{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P7RWRDBMSY35LBDEYNWTIS6NGT","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":"f7b26e877c42c06d34722bd02e0fd20a83ea32530d371d6294b13830a23c6592","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-21T15:14:52Z","title_canon_sha256":"7ca93a3ac745d06c2ba38700ebb82073d1723ad9c10c1aa2f8177eb220b31e07"},"schema_version":"1.0","source":{"id":"1810.08972","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08972","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08972v1","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08972","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"P7RWRDBMSY35","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P7RWRDBMSY35LBDE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P7RWRDBM","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:42bd5dc3f3efaa1dad0b2f6b8a32577c04d468ea87f2af6dcdd307ac7062bdef","target":"graph","created_at":"2026-05-18T00:02:41Z","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":"A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient {\\epsilon}, is investigated. Results obtained prove that for slow time {\\epsilon}t < 1 waves are propagated almost undisturbed, while for fast time t > 1 {\\epsilon} diffusion effects prevail.","authors_text":"Monica De Angelis","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-21T15:14:52Z","title":"A wave equation perturbed by viscous terms: fast and slow times diffusion effects in a Neumann problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08972","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":"sha256:2e45bcf45f01076336b09c2d27aa2e18a6cfb7fa560995309824e52181b0c850","target":"record","created_at":"2026-05-18T00:02:41Z","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":"f7b26e877c42c06d34722bd02e0fd20a83ea32530d371d6294b13830a23c6592","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-21T15:14:52Z","title_canon_sha256":"7ca93a3ac745d06c2ba38700ebb82073d1723ad9c10c1aa2f8177eb220b31e07"},"schema_version":"1.0","source":{"id":"1810.08972","kind":"arxiv","version":1}},"canonical_sha256":"7fe3688c2c9637d58464c36d344bcd34f94e080778df5fe6ca82a97d3c2dd331","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fe3688c2c9637d58464c36d344bcd34f94e080778df5fe6ca82a97d3c2dd331","first_computed_at":"2026-05-18T00:02:41.322255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:41.322255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TDHn+ujoRcX45A4PDU/W8sZkRdOV9XcX66Xd9ctimSJFl2Gcn6Bdp+d0clzQ0Rx06gRt4/nV/OpyJS3dlY2ADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:41.322898Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08972","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e45bcf45f01076336b09c2d27aa2e18a6cfb7fa560995309824e52181b0c850","sha256:42bd5dc3f3efaa1dad0b2f6b8a32577c04d468ea87f2af6dcdd307ac7062bdef"],"state_sha256":"cd6d2fc5161a0cc38d0918c7670095574b31c41361db5a4f4582934802f5945e"}