{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QHK7UN7DQMH35MHSYM4UFDJFGL","short_pith_number":"pith:QHK7UN7D","canonical_record":{"source":{"id":"1608.08771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-08-31T08:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"f8e4ec18d41f4c3da9fc534d78ed0a262ba556250650dac7776ab72deed05f72","abstract_canon_sha256":"42e6cc38fb70d13f59ef55050bd80e78ab16193d252728b01fa73599c6d34f21"},"schema_version":"1.0"},"canonical_sha256":"81d5fa37e3830fbeb0f2c339428d2532d4a66c58dd21cadf79b0832f43658643","source":{"kind":"arxiv","id":"1608.08771","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08771","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08771v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08771","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"QHK7UN7DQMH3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHK7UN7DQMH35MHS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHK7UN7D","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QHK7UN7DQMH35MHSYM4UFDJFGL","target":"record","payload":{"canonical_record":{"source":{"id":"1608.08771","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-08-31T08:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"f8e4ec18d41f4c3da9fc534d78ed0a262ba556250650dac7776ab72deed05f72","abstract_canon_sha256":"42e6cc38fb70d13f59ef55050bd80e78ab16193d252728b01fa73599c6d34f21"},"schema_version":"1.0"},"canonical_sha256":"81d5fa37e3830fbeb0f2c339428d2532d4a66c58dd21cadf79b0832f43658643","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:39.956667Z","signature_b64":"lq04idLau1ftIe3yvKvLOaImkMCBmyku5t1EKFlckBrpqE/nbj1G3fkCiBSBh0p+LnyCxzG+gp4/0c06eQflBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81d5fa37e3830fbeb0f2c339428d2532d4a66c58dd21cadf79b0832f43658643","last_reissued_at":"2026-05-18T01:06:39.956006Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:39.956006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.08771","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":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BUAXSLDPScDmueFJZ/BnqEQe1fst9AWwHRZMHM9rLzwWO6vaHD/lbjdzGp1tYnwL4PkmSjmze37ySEs2aoA4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:16:13.554169Z"},"content_sha256":"06e3d67717a59115347356573bc31ba5d1b013615587942a953ecc694db2bb42","schema_version":"1.0","event_id":"sha256:06e3d67717a59115347356573bc31ba5d1b013615587942a953ecc694db2bb42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QHK7UN7DQMH35MHSYM4UFDJFGL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optical Nonlinear Dark X-Waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"F. Baronio, M. Onorato, S. Chen, S. Trillo, S. Wabnitz, Y. Kodama","submitted_at":"2016-08-31T08:50:39Z","abstract_excerpt":"We introduce spatiotemporal optical dark X solitary waves of the (2+1)D {hyperbolic} nonlinear Schr\\\"odinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between such NLSE and a well known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08771","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HA04v3DEPQyVBC0WTQrmUJSynSSX5E05Q+ipycjlx4jZA6U7R5n9QYMDFazicQK8XhLWXOo6x65WhbYDpKDoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:16:13.555197Z"},"content_sha256":"1b9d07a7dec765ef3fb9392eb7d0625122c03502d031bc223a09fb410e432c9c","schema_version":"1.0","event_id":"sha256:1b9d07a7dec765ef3fb9392eb7d0625122c03502d031bc223a09fb410e432c9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/bundle.json","state_url":"https://pith.science/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/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":"2026-06-06T04:16:13Z","links":{"resolver":"https://pith.science/pith/QHK7UN7DQMH35MHSYM4UFDJFGL","bundle":"https://pith.science/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/bundle.json","state":"https://pith.science/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHK7UN7DQMH35MHSYM4UFDJFGL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QHK7UN7DQMH35MHSYM4UFDJFGL","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":"42e6cc38fb70d13f59ef55050bd80e78ab16193d252728b01fa73599c6d34f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-08-31T08:50:39Z","title_canon_sha256":"f8e4ec18d41f4c3da9fc534d78ed0a262ba556250650dac7776ab72deed05f72"},"schema_version":"1.0","source":{"id":"1608.08771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.08771","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"arxiv_version","alias_value":"1608.08771v1","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.08771","created_at":"2026-05-18T01:06:39Z"},{"alias_kind":"pith_short_12","alias_value":"QHK7UN7DQMH3","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QHK7UN7DQMH35MHS","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QHK7UN7D","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:1b9d07a7dec765ef3fb9392eb7d0625122c03502d031bc223a09fb410e432c9c","target":"graph","created_at":"2026-05-18T01:06:39Z","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":"We introduce spatiotemporal optical dark X solitary waves of the (2+1)D {hyperbolic} nonlinear Schr\\\"odinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between such NLSE and a well known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary ","authors_text":"F. Baronio, M. Onorato, S. Chen, S. Trillo, S. Wabnitz, Y. Kodama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-08-31T08:50:39Z","title":"Optical Nonlinear Dark X-Waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.08771","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":"sha256:06e3d67717a59115347356573bc31ba5d1b013615587942a953ecc694db2bb42","target":"record","created_at":"2026-05-18T01:06:39Z","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":"42e6cc38fb70d13f59ef55050bd80e78ab16193d252728b01fa73599c6d34f21","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2016-08-31T08:50:39Z","title_canon_sha256":"f8e4ec18d41f4c3da9fc534d78ed0a262ba556250650dac7776ab72deed05f72"},"schema_version":"1.0","source":{"id":"1608.08771","kind":"arxiv","version":1}},"canonical_sha256":"81d5fa37e3830fbeb0f2c339428d2532d4a66c58dd21cadf79b0832f43658643","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81d5fa37e3830fbeb0f2c339428d2532d4a66c58dd21cadf79b0832f43658643","first_computed_at":"2026-05-18T01:06:39.956006Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:39.956006Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lq04idLau1ftIe3yvKvLOaImkMCBmyku5t1EKFlckBrpqE/nbj1G3fkCiBSBh0p+LnyCxzG+gp4/0c06eQflBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:39.956667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.08771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06e3d67717a59115347356573bc31ba5d1b013615587942a953ecc694db2bb42","sha256:1b9d07a7dec765ef3fb9392eb7d0625122c03502d031bc223a09fb410e432c9c"],"state_sha256":"50805396f1b02ae5ec16dea956186002a6cdcd90e5c14e3c305f50fb84610c94"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Gorq7V9rxun3jWDy+TevYY2BHKydwY5WeRIhrgWyB/8h6s+8d+ubt//G9ENTR/+8G5TmgfBrJ+fEjwI7ctsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:16:13.558870Z","bundle_sha256":"cc677e394e72c1896d319b7c40b28ff3a158f3787407dbb08f9d159d3990b863"}}