{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:5DEZ4N5KVTIVKSHNWWC5NQPJCF","short_pith_number":"pith:5DEZ4N5K","canonical_record":{"source":{"id":"0705.3598","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-05-24T14:55:28Z","cross_cats_sorted":[],"title_canon_sha256":"2b400e22b741b1dfa29633ee641ef7503e9e1426fff7cfeb9b8ebb50dd92594c","abstract_canon_sha256":"7d8b405b5cd98e1663aa3cc7f1321e244d05bb16480d0a7ed62a00a0cbc6bcfa"},"schema_version":"1.0"},"canonical_sha256":"e8c99e37aaacd15548edb585d6c1e911625a656999aff8948fa02cc566199860","source":{"kind":"arxiv","id":"0705.3598","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3598","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3598v1","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3598","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"pith_short_12","alias_value":"5DEZ4N5KVTIV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5DEZ4N5KVTIVKSHN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5DEZ4N5K","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:5DEZ4N5KVTIVKSHNWWC5NQPJCF","target":"record","payload":{"canonical_record":{"source":{"id":"0705.3598","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-05-24T14:55:28Z","cross_cats_sorted":[],"title_canon_sha256":"2b400e22b741b1dfa29633ee641ef7503e9e1426fff7cfeb9b8ebb50dd92594c","abstract_canon_sha256":"7d8b405b5cd98e1663aa3cc7f1321e244d05bb16480d0a7ed62a00a0cbc6bcfa"},"schema_version":"1.0"},"canonical_sha256":"e8c99e37aaacd15548edb585d6c1e911625a656999aff8948fa02cc566199860","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:36.550509Z","signature_b64":"6VJ6s7XmwDJcU18MgliOwcgythP6kUwL4YH4bJPHzgpiSxLkbVV/mMqRdMRCsTd+Mil1EGQEHHQ2/I3I19gMAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8c99e37aaacd15548edb585d6c1e911625a656999aff8948fa02cc566199860","last_reissued_at":"2026-05-18T04:27:36.549881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:36.549881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.3598","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":"2026-05-18T04:27:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9z7sG/XvkDR3GlsJcnyjUVIVyuWWIM3qQ2R7fPp3y0ZhpWrz3/1HECJpTWvNyIXoOivS9kK7Zc4qGAcGaksFDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:04:03.420426Z"},"content_sha256":"803d0a8fbf496c68798700a853ccdbef72be61e6ff23e88eb224d25602baef47","schema_version":"1.0","event_id":"sha256:803d0a8fbf496c68798700a853ccdbef72be61e6ff23e88eb224d25602baef47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:5DEZ4N5KVTIVKSHNWWC5NQPJCF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pseudoprocesses governed by higher-order fractional differential equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luisa Beghin","submitted_at":"2007-05-24T14:55:28Z","abstract_excerpt":"We study here a heat-type differential equation of order n greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess (coinciding with the one governed by the standard, non-fractional, equation) with a time argument T which is itself random. The distribution of T is presented together with some features of the solution (such as analytic expressions for its moments)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3598","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":"2026-05-18T04:27:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7jrux9tB8bepOrgsTbeSx3cwTFZ7aH+KqOuwTgqUPCrDqxIFO9JVCoNKCbIqja5D2EZFQsJ96FQqUKpOeQJODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T22:04:03.420775Z"},"content_sha256":"e1c9f04af5b8657465cadf305b7577ee52a77fbaa8346e5b8f8f4da6edbd8526","schema_version":"1.0","event_id":"sha256:e1c9f04af5b8657465cadf305b7577ee52a77fbaa8346e5b8f8f4da6edbd8526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/bundle.json","state_url":"https://pith.science/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/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":"2026-06-27T22:04:03Z","links":{"resolver":"https://pith.science/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF","bundle":"https://pith.science/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/bundle.json","state":"https://pith.science/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DEZ4N5KVTIVKSHNWWC5NQPJCF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:5DEZ4N5KVTIVKSHNWWC5NQPJCF","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":"7d8b405b5cd98e1663aa3cc7f1321e244d05bb16480d0a7ed62a00a0cbc6bcfa","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-05-24T14:55:28Z","title_canon_sha256":"2b400e22b741b1dfa29633ee641ef7503e9e1426fff7cfeb9b8ebb50dd92594c"},"schema_version":"1.0","source":{"id":"0705.3598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3598","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3598v1","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3598","created_at":"2026-05-18T04:27:36Z"},{"alias_kind":"pith_short_12","alias_value":"5DEZ4N5KVTIV","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"5DEZ4N5KVTIVKSHN","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"5DEZ4N5K","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:e1c9f04af5b8657465cadf305b7577ee52a77fbaa8346e5b8f8f4da6edbd8526","target":"graph","created_at":"2026-05-18T04:27:36Z","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 study here a heat-type differential equation of order n greater than two, in the case where the time-derivative is supposed to be fractional. The corresponding solution can be described as the transition function of a pseudoprocess (coinciding with the one governed by the standard, non-fractional, equation) with a time argument T which is itself random. The distribution of T is presented together with some features of the solution (such as analytic expressions for its moments).","authors_text":"Luisa Beghin","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-05-24T14:55:28Z","title":"Pseudoprocesses governed by higher-order fractional differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3598","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":"sha256:803d0a8fbf496c68798700a853ccdbef72be61e6ff23e88eb224d25602baef47","target":"record","created_at":"2026-05-18T04:27:36Z","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":"7d8b405b5cd98e1663aa3cc7f1321e244d05bb16480d0a7ed62a00a0cbc6bcfa","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-05-24T14:55:28Z","title_canon_sha256":"2b400e22b741b1dfa29633ee641ef7503e9e1426fff7cfeb9b8ebb50dd92594c"},"schema_version":"1.0","source":{"id":"0705.3598","kind":"arxiv","version":1}},"canonical_sha256":"e8c99e37aaacd15548edb585d6c1e911625a656999aff8948fa02cc566199860","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8c99e37aaacd15548edb585d6c1e911625a656999aff8948fa02cc566199860","first_computed_at":"2026-05-18T04:27:36.549881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:36.549881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VJ6s7XmwDJcU18MgliOwcgythP6kUwL4YH4bJPHzgpiSxLkbVV/mMqRdMRCsTd+Mil1EGQEHHQ2/I3I19gMAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:36.550509Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.3598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:803d0a8fbf496c68798700a853ccdbef72be61e6ff23e88eb224d25602baef47","sha256:e1c9f04af5b8657465cadf305b7577ee52a77fbaa8346e5b8f8f4da6edbd8526"],"state_sha256":"019a2b3ee321b6f8d3be49743bf4b5afb8565b86c7dafa78ae75d67e18434637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Xp3DQAhRLxiHG3FCdrzuBKtIA4589YJb2r/9f48gm6yHgn6golkZ5BlyYFObK80sLjsFFkUvUILLhyYY16ZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T22:04:03.422690Z","bundle_sha256":"60b2fbfc7390689b8063e479b1bf6d92aaea624fb99098e6bce32313f7a920fa"}}