{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UVUGQQJR36ASJZSVDCLBJ5X3B7","short_pith_number":"pith:UVUGQQJR","canonical_record":{"source":{"id":"1309.6064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-24T07:11:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a6a3030ef60cf179d9386404488f82629d77acb4b82da3351e7354f6b8fda3d4","abstract_canon_sha256":"8108d40759b5d92e9d92b5184acf207466a5c3a28857e7f007ad561db8bb52df"},"schema_version":"1.0"},"canonical_sha256":"a568684131df8124e655189614f6fb0feccff84d28528f02ad7606b0cc80e65d","source":{"kind":"arxiv","id":"1309.6064","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6064","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6064v2","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6064","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"UVUGQQJR36AS","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_16","alias_value":"UVUGQQJR36ASJZSV","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_8","alias_value":"UVUGQQJR","created_at":"2026-06-04T14:09:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UVUGQQJR36ASJZSVDCLBJ5X3B7","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6064","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-24T07:11:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a6a3030ef60cf179d9386404488f82629d77acb4b82da3351e7354f6b8fda3d4","abstract_canon_sha256":"8108d40759b5d92e9d92b5184acf207466a5c3a28857e7f007ad561db8bb52df"},"schema_version":"1.0"},"canonical_sha256":"a568684131df8124e655189614f6fb0feccff84d28528f02ad7606b0cc80e65d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T14:09:11.801725Z","signature_b64":"0gwYpuzud/FRvdD+LYKvgPr4xhDjeMJKygbZzOOgCQ3bw586gU5quNXZp+yNfPN68iwTsPrfvCyCu8VDsAInCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a568684131df8124e655189614f6fb0feccff84d28528f02ad7606b0cc80e65d","last_reissued_at":"2026-06-04T14:09:11.801062Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T14:09:11.801062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6064","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-04T14:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bMSIWtJUMMk6ioe9mDVC/QNzl5hH9OO1BIF7BneyAZYd/larCOLV7eLO8bapSh3xUeP2VMxbYR60tEEvi50DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:16:41.981179Z"},"content_sha256":"244ae8830b5ed82b7289587d3403d9ef9d059ab1b8194c33c72293836df96c54","schema_version":"1.0","event_id":"sha256:244ae8830b5ed82b7289587d3403d9ef9d059ab1b8194c33c72293836df96c54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UVUGQQJR36ASJZSVDCLBJ5X3B7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical solutions of a class of second order boundary value problems on using Bernoulli Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Afroza Shirin, Md. Shafiqul Islam","submitted_at":"2013-09-24T07:11:16Z","abstract_excerpt":"The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6064","kind":"arxiv","version":2},"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/1309.6064/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":"2026-06-04T14:09:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8A19ThVfqXHADeHQemVnqGz+ucyEYbfktQFd3WY0yU9CaqquSAhLKfZL9Sssq1N+A/YghDibTMRQ9b16p7iDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:16:41.981567Z"},"content_sha256":"fa757c5a2add710442595b12b65a4fc02cffd3d39f1fcd4ae9d8300a62f6ca8c","schema_version":"1.0","event_id":"sha256:fa757c5a2add710442595b12b65a4fc02cffd3d39f1fcd4ae9d8300a62f6ca8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/bundle.json","state_url":"https://pith.science/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/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":"2026-06-25T23:16:41Z","links":{"resolver":"https://pith.science/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7","bundle":"https://pith.science/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/bundle.json","state":"https://pith.science/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UVUGQQJR36ASJZSVDCLBJ5X3B7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UVUGQQJR36ASJZSVDCLBJ5X3B7","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":"8108d40759b5d92e9d92b5184acf207466a5c3a28857e7f007ad561db8bb52df","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-24T07:11:16Z","title_canon_sha256":"a6a3030ef60cf179d9386404488f82629d77acb4b82da3351e7354f6b8fda3d4"},"schema_version":"1.0","source":{"id":"1309.6064","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6064","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6064v2","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6064","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_12","alias_value":"UVUGQQJR36AS","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_16","alias_value":"UVUGQQJR36ASJZSV","created_at":"2026-06-04T14:09:11Z"},{"alias_kind":"pith_short_8","alias_value":"UVUGQQJR","created_at":"2026-06-04T14:09:11Z"}],"graph_snapshots":[{"event_id":"sha256:fa757c5a2add710442595b12b65a4fc02cffd3d39f1fcd4ae9d8300a62f6ca8c","target":"graph","created_at":"2026-06-04T14:09:11Z","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/1309.6064/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care has been taken to satisfy the corresponding homogeneous form of the Dirichlet boundary conditions in the Galerkin weighted residual method. In addition to that the given differential equation over arbitr","authors_text":"Afroza Shirin, Md. Shafiqul Islam","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-24T07:11:16Z","title":"Numerical solutions of a class of second order boundary value problems on using Bernoulli Polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6064","kind":"arxiv","version":2},"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":"sha256:244ae8830b5ed82b7289587d3403d9ef9d059ab1b8194c33c72293836df96c54","target":"record","created_at":"2026-06-04T14:09:11Z","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":"8108d40759b5d92e9d92b5184acf207466a5c3a28857e7f007ad561db8bb52df","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-09-24T07:11:16Z","title_canon_sha256":"a6a3030ef60cf179d9386404488f82629d77acb4b82da3351e7354f6b8fda3d4"},"schema_version":"1.0","source":{"id":"1309.6064","kind":"arxiv","version":2}},"canonical_sha256":"a568684131df8124e655189614f6fb0feccff84d28528f02ad7606b0cc80e65d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a568684131df8124e655189614f6fb0feccff84d28528f02ad7606b0cc80e65d","first_computed_at":"2026-06-04T14:09:11.801062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T14:09:11.801062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0gwYpuzud/FRvdD+LYKvgPr4xhDjeMJKygbZzOOgCQ3bw586gU5quNXZp+yNfPN68iwTsPrfvCyCu8VDsAInCA==","signature_status":"signed_v1","signed_at":"2026-06-04T14:09:11.801725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6064","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:244ae8830b5ed82b7289587d3403d9ef9d059ab1b8194c33c72293836df96c54","sha256:fa757c5a2add710442595b12b65a4fc02cffd3d39f1fcd4ae9d8300a62f6ca8c"],"state_sha256":"a6dca60862f2e87c6138bfb7324efc479437375fa41010f33a677b8f39e7151b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l2z9AKT0EttMov0SQ7KGaQOpmBvsAkR5h+7xyPViW8c1ORuRKljCxWpbZCI/Z5ftpRo3dlZ2YzDatZNQTufMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:16:41.983547Z","bundle_sha256":"474d37abdc669bb843888b559ad517c5c2556dc176474d7bcd3b0292e5fc2ef6"}}