{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:Y2DJBFNQTR7VDRJHG7VD3IYYMX","short_pith_number":"pith:Y2DJBFNQ","canonical_record":{"source":{"id":"1908.06415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"870273455e72a467d386109864128e501f2162f63eeddb933d07cc17849f1a75","abstract_canon_sha256":"342450632b023222fce4dc1679feb62100d9dff0274bc21c6a568685a56ab911"},"schema_version":"1.0"},"canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","source":{"kind":"arxiv","id":"1908.06415","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06415","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06415v1","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06415","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"Y2DJBFNQTR7V","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_16","alias_value":"Y2DJBFNQTR7VDRJH","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_8","alias_value":"Y2DJBFNQ","created_at":"2026-07-05T02:50:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:Y2DJBFNQTR7VDRJHG7VD3IYYMX","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","cross_cats_sorted":["nlin.SI"],"title_canon_sha256":"870273455e72a467d386109864128e501f2162f63eeddb933d07cc17849f1a75","abstract_canon_sha256":"342450632b023222fce4dc1679feb62100d9dff0274bc21c6a568685a56ab911"},"schema_version":"1.0"},"canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:50:37.240599Z","signature_b64":"VOjaMHOLdtV/c3mqb4Y1DNCfaCYEFIOOFaAave1HNYwwiD4DMCx8BoS3ANgabVfYf/XarHGp/b3rVA66CmShDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","last_reissued_at":"2026-07-05T02:50:37.240029Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:50:37.240029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06415","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":"2026-07-05T02:50:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elAu9w+XHo2TOq0y8kP4mdwkCMsuJ5inHUk/ca8ZD/OypM7wpk9DPlXmAyQUO237vxkmPRd/xhhGq8Md1QpKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:24:31.556669Z"},"content_sha256":"4fb9476fcb7140c8620db35c602a662d6ee3e03b82a8dda0a89d16d56cba08a2","schema_version":"1.0","event_id":"sha256:4fb9476fcb7140c8620db35c602a662d6ee3e03b82a8dda0a89d16d56cba08a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:Y2DJBFNQTR7VDRJHG7VD3IYYMX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Long-time asymptotics for the integrable nonlocal focusing nonlinear Schr\\\"odinger equation for a family of step-like initial data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AP","authors_text":"Dmitry Shepelsky, Yan Rybalko","submitted_at":"2019-08-18T10:03:30Z","abstract_excerpt":"We study the Cauchy problem for the integrable nonlocal focusing nonlinear Schr\\\"odinger (NNLS) equation $\niq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\\bar{q}(-x,t)=0 $\nwith the step-like initial data close to the ``shifted step function'' $\\chi_R(x)=AH(x-R)$, where $H(x)$ is the Heaviside step function, and $A>0$ and $R>0$ are arbitrary constants. Our main aim is to study the large-$t$ behavior of the solution of this problem. We show that for $R\\in\\left(\\frac{(2n-1)\\pi}{2A},\\frac{(2n+1)\\pi}{2A}\\right)$, $n=1,2,\\dots$, the $(x,t)$ plane splits into\n  $4n+2$ sectors exhibiting different asymptotic beh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06415","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/1908.06415/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":"2026-07-05T02:50:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOOX3ID/m7Fhk3Zg2sO9LjBX6Ih9AsUqhZzl/ddbK3LsjjLCZ8uzjnD+bMtDVNQ1FszXmkvCHDrNbvI2lQHVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T05:24:31.557521Z"},"content_sha256":"99935843636deef04bc5230e0940e40a7adb8d8748d47437db9bf118b52292ba","schema_version":"1.0","event_id":"sha256:99935843636deef04bc5230e0940e40a7adb8d8748d47437db9bf118b52292ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/bundle.json","state_url":"https://pith.science/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/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":"2026-08-16T05:24:31Z","links":{"resolver":"https://pith.science/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX","bundle":"https://pith.science/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/bundle.json","state":"https://pith.science/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2DJBFNQTR7VDRJHG7VD3IYYMX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:Y2DJBFNQTR7VDRJHG7VD3IYYMX","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":"342450632b023222fce4dc1679feb62100d9dff0274bc21c6a568685a56ab911","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","title_canon_sha256":"870273455e72a467d386109864128e501f2162f63eeddb933d07cc17849f1a75"},"schema_version":"1.0","source":{"id":"1908.06415","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06415","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06415v1","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06415","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_12","alias_value":"Y2DJBFNQTR7V","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_16","alias_value":"Y2DJBFNQTR7VDRJH","created_at":"2026-07-05T02:50:37Z"},{"alias_kind":"pith_short_8","alias_value":"Y2DJBFNQ","created_at":"2026-07-05T02:50:37Z"}],"graph_snapshots":[{"event_id":"sha256:99935843636deef04bc5230e0940e40a7adb8d8748d47437db9bf118b52292ba","target":"graph","created_at":"2026-07-05T02:50:37Z","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/1908.06415/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the Cauchy problem for the integrable nonlocal focusing nonlinear Schr\\\"odinger (NNLS) equation $\niq_{t}(x,t)+q_{xx}(x,t)+2 q^{2}(x,t)\\bar{q}(-x,t)=0 $\nwith the step-like initial data close to the ``shifted step function'' $\\chi_R(x)=AH(x-R)$, where $H(x)$ is the Heaviside step function, and $A>0$ and $R>0$ are arbitrary constants. Our main aim is to study the large-$t$ behavior of the solution of this problem. We show that for $R\\in\\left(\\frac{(2n-1)\\pi}{2A},\\frac{(2n+1)\\pi}{2A}\\right)$, $n=1,2,\\dots$, the $(x,t)$ plane splits into\n  $4n+2$ sectors exhibiting different asymptotic beh","authors_text":"Dmitry Shepelsky, Yan Rybalko","cross_cats":["nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","title":"Long-time asymptotics for the integrable nonlocal focusing nonlinear Schr\\\"odinger equation for a family of step-like initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06415","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":"sha256:4fb9476fcb7140c8620db35c602a662d6ee3e03b82a8dda0a89d16d56cba08a2","target":"record","created_at":"2026-07-05T02:50:37Z","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":"342450632b023222fce4dc1679feb62100d9dff0274bc21c6a568685a56ab911","cross_cats_sorted":["nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-18T10:03:30Z","title_canon_sha256":"870273455e72a467d386109864128e501f2162f63eeddb933d07cc17849f1a75"},"schema_version":"1.0","source":{"id":"1908.06415","kind":"arxiv","version":1}},"canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6869095b09c7f51c52737ea3da31865c8b5f5d4132fb9dd9e3b08637dc93c7b","first_computed_at":"2026-07-05T02:50:37.240029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:50:37.240029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOjaMHOLdtV/c3mqb4Y1DNCfaCYEFIOOFaAave1HNYwwiD4DMCx8BoS3ANgabVfYf/XarHGp/b3rVA66CmShDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:50:37.240599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06415","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fb9476fcb7140c8620db35c602a662d6ee3e03b82a8dda0a89d16d56cba08a2","sha256:99935843636deef04bc5230e0940e40a7adb8d8748d47437db9bf118b52292ba"],"state_sha256":"8d4b9401fdc9f1833e625a269e6d9320a5a939b6bdace043cd3464aa0dbc8d0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49bg/oXtjg4BhtMSd3Zoxzc7v35ADvtgOfJe7iRdM/mgl7YwKX7QYoqLaYaOQtjM3S0rIn87DQjkto3Vh4RxCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T05:24:31.599394Z","bundle_sha256":"6b0c0c31b65db4cb67a8313c0c512a9c3c7cc652db4010020dd02c4acfb35d82"}}