{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:2YKW3PCMSS5WD66RNBVFDDHH4S","short_pith_number":"pith:2YKW3PCM","canonical_record":{"source":{"id":"1601.05371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-20T18:59:12Z","cross_cats_sorted":[],"title_canon_sha256":"16f7a5a6702e0b24383406ba0cd22b63480093495cf5b20b401b53fb0a6c4d4a","abstract_canon_sha256":"f0f9e8d383c281abd2d5dddfaf993673607ae82980ed93ea85a834ac3c8e2512"},"schema_version":"1.0"},"canonical_sha256":"d6156dbc4c94bb61fbd1686a518ce7e4b4bc8382f3e0243261ee0b007ed946d7","source":{"kind":"arxiv","id":"1601.05371","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05371","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05371v2","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05371","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"2YKW3PCMSS5W","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YKW3PCMSS5WD66R","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YKW3PCM","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:2YKW3PCMSS5WD66RNBVFDDHH4S","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05371","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-20T18:59:12Z","cross_cats_sorted":[],"title_canon_sha256":"16f7a5a6702e0b24383406ba0cd22b63480093495cf5b20b401b53fb0a6c4d4a","abstract_canon_sha256":"f0f9e8d383c281abd2d5dddfaf993673607ae82980ed93ea85a834ac3c8e2512"},"schema_version":"1.0"},"canonical_sha256":"d6156dbc4c94bb61fbd1686a518ce7e4b4bc8382f3e0243261ee0b007ed946d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:11.089755Z","signature_b64":"HpNijA22Tak3F9fhvd+nD7ZQdCco4qg59ObFmjkuaW9j6IArippz8cbcJEtdKOjYE0+CXWPcDIVSWA3fkrYHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6156dbc4c94bb61fbd1686a518ce7e4b4bc8382f3e0243261ee0b007ed946d7","last_reissued_at":"2026-05-18T01:22:11.089235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:11.089235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05371","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pEooRI0SNO/iRCuMkOj8lYq6b8SNoC6wahQkpakdF2aHFUUy5seqQmkt4R7yzJf7yN7Wf9pCpYSLvfxkjPoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:40:47.770883Z"},"content_sha256":"239a33ed900f612a75e2ffda298d4b61e3f8d21bbcff7e18050dba16a36c1ded","schema_version":"1.0","event_id":"sha256:239a33ed900f612a75e2ffda298d4b61e3f8d21bbcff7e18050dba16a36c1ded"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:2YKW3PCMSS5WD66RNBVFDDHH4S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On dispersive blow-ups for the nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Maja Taskovi\\'c, Younghun Hong","submitted_at":"2016-01-20T18:59:12Z","abstract_excerpt":"In this article, we provide a simple method for constructing dispersive blow-up solutions to the nonlinear Schr\\\"odinger equation. Our construction mainly follows the approach in Bona, Ponce, Saut and Sparber [2]. However, we make use of the dispersive estimate to enjoy the smoothing effect of the Schr\\\"odinger propagator in the integral term appearing in Duhamel's formula. In this way, not only do we simplify the argument, but we also reduce the regularity requirement to construct dispersive blow-ups. In addition, we provide more examples of dispersive blow-ups by constructing solutions that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05371","kind":"arxiv","version":2},"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":"2026-05-18T01:22:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hz7j0opWa88bGzmo65tRPRrQnKzPObuCZtNej3yYByIQeCjGNt3un2DUnCOO91q/1vWj1fLX6y5n8rSTOxm+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:40:47.771227Z"},"content_sha256":"b81dab7def543aa0a615dce6a4ec6b6cfe2bbb4c66357002244183544e252d74","schema_version":"1.0","event_id":"sha256:b81dab7def543aa0a615dce6a4ec6b6cfe2bbb4c66357002244183544e252d74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/bundle.json","state_url":"https://pith.science/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/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":"2026-05-28T11:40:47Z","links":{"resolver":"https://pith.science/pith/2YKW3PCMSS5WD66RNBVFDDHH4S","bundle":"https://pith.science/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/bundle.json","state":"https://pith.science/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2YKW3PCMSS5WD66RNBVFDDHH4S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2YKW3PCMSS5WD66RNBVFDDHH4S","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":"f0f9e8d383c281abd2d5dddfaf993673607ae82980ed93ea85a834ac3c8e2512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-20T18:59:12Z","title_canon_sha256":"16f7a5a6702e0b24383406ba0cd22b63480093495cf5b20b401b53fb0a6c4d4a"},"schema_version":"1.0","source":{"id":"1601.05371","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05371","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05371v2","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05371","created_at":"2026-05-18T01:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"2YKW3PCMSS5W","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2YKW3PCMSS5WD66R","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2YKW3PCM","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:b81dab7def543aa0a615dce6a4ec6b6cfe2bbb4c66357002244183544e252d74","target":"graph","created_at":"2026-05-18T01:22:11Z","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 provide a simple method for constructing dispersive blow-up solutions to the nonlinear Schr\\\"odinger equation. Our construction mainly follows the approach in Bona, Ponce, Saut and Sparber [2]. However, we make use of the dispersive estimate to enjoy the smoothing effect of the Schr\\\"odinger propagator in the integral term appearing in Duhamel's formula. In this way, not only do we simplify the argument, but we also reduce the regularity requirement to construct dispersive blow-ups. In addition, we provide more examples of dispersive blow-ups by constructing solutions that ","authors_text":"Maja Taskovi\\'c, Younghun Hong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-20T18:59:12Z","title":"On dispersive blow-ups for the nonlinear Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05371","kind":"arxiv","version":2},"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":"sha256:239a33ed900f612a75e2ffda298d4b61e3f8d21bbcff7e18050dba16a36c1ded","target":"record","created_at":"2026-05-18T01:22:11Z","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":"f0f9e8d383c281abd2d5dddfaf993673607ae82980ed93ea85a834ac3c8e2512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-20T18:59:12Z","title_canon_sha256":"16f7a5a6702e0b24383406ba0cd22b63480093495cf5b20b401b53fb0a6c4d4a"},"schema_version":"1.0","source":{"id":"1601.05371","kind":"arxiv","version":2}},"canonical_sha256":"d6156dbc4c94bb61fbd1686a518ce7e4b4bc8382f3e0243261ee0b007ed946d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6156dbc4c94bb61fbd1686a518ce7e4b4bc8382f3e0243261ee0b007ed946d7","first_computed_at":"2026-05-18T01:22:11.089235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:11.089235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HpNijA22Tak3F9fhvd+nD7ZQdCco4qg59ObFmjkuaW9j6IArippz8cbcJEtdKOjYE0+CXWPcDIVSWA3fkrYHCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:11.089755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05371","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:239a33ed900f612a75e2ffda298d4b61e3f8d21bbcff7e18050dba16a36c1ded","sha256:b81dab7def543aa0a615dce6a4ec6b6cfe2bbb4c66357002244183544e252d74"],"state_sha256":"04a9d30cebf58c3d3a0b3566fd51f331f6c7fe8ef7c7a9ab6f7f800827caf813"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrVNa6OfFszGLG+0mufCoIrJ4d2fjvLuS80pM21sZohFCAhrd6lwasNW+UabimmvSpNhK01bHJDIFGMP9VZzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:40:47.773268Z","bundle_sha256":"19edfd5bf4bd410f393e2fd48ef9ebab6307d4790d43535a42c1e44fd6da38e9"}}