167139b5f78298dc61","schema_version":"1.0","event_id":"sha256:5e6ddb176564f7fbbc5784acffb28212b13ad77cd020e8167139b5f78298dc61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:ZA6MTOSJGHAV4KXYC3VFXNDOXV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse Vector Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Shaon Sahoo","submitted_at":"2008-04-14T18:27:21Z","abstract_excerpt":"In different branches of physics, we frequently deal with vector del operator ($\\vec{\\nabla}$). This del operator is generally used to find curl or divergence of a vector function or gradient of a scalar function. In many important cases, we need to know the parent vector whose curl or divergence is known or require to find the parent scalar function whose gradient is known. But the task is not very easy, especially in case of finding vector potential whose curl is known. Here,'inverse curl', 'inverse divergence' and 'inverse gradient' operators are defined to solve those problems easily. All "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2239","kind":"arxiv","version":3},"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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ce4Jbe4W9hAsFTU6tdAPromrl+q9J1RZNGoGTJ9wRlNj2XVeLROagSYIJ0myUJ/Hb1sbiRkJEQpdkEEKWw76Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T00:05:44.122210Z"},"content_sha256":"1c0633cfc4438acd12e59452a4d5208cb2d42930124e7e233f39464d77bb1c57","schema_version":"1.0","event_id":"sha256:1c0633cfc4438acd12e59452a4d5208cb2d42930124e7e233f39464d77bb1c57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/bundle.json","state_url":"https://pith.science/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/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":"2026-05-20T00:05:44Z","links":{"resolver":"https://pith.science/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV","bundle":"https://pith.science/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/bundle.json","state":"https://pith.science/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZA6MTOSJGHAV4KXYC3VFXNDOXV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ZA6MTOSJGHAV4KXYC3VFXNDOXV","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":"23f9b78a3dced0265b2109938b953d4d25712eeaab159777bd6ed9a21274a6c8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-14T18:27:21Z","title_canon_sha256":"236926ba30dcf168132d70aeddfca607177cd29e27350da44b394ee116124690"},"schema_version":"1.0","source":{"id":"0804.2239","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.2239","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"0804.2239v3","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.2239","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZA6MTOSJGHAV","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZA6MTOSJGHAV4KXY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZA6MTOSJ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:1c0633cfc4438acd12e59452a4d5208cb2d42930124e7e233f39464d77bb1c57","target":"graph","created_at":"2026-05-18T04:41:54Z","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":"In different branches of physics, we frequently deal with vector del operator ($\\vec{\\nabla}$). This del operator is generally used to find curl or divergence of a vector function or gradient of a scalar function. In many important cases, we need to know the parent vector whose curl or divergence is known or require to find the parent scalar function whose gradient is known. But the task is not very easy, especially in case of finding vector potential whose curl is known. Here,'inverse curl', 'inverse divergence' and 'inverse gradient' operators are defined to solve those problems easily. All ","authors_text":"Shaon Sahoo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-14T18:27:21Z","title":"Inverse Vector Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.2239","kind":"arxiv","version":3},"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":"sha256:5e6ddb176564f7fbbc5784acffb28212b13ad77cd020e8167139b5f78298dc61","target":"record","created_at":"2026-05-18T04:41:54Z","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":"23f9b78a3dced0265b2109938b953d4d25712eeaab159777bd6ed9a21274a6c8","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-04-14T18:27:21Z","title_canon_sha256":"236926ba30dcf168132d70aeddfca607177cd29e27350da44b394ee116124690"},"schema_version":"1.0","source":{"id":"0804.2239","kind":"arxiv","version":3}},"canonical_sha256":"c83cc9ba4931c15e2af816ea5bb46ebd74ba39b61750ba47b5bc7efdbef1283e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c83cc9ba4931c15e2af816ea5bb46ebd74ba39b61750ba47b5bc7efdbef1283e","first_computed_at":"2026-05-18T04:41:54.963846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.963846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZN6QYobltpushM0UXrB7PJSeXuExNIdvyDPCIpldKcLMXzS+fHZalSuR3fgl9qjavILEQ+Wfa+7y74VKhpjCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.964469Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.2239","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e6ddb176564f7fbbc5784acffb28212b13ad77cd020e8167139b5f78298dc61","sha256:1c0633cfc4438acd12e59452a4d5208cb2d42930124e7e233f39464d77bb1c57"],"state_sha256":"56dd04f627a752b6cd710300db771ed3ce018fdda9f71ac0190edd556cf0d45d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2baEJREPneYoiI8fh8kV/MdB4QdghYp5WWlUMug5cBrdhKEmgESkbHHamKKsFZ/ve8xleABPf58Jn2qg800lDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T00:05:44.124891Z","bundle_sha256":"fbe4b87c83004fed793de3660df7d4328d23027bf4adffe6dfcf78d63414d2ca"}}