{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:N6JAOCMZKGBNCZLIV4RSF7NOOX","short_pith_number":"pith:N6JAOCMZ","schema_version":"1.0","canonical_sha256":"6f920709995182d16568af2322fdae75dfa18a8592e885fdb58d5f8d52087419","source":{"kind":"arxiv","id":"1609.04441","version":1},"attestation_state":"computed","paper":{"title":"Long-time behavior for crystal dislocation dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Stefania Patrizi","submitted_at":"2016-09-14T20:52:18Z","abstract_excerpt":"We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal.\n  More precisely, we can describe accurately the \"smoothing effect\" on the dislocation function occurring slightly after a \"particle collision\" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.04441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-14T20:52:18Z","cross_cats_sorted":[],"title_canon_sha256":"e873b1a895d2f3f54a2eb47e3c300043a6804cc343a5b801535f306cd04d470a","abstract_canon_sha256":"a05c61ae3da248118b125c03d5c261229dfc686dc580c05a8a1b89ec43252ee0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:36.718928Z","signature_b64":"/7rjD81yLTuW43JUarrdgBFnzC66PssCppU0ipTMHGILAsXcWB9Ug/XmG8D84lPRg51ix1HgREgT8HfrzhFFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f920709995182d16568af2322fdae75dfa18a8592e885fdb58d5f8d52087419","last_reissued_at":"2026-05-18T01:04:36.718264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:36.718264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time behavior for crystal dislocation dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enrico Valdinoci, Stefania Patrizi","submitted_at":"2016-09-14T20:52:18Z","abstract_excerpt":"We describe the asymptotic states for the solutions of a nonlocal equation of evolutionary type, which have the physical meaning of the atom dislocation function in a periodic crystal.\n  More precisely, we can describe accurately the \"smoothing effect\" on the dislocation function occurring slightly after a \"particle collision\" (roughly speaking, two opposite transitions layers average out) and, in this way, we can trap the atom dislocation function between a superposition of transition layers which, as time flows, approaches either a constant function or a single heteroclinic (depending on the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04441","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.04441","created_at":"2026-05-18T01:04:36.718377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04441v1","created_at":"2026-05-18T01:04:36.718377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04441","created_at":"2026-05-18T01:04:36.718377+00:00"},{"alias_kind":"pith_short_12","alias_value":"N6JAOCMZKGBN","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"N6JAOCMZKGBNCZLI","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"N6JAOCMZ","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX","json":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX.json","graph_json":"https://pith.science/api/pith-number/N6JAOCMZKGBNCZLIV4RSF7NOOX/graph.json","events_json":"https://pith.science/api/pith-number/N6JAOCMZKGBNCZLIV4RSF7NOOX/events.json","paper":"https://pith.science/paper/N6JAOCMZ"},"agent_actions":{"view_html":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX","download_json":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX.json","view_paper":"https://pith.science/paper/N6JAOCMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04441&json=true","fetch_graph":"https://pith.science/api/pith-number/N6JAOCMZKGBNCZLIV4RSF7NOOX/graph.json","fetch_events":"https://pith.science/api/pith-number/N6JAOCMZKGBNCZLIV4RSF7NOOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX/action/storage_attestation","attest_author":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX/action/author_attestation","sign_citation":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX/action/citation_signature","submit_replication":"https://pith.science/pith/N6JAOCMZKGBNCZLIV4RSF7NOOX/action/replication_record"}},"created_at":"2026-05-18T01:04:36.718377+00:00","updated_at":"2026-05-18T01:04:36.718377+00:00"}