{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4ECU345MPPRBT2JM42XCCBAGIT","short_pith_number":"pith:4ECU345M","canonical_record":{"source":{"id":"1305.3935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-05-16T21:03:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"716b23c662fd8ee9743bfc761015fd6cc3e0524c72256b35bcab80e0a2045729","abstract_canon_sha256":"66d19250a4c836b2ebd5351a45b28636c01ed400aefe9465836b4cca709af760"},"schema_version":"1.0"},"canonical_sha256":"e1054df3ac7be219e92ce6ae21040644cb5575cc60c23c970e634ccaaf1d4925","source":{"kind":"arxiv","id":"1305.3935","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3935","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3935v2","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3935","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"4ECU345MPPRB","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4ECU345MPPRBT2JM","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4ECU345M","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4ECU345MPPRBT2JM42XCCBAGIT","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3935","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-05-16T21:03:07Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"716b23c662fd8ee9743bfc761015fd6cc3e0524c72256b35bcab80e0a2045729","abstract_canon_sha256":"66d19250a4c836b2ebd5351a45b28636c01ed400aefe9465836b4cca709af760"},"schema_version":"1.0"},"canonical_sha256":"e1054df3ac7be219e92ce6ae21040644cb5575cc60c23c970e634ccaaf1d4925","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:49.508412Z","signature_b64":"eGQFgg1zABmaXHIZahUuPzsYzlN+Aza4uoqijlRc/FOpGDd40vZhygoaRfx27fT1q5KynrEPMwlGzTFMqyJbBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1054df3ac7be219e92ce6ae21040644cb5575cc60c23c970e634ccaaf1d4925","last_reissued_at":"2026-05-18T01:49:49.507939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:49.507939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3935","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":"2026-05-18T01:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LxaIrD0KB6dbBmKQIHG9ffMfrM19lJs5JoJSmcAsZ3WkT7T2gyv33UHs+Yc2qlV6dk1D/KNv535GVh3wewzYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:28:18.007116Z"},"content_sha256":"a333df30b9597589d879260ede62c1811c1dc902eff2553f8882b0d79e2f29cf","schema_version":"1.0","event_id":"sha256:a333df30b9597589d879260ede62c1811c1dc902eff2553f8882b0d79e2f29cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4ECU345MPPRBT2JM42XCCBAGIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Higher-Order Heat-Type Equations via signed L\\'{e}vy stable and generalized Airy functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"cond-mat.stat-mech","authors_text":"A. Horzela, G. Dattoli, K. A. Penson, K. Gorska","submitted_at":"2013-05-16T21:03:07Z","abstract_excerpt":"We study the higher-order heat-type equation with first time and M-th spatial partial derivatives, M = 2, 3, ... . We demonstrate that its exact solutions for M even can be constructed with the help of signed Levy stable functions. For M odd the same role is played by a special generalization of Airy Ai function that we introduce and study. This permits one to generate the exact and explicit heat kernels pertaining to these equations. We examine analytically and graphically the spacial and temporary evolution of particular solutions for simple initial conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3935","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":"2026-05-18T01:49:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8x6D6GIR65W0pjmXjQS6Amr4+tzD3sk6WtaCXex+g1/vflc0s0AKjFx1klyRTHQlL1I6p8Y2j1KPgRBxvpeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:28:18.007579Z"},"content_sha256":"d8c4a2a3b0476fa09c519058d63e9543a5fc9a2f8b1163e98c03d7de15e29d08","schema_version":"1.0","event_id":"sha256:d8c4a2a3b0476fa09c519058d63e9543a5fc9a2f8b1163e98c03d7de15e29d08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ECU345MPPRBT2JM42XCCBAGIT/bundle.json","state_url":"https://pith.science/pith/4ECU345MPPRBT2JM42XCCBAGIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ECU345MPPRBT2JM42XCCBAGIT/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":"2026-05-30T23:28:18Z","links":{"resolver":"https://pith.science/pith/4ECU345MPPRBT2JM42XCCBAGIT","bundle":"https://pith.science/pith/4ECU345MPPRBT2JM42XCCBAGIT/bundle.json","state":"https://pith.science/pith/4ECU345MPPRBT2JM42XCCBAGIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ECU345MPPRBT2JM42XCCBAGIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4ECU345MPPRBT2JM42XCCBAGIT","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":"66d19250a4c836b2ebd5351a45b28636c01ed400aefe9465836b4cca709af760","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-05-16T21:03:07Z","title_canon_sha256":"716b23c662fd8ee9743bfc761015fd6cc3e0524c72256b35bcab80e0a2045729"},"schema_version":"1.0","source":{"id":"1305.3935","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3935","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3935v2","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3935","created_at":"2026-05-18T01:49:49Z"},{"alias_kind":"pith_short_12","alias_value":"4ECU345MPPRB","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"4ECU345MPPRBT2JM","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"4ECU345M","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:d8c4a2a3b0476fa09c519058d63e9543a5fc9a2f8b1163e98c03d7de15e29d08","target":"graph","created_at":"2026-05-18T01:49:49Z","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 the higher-order heat-type equation with first time and M-th spatial partial derivatives, M = 2, 3, ... . We demonstrate that its exact solutions for M even can be constructed with the help of signed Levy stable functions. For M odd the same role is played by a special generalization of Airy Ai function that we introduce and study. This permits one to generate the exact and explicit heat kernels pertaining to these equations. We examine analytically and graphically the spacial and temporary evolution of particular solutions for simple initial conditions.","authors_text":"A. Horzela, G. Dattoli, K. A. Penson, K. Gorska","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-05-16T21:03:07Z","title":"The Higher-Order Heat-Type Equations via signed L\\'{e}vy stable and generalized Airy functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3935","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:a333df30b9597589d879260ede62c1811c1dc902eff2553f8882b0d79e2f29cf","target":"record","created_at":"2026-05-18T01:49:49Z","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":"66d19250a4c836b2ebd5351a45b28636c01ed400aefe9465836b4cca709af760","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-05-16T21:03:07Z","title_canon_sha256":"716b23c662fd8ee9743bfc761015fd6cc3e0524c72256b35bcab80e0a2045729"},"schema_version":"1.0","source":{"id":"1305.3935","kind":"arxiv","version":2}},"canonical_sha256":"e1054df3ac7be219e92ce6ae21040644cb5575cc60c23c970e634ccaaf1d4925","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1054df3ac7be219e92ce6ae21040644cb5575cc60c23c970e634ccaaf1d4925","first_computed_at":"2026-05-18T01:49:49.507939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:49.507939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eGQFgg1zABmaXHIZahUuPzsYzlN+Aza4uoqijlRc/FOpGDd40vZhygoaRfx27fT1q5KynrEPMwlGzTFMqyJbBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:49.508412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3935","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a333df30b9597589d879260ede62c1811c1dc902eff2553f8882b0d79e2f29cf","sha256:d8c4a2a3b0476fa09c519058d63e9543a5fc9a2f8b1163e98c03d7de15e29d08"],"state_sha256":"61c969992105564bdbfd5aa161685fc7a4af2a61a9c9b6e64fc4b4ac79361d0f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"na/AA+r8ZzV/EmNe7AiVaM3AiUwt4mjqCaVDREjbDs7ObhzUgaOaqbWYIjYVljjJoSeWthkkOmlo9Qcp4FUWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:28:18.009772Z","bundle_sha256":"b66123c353812fe320d8a66a1ea2ea70d1a1996b5e929fa07a8565303d5e888a"}}