{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VAHDMS2MJZBHE4M4656YUKASX5","short_pith_number":"pith:VAHDMS2M","canonical_record":{"source":{"id":"2409.01135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2024-09-02T10:16:53Z","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"title_canon_sha256":"647b65387f7f0ba4d6d60781dfee6bcbd9915460b3ab868c53097dc156e0c39c","abstract_canon_sha256":"5ac977c4d3f2d297a577892d0db0a4b0deab28b02168b4a9ed6a6bae7ee2f355"},"schema_version":"1.0"},"canonical_sha256":"a80e364b4c4e4272719cf77d8a2812bf4eb3c6b64f0064c12195258adc580e12","source":{"kind":"arxiv","id":"2409.01135","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01135","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01135v1","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01135","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"VAHDMS2MJZBH","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_16","alias_value":"VAHDMS2MJZBHE4M4","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_8","alias_value":"VAHDMS2M","created_at":"2026-07-05T09:01:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VAHDMS2MJZBHE4M4656YUKASX5","target":"record","payload":{"canonical_record":{"source":{"id":"2409.01135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2024-09-02T10:16:53Z","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"title_canon_sha256":"647b65387f7f0ba4d6d60781dfee6bcbd9915460b3ab868c53097dc156e0c39c","abstract_canon_sha256":"5ac977c4d3f2d297a577892d0db0a4b0deab28b02168b4a9ed6a6bae7ee2f355"},"schema_version":"1.0"},"canonical_sha256":"a80e364b4c4e4272719cf77d8a2812bf4eb3c6b64f0064c12195258adc580e12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:01:59.479491Z","signature_b64":"x1mlJXK9R/c6rn42f42OC4JPXcP/3mDFVL2sNmlbBcHLn2rfDlh6PWvIPie8N60UqNTY+MkfAFvxCve20zWCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a80e364b4c4e4272719cf77d8a2812bf4eb3c6b64f0064c12195258adc580e12","last_reissued_at":"2026-07-05T09:01:59.479033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:01:59.479033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.01135","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"53+xJpupPNr3Umuj3L7GD9zz8Kzvv3ytFUH1NYk2+kwPTt7A8PkEu+lAl4T5ZK838iOPvRri35I6rcxawOeECw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:43:28.124746Z"},"content_sha256":"b4e094faa237027179d4afe78f2cfe09535537750954b78b706c43a421390ab7","schema_version":"1.0","event_id":"sha256:b4e094faa237027179d4afe78f2cfe09535537750954b78b706c43a421390ab7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VAHDMS2MJZBHE4M4656YUKASX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-L\\'evy-index fractional Kerr media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"primary_cat":"nlin.PS","authors_text":"Boris A. Malomed, Ming Zhong, Yong Chen, Zhenya Yan","submitted_at":"2024-09-02T10:16:53Z","abstract_excerpt":"s in laser systems with two fractional-dispersion/diffraction terms, quantified by their L\\'{e}vy indices, $\\alpha_{1}\\, \\alpha_{2}\\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schr\\\"{o}dinger equation with only one L\\'{e}vy index $\\alpha =1$, can be suppressed in the two-L\\'{e}vy-index fractional nonlinear Schr\\\"{o}dinger system. Stability of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01135","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.01135/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:01:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuytGsUHr2aeXSRFOhsQotuvadDQSf5DioLo3Sp3fxACUiN7T3GpIaU+/x4s4b08JFuix1//416Iv7dSpDq7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T18:43:28.125297Z"},"content_sha256":"723637ec3efc4aac7a07ec239ee194ba11e3c14922be56cc8f1e50e97f5519a5","schema_version":"1.0","event_id":"sha256:723637ec3efc4aac7a07ec239ee194ba11e3c14922be56cc8f1e50e97f5519a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VAHDMS2MJZBHE4M4656YUKASX5/bundle.json","state_url":"https://pith.science/pith/VAHDMS2MJZBHE4M4656YUKASX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VAHDMS2MJZBHE4M4656YUKASX5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T18:43:28Z","links":{"resolver":"https://pith.science/pith/VAHDMS2MJZBHE4M4656YUKASX5","bundle":"https://pith.science/pith/VAHDMS2MJZBHE4M4656YUKASX5/bundle.json","state":"https://pith.science/pith/VAHDMS2MJZBHE4M4656YUKASX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VAHDMS2MJZBHE4M4656YUKASX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VAHDMS2MJZBHE4M4656YUKASX5","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":"5ac977c4d3f2d297a577892d0db0a4b0deab28b02168b4a9ed6a6bae7ee2f355","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2024-09-02T10:16:53Z","title_canon_sha256":"647b65387f7f0ba4d6d60781dfee6bcbd9915460b3ab868c53097dc156e0c39c"},"schema_version":"1.0","source":{"id":"2409.01135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01135","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01135v1","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01135","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_12","alias_value":"VAHDMS2MJZBH","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_16","alias_value":"VAHDMS2MJZBHE4M4","created_at":"2026-07-05T09:01:59Z"},{"alias_kind":"pith_short_8","alias_value":"VAHDMS2M","created_at":"2026-07-05T09:01:59Z"}],"graph_snapshots":[{"event_id":"sha256:723637ec3efc4aac7a07ec239ee194ba11e3c14922be56cc8f1e50e97f5519a5","target":"graph","created_at":"2026-07-05T09:01:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.01135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"s in laser systems with two fractional-dispersion/diffraction terms, quantified by their L\\'{e}vy indices, $\\alpha_{1}\\, \\alpha_{2}\\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schr\\\"{o}dinger equation with only one L\\'{e}vy index $\\alpha =1$, can be suppressed in the two-L\\'{e}vy-index fractional nonlinear Schr\\\"{o}dinger system. Stability of th","authors_text":"Boris A. Malomed, Ming Zhong, Yong Chen, Zhenya Yan","cross_cats":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2024-09-02T10:16:53Z","title":"Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-L\\'evy-index fractional Kerr media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01135","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:b4e094faa237027179d4afe78f2cfe09535537750954b78b706c43a421390ab7","target":"record","created_at":"2026-07-05T09:01:59Z","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":"5ac977c4d3f2d297a577892d0db0a4b0deab28b02168b4a9ed6a6bae7ee2f355","cross_cats_sorted":["math-ph","math.MP","physics.comp-ph","physics.optics","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2024-09-02T10:16:53Z","title_canon_sha256":"647b65387f7f0ba4d6d60781dfee6bcbd9915460b3ab868c53097dc156e0c39c"},"schema_version":"1.0","source":{"id":"2409.01135","kind":"arxiv","version":1}},"canonical_sha256":"a80e364b4c4e4272719cf77d8a2812bf4eb3c6b64f0064c12195258adc580e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a80e364b4c4e4272719cf77d8a2812bf4eb3c6b64f0064c12195258adc580e12","first_computed_at":"2026-07-05T09:01:59.479033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:01:59.479033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1mlJXK9R/c6rn42f42OC4JPXcP/3mDFVL2sNmlbBcHLn2rfDlh6PWvIPie8N60UqNTY+MkfAFvxCve20zWCBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:01:59.479491Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.01135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4e094faa237027179d4afe78f2cfe09535537750954b78b706c43a421390ab7","sha256:723637ec3efc4aac7a07ec239ee194ba11e3c14922be56cc8f1e50e97f5519a5"],"state_sha256":"74958ccda1f995d4ef1e073eac0780f7860a4f58b251f3d938d4bbe3bb3a6965"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASJeSCrcu8hl+AOnIby6dTFV2PscWrYD2tLRtp3+z7ev+Tir9p2WDNg90xO9lEXdvapzB7IjjYRkfuyZ5bGbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T18:43:28.381703Z","bundle_sha256":"a176beaaa0d08ed1d084fc84025b233afa1271636daa0bffb9454699db104f34"}}