{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OFSUOW7OI7JCPEE5QSL4Y6MCPF","short_pith_number":"pith:OFSUOW7O","canonical_record":{"source":{"id":"1212.1393","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-12-06T17:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"2c91cae2ece8a351d994b57472d947af43fb9a7a14bd2ef12971e831612c517f","abstract_canon_sha256":"bd5dbf224a5046e8541890d7f7c0fe82fce50e579d3bf59bf9b4a320d03aad4d"},"schema_version":"1.0"},"canonical_sha256":"7165475bee47d227909d8497cc7982797065bb3967da0ec0627995edd3492422","source":{"kind":"arxiv","id":"1212.1393","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1393","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1393v3","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1393","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"OFSUOW7OI7JC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OFSUOW7OI7JCPEE5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OFSUOW7O","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OFSUOW7OI7JCPEE5QSL4Y6MCPF","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1393","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-12-06T17:47:25Z","cross_cats_sorted":[],"title_canon_sha256":"2c91cae2ece8a351d994b57472d947af43fb9a7a14bd2ef12971e831612c517f","abstract_canon_sha256":"bd5dbf224a5046e8541890d7f7c0fe82fce50e579d3bf59bf9b4a320d03aad4d"},"schema_version":"1.0"},"canonical_sha256":"7165475bee47d227909d8497cc7982797065bb3967da0ec0627995edd3492422","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:27.104903Z","signature_b64":"6lIOvkI0Cwtopay4Njs3yAhnEwHaP+44VcGJgbSAKuJzaULRwDzPXjQGwVXcWO/p3kQerDBMGYONoo7mZz7gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7165475bee47d227909d8497cc7982797065bb3967da0ec0627995edd3492422","last_reissued_at":"2026-05-18T03:16:27.100944Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:27.100944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1393","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UdrHT1HagZr3k4FD8feG+cmUUE/eblt9c1stI+kmxLvYfbwJUhRNN3ambb2g0j9UVaYG8My3SIPXNml9Sp9mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:16.043649Z"},"content_sha256":"ec0545a94d25edfee141660f65d56a84ce69e389339369843ab3ba5144e9e974","schema_version":"1.0","event_id":"sha256:ec0545a94d25edfee141660f65d56a84ce69e389339369843ab3ba5144e9e974"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OFSUOW7OI7JCPEE5QSL4Y6MCPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the nonlinear stage of Modulation Instability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. A. Gelash, V. E. Zakharov","submitted_at":"2012-12-06T17:47:25Z","abstract_excerpt":"We study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schr\\\"{o}dinger Equation. We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We separate a special designated class of \"regular solitonic solutions\" that do not disturb phases of the condensate at infinity by coordinate. All regular solitonic solutions can be treated as localized perturbations of the condensate. We find an important class of \"superregular solitonic solutions\" which are small perturbations at"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1393","kind":"arxiv","version":3},"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":"2026-05-18T03:16:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MB+DwoqV+ez8zFfc5j7xVmCgwtPtKys7EsgvweA8L7Icq7mBzwRkYW6SJ16cfH3DO6ipbGTHjaeo3i6EuD4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:44:16.043984Z"},"content_sha256":"d6fd3ef5e9ee4540460a4aef7479a632aaec2026e3cd15185a3009c80190bade","schema_version":"1.0","event_id":"sha256:d6fd3ef5e9ee4540460a4aef7479a632aaec2026e3cd15185a3009c80190bade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/bundle.json","state_url":"https://pith.science/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/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":"2026-06-25T19:44:16Z","links":{"resolver":"https://pith.science/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF","bundle":"https://pith.science/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/bundle.json","state":"https://pith.science/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFSUOW7OI7JCPEE5QSL4Y6MCPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OFSUOW7OI7JCPEE5QSL4Y6MCPF","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":"bd5dbf224a5046e8541890d7f7c0fe82fce50e579d3bf59bf9b4a320d03aad4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-12-06T17:47:25Z","title_canon_sha256":"2c91cae2ece8a351d994b57472d947af43fb9a7a14bd2ef12971e831612c517f"},"schema_version":"1.0","source":{"id":"1212.1393","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1393","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1393v3","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1393","created_at":"2026-05-18T03:16:27Z"},{"alias_kind":"pith_short_12","alias_value":"OFSUOW7OI7JC","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OFSUOW7OI7JCPEE5","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OFSUOW7O","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d6fd3ef5e9ee4540460a4aef7479a632aaec2026e3cd15185a3009c80190bade","target":"graph","created_at":"2026-05-18T03:16:27Z","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 study the nonlinear stage of the modulation instability of a condensate in the framework of the focusing Nonlinear Schr\\\"{o}dinger Equation. We find a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We separate a special designated class of \"regular solitonic solutions\" that do not disturb phases of the condensate at infinity by coordinate. All regular solitonic solutions can be treated as localized perturbations of the condensate. We find an important class of \"superregular solitonic solutions\" which are small perturbations at","authors_text":"A. A. Gelash, V. E. Zakharov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-12-06T17:47:25Z","title":"On the nonlinear stage of Modulation Instability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1393","kind":"arxiv","version":3},"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:ec0545a94d25edfee141660f65d56a84ce69e389339369843ab3ba5144e9e974","target":"record","created_at":"2026-05-18T03:16:27Z","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":"bd5dbf224a5046e8541890d7f7c0fe82fce50e579d3bf59bf9b4a320d03aad4d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2012-12-06T17:47:25Z","title_canon_sha256":"2c91cae2ece8a351d994b57472d947af43fb9a7a14bd2ef12971e831612c517f"},"schema_version":"1.0","source":{"id":"1212.1393","kind":"arxiv","version":3}},"canonical_sha256":"7165475bee47d227909d8497cc7982797065bb3967da0ec0627995edd3492422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7165475bee47d227909d8497cc7982797065bb3967da0ec0627995edd3492422","first_computed_at":"2026-05-18T03:16:27.100944Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:27.100944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6lIOvkI0Cwtopay4Njs3yAhnEwHaP+44VcGJgbSAKuJzaULRwDzPXjQGwVXcWO/p3kQerDBMGYONoo7mZz7gCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:27.104903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1393","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec0545a94d25edfee141660f65d56a84ce69e389339369843ab3ba5144e9e974","sha256:d6fd3ef5e9ee4540460a4aef7479a632aaec2026e3cd15185a3009c80190bade"],"state_sha256":"1202d450d808a8fe3d095e3476ab5ff0312322efc56998a91380923dd2e9e71f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ApVR0xIJgJyeHTjabdWE3xJYM/u4KEMYkU+pwBqc78er8+R+rSZFRBY0RTuv80YFHSTwJhbd8jDnWRW3+t9RBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:44:16.045797Z","bundle_sha256":"11b897ffd8af3552b310b1d269c9d7c812477d2e0ad2829aa5ca4ce89bad1304"}}