{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4YTBGYMAS5D7CDW4RRCVS5QUZH","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":"8185911aff4315a74cd4f6a974f0372e9ba8e7b63e71d23810f329a8423e7378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T22:20:25Z","title_canon_sha256":"1931ddc6afaa6db0cf8b6b40e23806671930617483ef286cffcb3942feb00e01"},"schema_version":"1.0","source":{"id":"1304.1057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1057","created_at":"2026-05-18T03:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1057v1","created_at":"2026-05-18T03:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1057","created_at":"2026-05-18T03:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"4YTBGYMAS5D7","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4YTBGYMAS5D7CDW4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4YTBGYMA","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c8b70c83491ca9ac14a07e5433e9191760535e00bd27cb98956505fd31d79dd3","target":"graph","created_at":"2026-05-18T03:29:05Z","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":"In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behaviour is to introduce a memory formalism, including thus the time dependent viscosity by using an integro-differential term and therefore generalizing the classical equation of a Newtonian viscous fluid. A possible useful choice, in this framework, is to use a rheology based on stress/strain relation generalized by fractional calculus modelling. This is a model that can be used in applied problems, taking into account a","authors_text":"Federico Polito, Roberto Garra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T22:20:25Z","title":"Fractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1057","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":"sha256:8bbd68b08512e34aa8b6537d3e07807d6ed20607f7a994580be21fed20edd3ae","target":"record","created_at":"2026-05-18T03:29:05Z","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":"8185911aff4315a74cd4f6a974f0372e9ba8e7b63e71d23810f329a8423e7378","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-26T22:20:25Z","title_canon_sha256":"1931ddc6afaa6db0cf8b6b40e23806671930617483ef286cffcb3942feb00e01"},"schema_version":"1.0","source":{"id":"1304.1057","kind":"arxiv","version":1}},"canonical_sha256":"e6261361809747f10edc8c45597614c9f28e2a8e3278050ab5e854f87aaca7ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6261361809747f10edc8c45597614c9f28e2a8e3278050ab5e854f87aaca7ea","first_computed_at":"2026-05-18T03:29:05.419197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:05.419197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yi4GqwKjtYjABQIG2pHiGXUa0X9/yvK2KXOQalipZqulJWU4imgNC1hVnG7wJ5QBosjg/26K4sjMgl5Df16CAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:05.419711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bbd68b08512e34aa8b6537d3e07807d6ed20607f7a994580be21fed20edd3ae","sha256:c8b70c83491ca9ac14a07e5433e9191760535e00bd27cb98956505fd31d79dd3"],"state_sha256":"c2058a0da454b1d8f0993524c233c5b2bc4e52c6560c55ad5959436c5d66277d"}