{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NYPY6PJ74CGZ4QJURFII7DF3RL","short_pith_number":"pith:NYPY6PJ7","canonical_record":{"source":{"id":"1001.2181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-13T14:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"1b341182a8b550d709b349f137e55e88005a4c4e491a011f76f322ba1baf84e2","abstract_canon_sha256":"ee6c7cbc7e10478ac82595fd7864c4abc085c10a8fef74968a7ff870282f094e"},"schema_version":"1.0"},"canonical_sha256":"6e1f8f3d3fe08d9e413489508f8cbb8acd986d97efdf81bb79ecac7e580054c5","source":{"kind":"arxiv","id":"1001.2181","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2181","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2181v2","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2181","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"NYPY6PJ74CGZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NYPY6PJ74CGZ4QJU","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NYPY6PJ7","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NYPY6PJ74CGZ4QJURFII7DF3RL","target":"record","payload":{"canonical_record":{"source":{"id":"1001.2181","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-13T14:40:32Z","cross_cats_sorted":[],"title_canon_sha256":"1b341182a8b550d709b349f137e55e88005a4c4e491a011f76f322ba1baf84e2","abstract_canon_sha256":"ee6c7cbc7e10478ac82595fd7864c4abc085c10a8fef74968a7ff870282f094e"},"schema_version":"1.0"},"canonical_sha256":"6e1f8f3d3fe08d9e413489508f8cbb8acd986d97efdf81bb79ecac7e580054c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:01.638735Z","signature_b64":"ZwAiK0smBYHjOeOi8hxa1dd5ihDBHD3Q/f/tXw9ydmezDxOaR/iCbpKLuV7nHvNiT5MzdXOseL4cRcpu1Ru1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e1f8f3d3fe08d9e413489508f8cbb8acd986d97efdf81bb79ecac7e580054c5","last_reissued_at":"2026-05-18T03:41:01.638202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:01.638202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.2181","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":"2026-05-18T03:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqtvEj/CLRq+VedFn0UvAj83b/nUXupLmbwOt8JJlNk7TTTuOCQIC7kdmIopUHL2Vb89woFTsDBzOoVLKcUADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:44:47.640879Z"},"content_sha256":"cc6249027958361614bba78e9f48d1f35d6f8a654f0f205cd5c59919b03cf806","schema_version":"1.0","event_id":"sha256:cc6249027958361614bba78e9f48d1f35d6f8a654f0f205cd5c59919b03cf806"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NYPY6PJ74CGZ4QJURFII7DF3RL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A detailed analysis of the brachistochrone problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Rodney Coleman (LJK)","submitted_at":"2010-01-13T14:40:32Z","abstract_excerpt":"If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by the object gives rise to a mathematical optimisation problem involving an indefinite integral. Although the solution of this problem is known, a full detailed handling of the problem does not seem to be available. The aim of this article is to provide such a detailed study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2181","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":""},"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":"2026-05-18T03:41:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+EmbkW0uF2T+GWZJ3jx5orgt38Nn0kprurgDG5jpYmlEr9/sx0QqDziBnpiM0pgTg8ypL3wi3xLlAfZVG1zCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T08:44:47.641230Z"},"content_sha256":"cb15805616c29cc4f13bb42b88e7a74e95855f183396e13837c4d6566310a45c","schema_version":"1.0","event_id":"sha256:cb15805616c29cc4f13bb42b88e7a74e95855f183396e13837c4d6566310a45c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/bundle.json","state_url":"https://pith.science/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/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":"2026-06-12T08:44:47Z","links":{"resolver":"https://pith.science/pith/NYPY6PJ74CGZ4QJURFII7DF3RL","bundle":"https://pith.science/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/bundle.json","state":"https://pith.science/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYPY6PJ74CGZ4QJURFII7DF3RL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NYPY6PJ74CGZ4QJURFII7DF3RL","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":"ee6c7cbc7e10478ac82595fd7864c4abc085c10a8fef74968a7ff870282f094e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-13T14:40:32Z","title_canon_sha256":"1b341182a8b550d709b349f137e55e88005a4c4e491a011f76f322ba1baf84e2"},"schema_version":"1.0","source":{"id":"1001.2181","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2181","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2181v2","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2181","created_at":"2026-05-18T03:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"NYPY6PJ74CGZ","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"NYPY6PJ74CGZ4QJU","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"NYPY6PJ7","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:cb15805616c29cc4f13bb42b88e7a74e95855f183396e13837c4d6566310a45c","target":"graph","created_at":"2026-05-18T03:41:01Z","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":"If A and B are two points in the plane, with B lower and to the right of A, then we may consider the trajectory of an object travelling from A to B under the influence of gravity. The search for the trajectory minimising the time taken by the object gives rise to a mathematical optimisation problem involving an indefinite integral. Although the solution of this problem is known, a full detailed handling of the problem does not seem to be available. The aim of this article is to provide such a detailed study.","authors_text":"Rodney Coleman (LJK)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-13T14:40:32Z","title":"A detailed analysis of the brachistochrone problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2181","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:cc6249027958361614bba78e9f48d1f35d6f8a654f0f205cd5c59919b03cf806","target":"record","created_at":"2026-05-18T03:41:01Z","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":"ee6c7cbc7e10478ac82595fd7864c4abc085c10a8fef74968a7ff870282f094e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-13T14:40:32Z","title_canon_sha256":"1b341182a8b550d709b349f137e55e88005a4c4e491a011f76f322ba1baf84e2"},"schema_version":"1.0","source":{"id":"1001.2181","kind":"arxiv","version":2}},"canonical_sha256":"6e1f8f3d3fe08d9e413489508f8cbb8acd986d97efdf81bb79ecac7e580054c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e1f8f3d3fe08d9e413489508f8cbb8acd986d97efdf81bb79ecac7e580054c5","first_computed_at":"2026-05-18T03:41:01.638202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:01.638202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZwAiK0smBYHjOeOi8hxa1dd5ihDBHD3Q/f/tXw9ydmezDxOaR/iCbpKLuV7nHvNiT5MzdXOseL4cRcpu1Ru1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:01.638735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2181","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc6249027958361614bba78e9f48d1f35d6f8a654f0f205cd5c59919b03cf806","sha256:cb15805616c29cc4f13bb42b88e7a74e95855f183396e13837c4d6566310a45c"],"state_sha256":"eb566f6305f679a04b1829025ab3e1f347f5c8e1cb44da7403599f885d8bb3cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wGTCPrcz0I3bDBpCR1HikiqLh7p7kpCHwaJKsUknD2Epe2musA+X85GDBbJnJN+5teBdYlRKvD+/n8t/++0nDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:44:47.643095Z","bundle_sha256":"74badcde1a1ccb27a2e2675e25baf7b70e18629c7798a52456f0ad79b90da712"}}