{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ILEX5GS5ZSG266XUMUOZ6VRWL2","short_pith_number":"pith:ILEX5GS5","canonical_record":{"source":{"id":"1312.5249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-18T18:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"0e3d1089b8e591e59d6ea8f554f08b72c2ff19a3d1b7c8235da2fb82b4fbcfa9","abstract_canon_sha256":"a04b0aa24ff14dbf96332b1a314d645caeafc7480bddc93a7f2430d48dcbd26e"},"schema_version":"1.0"},"canonical_sha256":"42c97e9a5dcc8daf7af4651d9f56365ea16db61999cc3a4f501f8d29b39d758f","source":{"kind":"arxiv","id":"1312.5249","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5249","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5249v1","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5249","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"ILEX5GS5ZSG2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ILEX5GS5ZSG266XU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ILEX5GS5","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ILEX5GS5ZSG266XUMUOZ6VRWL2","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-18T18:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"0e3d1089b8e591e59d6ea8f554f08b72c2ff19a3d1b7c8235da2fb82b4fbcfa9","abstract_canon_sha256":"a04b0aa24ff14dbf96332b1a314d645caeafc7480bddc93a7f2430d48dcbd26e"},"schema_version":"1.0"},"canonical_sha256":"42c97e9a5dcc8daf7af4651d9f56365ea16db61999cc3a4f501f8d29b39d758f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:15.936291Z","signature_b64":"QyJkylOS6Ib5YT1Rc4N5GndpQFzH/dpdleiwa5L5+KXod3IVD8gKh5vN3NchjsZdDbUutAcdLc7Pdwjp3lSTCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42c97e9a5dcc8daf7af4651d9f56365ea16db61999cc3a4f501f8d29b39d758f","last_reissued_at":"2026-05-18T03:04:15.935747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:15.935747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5249","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":"2026-05-18T03:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLdKj9FvF85Qf8X96RXaZYoUxe6xBKwGpJEI0BeqMz1ajbROd0Hx5evZJ9UfUR4WoY/HprRo9fGY8upt87K+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:46:45.447286Z"},"content_sha256":"1fd966522724794c8182c1937175cc34b6092dfe20a2a62f62ba1b30c59a6c86","schema_version":"1.0","event_id":"sha256:1fd966522724794c8182c1937175cc34b6092dfe20a2a62f62ba1b30c59a6c86"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ILEX5GS5ZSG266XUMUOZ6VRWL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence and Uniqueness theory for the fractional Schr\\\"odinger equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. B. Erdo\\u{g}an, N. Tzirakis, S. Demirbas","submitted_at":"2013-12-18T18:03:00Z","abstract_excerpt":"We study the Cauchy problem for the $1$-d periodic fractional Schr\\\"odinger equation with cubic nonlinearity. In particular we prove local well-posedness in Sobolev spaces, for solutions evolving from rough initial data. In addition we show the existence of global-in-time infinite energy solutions. Our tools include a new Strichartz estimate on the torus along with ideas that Bourgain developed in studying the periodic cubic NLS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5249","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":"2026-05-18T03:04:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nw4ORpB8WyY1r4uPOl4dMulxD0oNq2AQrM/O7b/pTIezNBATWY1MjOS/5iffcmvV+tnrOdoLrfTsDUjj2OQxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:46:45.447938Z"},"content_sha256":"6d21397212207690904488bcee3d5d2318e68f7fa8fa9276da54b4da7452d642","schema_version":"1.0","event_id":"sha256:6d21397212207690904488bcee3d5d2318e68f7fa8fa9276da54b4da7452d642"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/bundle.json","state_url":"https://pith.science/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/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":"2026-05-28T21:46:45Z","links":{"resolver":"https://pith.science/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2","bundle":"https://pith.science/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/bundle.json","state":"https://pith.science/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ILEX5GS5ZSG266XUMUOZ6VRWL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ILEX5GS5ZSG266XUMUOZ6VRWL2","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":"a04b0aa24ff14dbf96332b1a314d645caeafc7480bddc93a7f2430d48dcbd26e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-18T18:03:00Z","title_canon_sha256":"0e3d1089b8e591e59d6ea8f554f08b72c2ff19a3d1b7c8235da2fb82b4fbcfa9"},"schema_version":"1.0","source":{"id":"1312.5249","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5249","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5249v1","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5249","created_at":"2026-05-18T03:04:15Z"},{"alias_kind":"pith_short_12","alias_value":"ILEX5GS5ZSG2","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"ILEX5GS5ZSG266XU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"ILEX5GS5","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:6d21397212207690904488bcee3d5d2318e68f7fa8fa9276da54b4da7452d642","target":"graph","created_at":"2026-05-18T03:04:15Z","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 Cauchy problem for the $1$-d periodic fractional Schr\\\"odinger equation with cubic nonlinearity. In particular we prove local well-posedness in Sobolev spaces, for solutions evolving from rough initial data. In addition we show the existence of global-in-time infinite energy solutions. Our tools include a new Strichartz estimate on the torus along with ideas that Bourgain developed in studying the periodic cubic NLS.","authors_text":"M. B. Erdo\\u{g}an, N. Tzirakis, S. Demirbas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-18T18:03:00Z","title":"Existence and Uniqueness theory for the fractional Schr\\\"odinger equation on the torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5249","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":"sha256:1fd966522724794c8182c1937175cc34b6092dfe20a2a62f62ba1b30c59a6c86","target":"record","created_at":"2026-05-18T03:04:15Z","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":"a04b0aa24ff14dbf96332b1a314d645caeafc7480bddc93a7f2430d48dcbd26e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-12-18T18:03:00Z","title_canon_sha256":"0e3d1089b8e591e59d6ea8f554f08b72c2ff19a3d1b7c8235da2fb82b4fbcfa9"},"schema_version":"1.0","source":{"id":"1312.5249","kind":"arxiv","version":1}},"canonical_sha256":"42c97e9a5dcc8daf7af4651d9f56365ea16db61999cc3a4f501f8d29b39d758f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42c97e9a5dcc8daf7af4651d9f56365ea16db61999cc3a4f501f8d29b39d758f","first_computed_at":"2026-05-18T03:04:15.935747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:15.935747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QyJkylOS6Ib5YT1Rc4N5GndpQFzH/dpdleiwa5L5+KXod3IVD8gKh5vN3NchjsZdDbUutAcdLc7Pdwjp3lSTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:15.936291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5249","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fd966522724794c8182c1937175cc34b6092dfe20a2a62f62ba1b30c59a6c86","sha256:6d21397212207690904488bcee3d5d2318e68f7fa8fa9276da54b4da7452d642"],"state_sha256":"a371c04c00d9bd5d6ed21b874ea4ca7f2d9cbdc6ce85c5dce7173cbc49b4f797"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3atFermhuTwOGunZOzxMdJT6xn6V6oAF+dBgPt72LEVQUgLkGIv23NblPz0eHeOsf5+8WI+rBgHno6kmww2QBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:46:45.450713Z","bundle_sha256":"2f529451bb0219586732b6af4dad89d3acfb3be81a934c7fd738cafdbadf3ffb"}}