{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LCT5XXLOP24LUXGBU6UCPDYXWP","short_pith_number":"pith:LCT5XXLO","schema_version":"1.0","canonical_sha256":"58a7dbdd6e7eb8ba5cc1a7a8278f17b3cba961e272dec5aacfc76d9592fcd25e","source":{"kind":"arxiv","id":"1208.4425","version":2},"attestation_state":"computed","paper":{"title":"Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Natalia Vladimirova, Pavel M. Lushnikov, Sergey A. Dyachenko","submitted_at":"2012-08-22T05:37:42Z","abstract_excerpt":"We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\\propto (\\ln|\\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which d"},"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":"1208.4425","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-08-22T05:37:42Z","cross_cats_sorted":["math.AP","physics.optics"],"title_canon_sha256":"b2b0861177db6285c4eed1a82cc5d40c245fe06594ffc69791d6a14f39ac346f","abstract_canon_sha256":"64e8be0019dbf15bcac7dad066cdf5b3bf5ce3e5d5f1d17702da0810e302ff46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:24.879991Z","signature_b64":"uTHHlhxLEjWcd6v/Xdukf8oT69x9vxl9/hj3vWE9srrUmSJzVVaiONJll3hSjJIf3RVZ8Ea2cIp8pyq2gUgGAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58a7dbdd6e7eb8ba5cc1a7a8278f17b3cba961e272dec5aacfc76d9592fcd25e","last_reissued_at":"2026-05-18T03:17:24.879381Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:24.879381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","physics.optics"],"primary_cat":"nlin.PS","authors_text":"Natalia Vladimirova, Pavel M. Lushnikov, Sergey A. Dyachenko","submitted_at":"2012-08-22T05:37:42Z","abstract_excerpt":"We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance $z=z_c$ obeys $(z_c-z)^{1/2}$ scaling law with the well-known leading order modification of loglog type $\\propto (\\ln|\\ln(z_c-z)|)^{-1/2}$. We show that the validity of the loglog modification requires double-exponentially large amplitudes of the solution $\\sim {10^{10}}^{100}$, which is unrealistic to achieve in either physical experiments or numerical simulations. We derive a new equation for the adiabatically slow parameter which d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4425","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.4425","created_at":"2026-05-18T03:17:24.879465+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4425v2","created_at":"2026-05-18T03:17:24.879465+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4425","created_at":"2026-05-18T03:17:24.879465+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCT5XXLOP24L","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCT5XXLOP24LUXGB","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCT5XXLO","created_at":"2026-05-18T12:27:14.488303+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/LCT5XXLOP24LUXGBU6UCPDYXWP","json":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP.json","graph_json":"https://pith.science/api/pith-number/LCT5XXLOP24LUXGBU6UCPDYXWP/graph.json","events_json":"https://pith.science/api/pith-number/LCT5XXLOP24LUXGBU6UCPDYXWP/events.json","paper":"https://pith.science/paper/LCT5XXLO"},"agent_actions":{"view_html":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP","download_json":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP.json","view_paper":"https://pith.science/paper/LCT5XXLO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4425&json=true","fetch_graph":"https://pith.science/api/pith-number/LCT5XXLOP24LUXGBU6UCPDYXWP/graph.json","fetch_events":"https://pith.science/api/pith-number/LCT5XXLOP24LUXGBU6UCPDYXWP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP/action/storage_attestation","attest_author":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP/action/author_attestation","sign_citation":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP/action/citation_signature","submit_replication":"https://pith.science/pith/LCT5XXLOP24LUXGBU6UCPDYXWP/action/replication_record"}},"created_at":"2026-05-18T03:17:24.879465+00:00","updated_at":"2026-05-18T03:17:24.879465+00:00"}