{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:TBHYW4YLQBFOBLVZUOSLWY3VVT","short_pith_number":"pith:TBHYW4YL","schema_version":"1.0","canonical_sha256":"984f8b730b804ae0aeb9a3a4bb6375acd3d73bfbb9006538380fb5a31c7cd69a","source":{"kind":"arxiv","id":"1810.11504","version":1},"attestation_state":"computed","paper":{"title":"Riemann problems and dispersive shocks in self-focusing media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Gino Biondini","submitted_at":"2018-10-26T18:57:32Z","abstract_excerpt":"The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions with a jump in either or both the amplitude and the local wavenumber are considered. It is shown analytically and numerically that the space-time plane divides into expanding domains in which the solution is described by a slow modulation of genus-zero, genus-one or genus-two solutions, their precise arrangement depending on the specifics of the initial datu"},"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":"1810.11504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2018-10-26T18:57:32Z","cross_cats_sorted":[],"title_canon_sha256":"8ac451c3dd1452734fb0cde354e0ecbdb8d4c666cdcc5f598ea0868c9318e4c8","abstract_canon_sha256":"1cb52444528003028802d0f140e926e72f9133fef77e4f7da80208cdb4357112"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:04.368914Z","signature_b64":"VcQk74dTWfIEFFtgNf82jSBPcZeLoAj21w6SUXE1bx9+3e6PTK6yMqmog0KqmkG/vnDSJwVCxABfggfYyScvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"984f8b730b804ae0aeb9a3a4bb6375acd3d73bfbb9006538380fb5a31c7cd69a","last_reissued_at":"2026-05-17T23:59:04.368526Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:04.368526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riemann problems and dispersive shocks in self-focusing media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Gino Biondini","submitted_at":"2018-10-26T18:57:32Z","abstract_excerpt":"The dynamical behavior resulting from an initial discontinuity in focusing media is investigated using a combination of numerical simulations and Whitham modulation theory for the focusing nonlinear Schrodinger equation. Initial conditions with a jump in either or both the amplitude and the local wavenumber are considered. It is shown analytically and numerically that the space-time plane divides into expanding domains in which the solution is described by a slow modulation of genus-zero, genus-one or genus-two solutions, their precise arrangement depending on the specifics of the initial datu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11504","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":"1810.11504","created_at":"2026-05-17T23:59:04.368584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.11504v1","created_at":"2026-05-17T23:59:04.368584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.11504","created_at":"2026-05-17T23:59:04.368584+00:00"},{"alias_kind":"pith_short_12","alias_value":"TBHYW4YLQBFO","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TBHYW4YLQBFOBLVZ","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TBHYW4YL","created_at":"2026-05-18T12:32:53.628368+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/TBHYW4YLQBFOBLVZUOSLWY3VVT","json":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT.json","graph_json":"https://pith.science/api/pith-number/TBHYW4YLQBFOBLVZUOSLWY3VVT/graph.json","events_json":"https://pith.science/api/pith-number/TBHYW4YLQBFOBLVZUOSLWY3VVT/events.json","paper":"https://pith.science/paper/TBHYW4YL"},"agent_actions":{"view_html":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT","download_json":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT.json","view_paper":"https://pith.science/paper/TBHYW4YL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.11504&json=true","fetch_graph":"https://pith.science/api/pith-number/TBHYW4YLQBFOBLVZUOSLWY3VVT/graph.json","fetch_events":"https://pith.science/api/pith-number/TBHYW4YLQBFOBLVZUOSLWY3VVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT/action/storage_attestation","attest_author":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT/action/author_attestation","sign_citation":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT/action/citation_signature","submit_replication":"https://pith.science/pith/TBHYW4YLQBFOBLVZUOSLWY3VVT/action/replication_record"}},"created_at":"2026-05-17T23:59:04.368584+00:00","updated_at":"2026-05-17T23:59:04.368584+00:00"}