{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VTKQGEFMBPKCMQTFJS4GZUCYSX","short_pith_number":"pith:VTKQGEFM","canonical_record":{"source":{"id":"1809.01527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52d255b73c8fa3af449847d66e5aeeae67c6560cc6ba3789242d7791d221f6c1","abstract_canon_sha256":"5a607867c2b5ff6a10f3ab94e03615691e9e42b4cc8253379c93d705d8fa875e"},"schema_version":"1.0"},"canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","source":{"kind":"arxiv","id":"1809.01527","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01527","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01527v1","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01527","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"VTKQGEFMBPKC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTKQGEFMBPKCMQTF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTKQGEFM","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VTKQGEFMBPKCMQTFJS4GZUCYSX","target":"record","payload":{"canonical_record":{"source":{"id":"1809.01527","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52d255b73c8fa3af449847d66e5aeeae67c6560cc6ba3789242d7791d221f6c1","abstract_canon_sha256":"5a607867c2b5ff6a10f3ab94e03615691e9e42b4cc8253379c93d705d8fa875e"},"schema_version":"1.0"},"canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:27.327671Z","signature_b64":"jO8qw5dsAY75LpVRAJhU310Xoixb38IrDZ2cHqOn2VPM95/hhrHUe2cyvC/aynJfzeQR7/PBu/HiC+3YHyXZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","last_reissued_at":"2026-05-18T00:06:27.327143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:27.327143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.01527","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":"2026-05-18T00:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2hZ1uIctj4mdcg+VgVKREkTu3sxdEOeEwjvlUKU9VEQFLNMNAYHExr5lGuvR8pOklsWEL096m15PGtXAgKXiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:26.331139Z"},"content_sha256":"c7fe21ea97dd16d9d2b8c0e7ab15c4c840ea0f75aee313d690b290137d968e46","schema_version":"1.0","event_id":"sha256:c7fe21ea97dd16d9d2b8c0e7ab15c4c840ea0f75aee313d690b290137d968e46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VTKQGEFMBPKCMQTFJS4GZUCYSX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On scattering for the defocusing quintic nonlinear Schr\\\"odinger equation on the two-dimensional cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Xing Cheng, Zehua Zhao, Zihua Guo","submitted_at":"2018-09-05T14:07:56Z","abstract_excerpt":"In this article, we prove the scattering for the quintic defocusing nonlinear Schr\\\"odinger equation on cylinder $\\mathbb{R} \\times \\mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^\\alpha$, $0 < \\alpha \\le 1$, motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^d )$, $d\\ge 1$. Then by using the solution of the one-discrete-component quintic resonant nonlinear Schr\\\"odinger system, whose scattering can be proved by using the techniques in $1d$ mass critical NLS problem by B. Dodson, to approximate th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01527","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":"2026-05-18T00:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s9hGuHkcER0cADYhqghtSii0n5UN6HlkxbswHaoJHyehVMZ4tSap4Ad08LhkfOKHhBDK/db9LgtCerjR3L7GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:39:26.331858Z"},"content_sha256":"71dc2b068c3cd43ba8153557e49ff34b109286f722d3d03a3d34f2a1a0ab0d70","schema_version":"1.0","event_id":"sha256:71dc2b068c3cd43ba8153557e49ff34b109286f722d3d03a3d34f2a1a0ab0d70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/bundle.json","state_url":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/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":"2026-05-27T14:39:26Z","links":{"resolver":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX","bundle":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/bundle.json","state":"https://pith.science/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTKQGEFMBPKCMQTFJS4GZUCYSX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VTKQGEFMBPKCMQTFJS4GZUCYSX","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":"5a607867c2b5ff6a10f3ab94e03615691e9e42b4cc8253379c93d705d8fa875e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","title_canon_sha256":"52d255b73c8fa3af449847d66e5aeeae67c6560cc6ba3789242d7791d221f6c1"},"schema_version":"1.0","source":{"id":"1809.01527","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01527","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01527v1","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01527","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"VTKQGEFMBPKC","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VTKQGEFMBPKCMQTF","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VTKQGEFM","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:71dc2b068c3cd43ba8153557e49ff34b109286f722d3d03a3d34f2a1a0ab0d70","target":"graph","created_at":"2026-05-18T00:06:27Z","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":"In this article, we prove the scattering for the quintic defocusing nonlinear Schr\\\"odinger equation on cylinder $\\mathbb{R} \\times \\mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^\\alpha$, $0 < \\alpha \\le 1$, motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^d )$, $d\\ge 1$. Then by using the solution of the one-discrete-component quintic resonant nonlinear Schr\\\"odinger system, whose scattering can be proved by using the techniques in $1d$ mass critical NLS problem by B. Dodson, to approximate th","authors_text":"Xing Cheng, Zehua Zhao, Zihua Guo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","title":"On scattering for the defocusing quintic nonlinear Schr\\\"odinger equation on the two-dimensional cylinder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01527","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:c7fe21ea97dd16d9d2b8c0e7ab15c4c840ea0f75aee313d690b290137d968e46","target":"record","created_at":"2026-05-18T00:06:27Z","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":"5a607867c2b5ff6a10f3ab94e03615691e9e42b4cc8253379c93d705d8fa875e","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-09-05T14:07:56Z","title_canon_sha256":"52d255b73c8fa3af449847d66e5aeeae67c6560cc6ba3789242d7791d221f6c1"},"schema_version":"1.0","source":{"id":"1809.01527","kind":"arxiv","version":1}},"canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acd50310ac0bd42642654cb86cd05895dd4018ccc09749c21e8044203bac79c1","first_computed_at":"2026-05-18T00:06:27.327143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:27.327143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jO8qw5dsAY75LpVRAJhU310Xoixb38IrDZ2cHqOn2VPM95/hhrHUe2cyvC/aynJfzeQR7/PBu/HiC+3YHyXZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:27.327671Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01527","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7fe21ea97dd16d9d2b8c0e7ab15c4c840ea0f75aee313d690b290137d968e46","sha256:71dc2b068c3cd43ba8153557e49ff34b109286f722d3d03a3d34f2a1a0ab0d70"],"state_sha256":"b09852dad73b4a0d55abbdc8606a651aa5d5c213ece79e8ed3d37c333ce4f0f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K0AukxtUFsF0pdcYpxqpwTtW0Ud+empW5rBEUnC+eWK/0r5pGSEjeq0/6iRG99Gl1U4CZziTBGUUYtwnZnTQAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:39:26.335864Z","bundle_sha256":"89809b910e949fb10eb2fbf10736b3f26c3d62361ab6e826a1b2fff3795e8268"}}