{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P2MVWODUR6UPDVD5CPB3CY7MHB","short_pith_number":"pith:P2MVWODU","canonical_record":{"source":{"id":"1702.05553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-18T01:12:02Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"901cdcaf987811b4336fa92b05b7dd3cfe026d34dc626cf8663759c246f4e16a","abstract_canon_sha256":"33342150076074af898882b16177dc8a51493a50747c2e85977122176e2498b4"},"schema_version":"1.0"},"canonical_sha256":"7e995b38748fa8f1d47d13c3b163ec38519a7045fbec6f1f6205cc064fc0d62d","source":{"kind":"arxiv","id":"1702.05553","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05553","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05553v2","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05553","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"pith_short_12","alias_value":"P2MVWODUR6UP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P2MVWODUR6UPDVD5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P2MVWODU","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P2MVWODUR6UPDVD5CPB3CY7MHB","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-18T01:12:02Z","cross_cats_sorted":["q-bio.NC"],"title_canon_sha256":"901cdcaf987811b4336fa92b05b7dd3cfe026d34dc626cf8663759c246f4e16a","abstract_canon_sha256":"33342150076074af898882b16177dc8a51493a50747c2e85977122176e2498b4"},"schema_version":"1.0"},"canonical_sha256":"7e995b38748fa8f1d47d13c3b163ec38519a7045fbec6f1f6205cc064fc0d62d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:19.582938Z","signature_b64":"+KFC3DCMlaqIG6uoKMYyx/2IqXKagTIiZBbJAdPf/tiKlYvc+39rTtTUXBesAJW51iLrN8txcyNXte326H6UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e995b38748fa8f1d47d13c3b163ec38519a7045fbec6f1f6205cc064fc0d62d","last_reissued_at":"2026-05-18T00:17:19.582383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:19.582383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05553","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":"2026-05-18T00:17:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/4FoWoEnldVie5x1myUBFu6nVNNh+o/eqQioJ/uvqOrvsi0V9oBkmboQUxVb1uR4J9aMSLpOXrTPRoTBmcIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:40:46.850897Z"},"content_sha256":"1c224254240126d13b4a1626f35332b8003a20f3cab188da2daad3382cf7465f","schema_version":"1.0","event_id":"sha256:1c224254240126d13b4a1626f35332b8003a20f3cab188da2daad3382cf7465f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P2MVWODUR6UPDVD5CPB3CY7MHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Serena Dipierro","submitted_at":"2017-02-18T01:12:02Z","abstract_excerpt":"Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurringin the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05553","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":"2026-05-18T00:17:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFwNgnI7lnbyEu0vgdY9vxfF5WYAt0skV8mPnM/BfqqOmWp+ZuPuRvD2pT7zCRmmFfVo78uRD6oDhmQbv03nAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T17:40:46.851252Z"},"content_sha256":"874ca4b838ed2c4d836075e98c1fefb6b4fcc6672005571857f6ef5127de5a22","schema_version":"1.0","event_id":"sha256:874ca4b838ed2c4d836075e98c1fefb6b4fcc6672005571857f6ef5127de5a22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/bundle.json","state_url":"https://pith.science/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/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":"2026-06-05T17:40:46Z","links":{"resolver":"https://pith.science/pith/P2MVWODUR6UPDVD5CPB3CY7MHB","bundle":"https://pith.science/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/bundle.json","state":"https://pith.science/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2MVWODUR6UPDVD5CPB3CY7MHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P2MVWODUR6UPDVD5CPB3CY7MHB","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":"33342150076074af898882b16177dc8a51493a50747c2e85977122176e2498b4","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-18T01:12:02Z","title_canon_sha256":"901cdcaf987811b4336fa92b05b7dd3cfe026d34dc626cf8663759c246f4e16a"},"schema_version":"1.0","source":{"id":"1702.05553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05553","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05553v2","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05553","created_at":"2026-05-18T00:17:19Z"},{"alias_kind":"pith_short_12","alias_value":"P2MVWODUR6UP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P2MVWODUR6UPDVD5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P2MVWODU","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:874ca4b838ed2c4d836075e98c1fefb6b4fcc6672005571857f6ef5127de5a22","target":"graph","created_at":"2026-05-18T00:17:19Z","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":"Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurringin the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may ","authors_text":"Enrico Valdinoci, Serena Dipierro","cross_cats":["q-bio.NC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-18T01:12:02Z","title":"A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05553","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":"sha256:1c224254240126d13b4a1626f35332b8003a20f3cab188da2daad3382cf7465f","target":"record","created_at":"2026-05-18T00:17:19Z","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":"33342150076074af898882b16177dc8a51493a50747c2e85977122176e2498b4","cross_cats_sorted":["q-bio.NC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-18T01:12:02Z","title_canon_sha256":"901cdcaf987811b4336fa92b05b7dd3cfe026d34dc626cf8663759c246f4e16a"},"schema_version":"1.0","source":{"id":"1702.05553","kind":"arxiv","version":2}},"canonical_sha256":"7e995b38748fa8f1d47d13c3b163ec38519a7045fbec6f1f6205cc064fc0d62d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e995b38748fa8f1d47d13c3b163ec38519a7045fbec6f1f6205cc064fc0d62d","first_computed_at":"2026-05-18T00:17:19.582383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:19.582383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+KFC3DCMlaqIG6uoKMYyx/2IqXKagTIiZBbJAdPf/tiKlYvc+39rTtTUXBesAJW51iLrN8txcyNXte326H6UBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:19.582938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c224254240126d13b4a1626f35332b8003a20f3cab188da2daad3382cf7465f","sha256:874ca4b838ed2c4d836075e98c1fefb6b4fcc6672005571857f6ef5127de5a22"],"state_sha256":"dc9b33cd7eef48940cc5a09e4f9c8f99db615c1542859a9a055b93d6174884eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0zXlxuANpRgy4igPfZbedCGdRCYxwP3BGChxUtKEVQSbqBfQIHypkPPvH3bRQtXYKkrv4FI60t47r/UgKzICA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T17:40:46.853302Z","bundle_sha256":"ea6dc9f5f74ce50602dd8d26edd4d0e808aa742a40437d5452f66632f12b413f"}}