{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:EDGZEZRAKTAFHDS4FC3JHTQGBF","short_pith_number":"pith:EDGZEZRA","canonical_record":{"source":{"id":"2204.07320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T04:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"2118d3007eb2582fb449d8e18d317bff65efc8db2bea3246b7ce404ad5d23708","abstract_canon_sha256":"d67ab659e8c22a561b0374ad07070c757fb794593b72f0baed86cddca33a731e"},"schema_version":"1.0"},"canonical_sha256":"20cd92662054c0538e5c28b693ce06096cbabd591f560969781a29c4685d9d5e","source":{"kind":"arxiv","id":"2204.07320","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.07320","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2204.07320v1","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.07320","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"EDGZEZRAKTAF","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"EDGZEZRAKTAFHDS4","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"EDGZEZRA","created_at":"2026-07-05T05:16:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:EDGZEZRAKTAFHDS4FC3JHTQGBF","target":"record","payload":{"canonical_record":{"source":{"id":"2204.07320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T04:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"2118d3007eb2582fb449d8e18d317bff65efc8db2bea3246b7ce404ad5d23708","abstract_canon_sha256":"d67ab659e8c22a561b0374ad07070c757fb794593b72f0baed86cddca33a731e"},"schema_version":"1.0"},"canonical_sha256":"20cd92662054c0538e5c28b693ce06096cbabd591f560969781a29c4685d9d5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:16:50.609146Z","signature_b64":"wQEtO1wyAqGxEseOpzyQBiyHN6PAOZImta0LaH1765KXp/jJYvPkVSiVw6Y+H9cnFUvc4tqdQ47EmWPkqcKNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20cd92662054c0538e5c28b693ce06096cbabd591f560969781a29c4685d9d5e","last_reissued_at":"2026-07-05T05:16:50.608752Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:16:50.608752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.07320","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":"2026-07-05T05:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tsA2mQVY/J5ZzWlGdQYd0xqo17zctUmKGWz70bfe371MnXvL56mZm6+vjYw7o3tBtn5bdH0ahGrXzYnxgmOCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-21T04:22:14.835269Z"},"content_sha256":"556ef14eeba5574274cb132d8384fd582f106e0a92785786bd091480f4823edb","schema_version":"1.0","event_id":"sha256:556ef14eeba5574274cb132d8384fd582f106e0a92785786bd091480f4823edb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:EDGZEZRAKTAFHDS4FC3JHTQGBF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chunhua Li, Hideaki Sunagawa, Yoshinori Nishii, Yuji Sagawa","submitted_at":"2022-04-15T04:00:25Z","abstract_excerpt":"We consider the initial value problem for cubic derivative nonlinear Schr\\\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\\log t)^{-1/4})$ in $L^2$ as $t\\to +\\infty$. Furthermore, we find that this $L^2$-decay rate is optimal by giving a lower estimate of the same order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07320","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/2204.07320/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":"2026-07-05T05:16:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"90I3kOJndV/ZxlZCK7P010X3IdRNCerFS199qoylsZXrvLKJGWVAqYfouNqsbwSySzdWUA0gnzacELH7tPaRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-21T04:22:14.835650Z"},"content_sha256":"dca12341d0506e2d6bb2d62cf4b73c8a951f967110bf67a7dae1e0a27f6dea92","schema_version":"1.0","event_id":"sha256:dca12341d0506e2d6bb2d62cf4b73c8a951f967110bf67a7dae1e0a27f6dea92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/bundle.json","state_url":"https://pith.science/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/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":"2026-07-21T04:22:14Z","links":{"resolver":"https://pith.science/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF","bundle":"https://pith.science/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/bundle.json","state":"https://pith.science/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDGZEZRAKTAFHDS4FC3JHTQGBF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EDGZEZRAKTAFHDS4FC3JHTQGBF","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":"d67ab659e8c22a561b0374ad07070c757fb794593b72f0baed86cddca33a731e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T04:00:25Z","title_canon_sha256":"2118d3007eb2582fb449d8e18d317bff65efc8db2bea3246b7ce404ad5d23708"},"schema_version":"1.0","source":{"id":"2204.07320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.07320","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"arxiv_version","alias_value":"2204.07320v1","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.07320","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_12","alias_value":"EDGZEZRAKTAF","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_16","alias_value":"EDGZEZRAKTAFHDS4","created_at":"2026-07-05T05:16:50Z"},{"alias_kind":"pith_short_8","alias_value":"EDGZEZRA","created_at":"2026-07-05T05:16:50Z"}],"graph_snapshots":[{"event_id":"sha256:dca12341d0506e2d6bb2d62cf4b73c8a951f967110bf67a7dae1e0a27f6dea92","target":"graph","created_at":"2026-07-05T05:16:50Z","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/2204.07320/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the initial value problem for cubic derivative nonlinear Schr\\\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\\log t)^{-1/4})$ in $L^2$ as $t\\to +\\infty$. Furthermore, we find that this $L^2$-decay rate is optimal by giving a lower estimate of the same order.","authors_text":"Chunhua Li, Hideaki Sunagawa, Yoshinori Nishii, Yuji Sagawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T04:00:25Z","title":"Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.07320","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":"sha256:556ef14eeba5574274cb132d8384fd582f106e0a92785786bd091480f4823edb","target":"record","created_at":"2026-07-05T05:16:50Z","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":"d67ab659e8c22a561b0374ad07070c757fb794593b72f0baed86cddca33a731e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-04-15T04:00:25Z","title_canon_sha256":"2118d3007eb2582fb449d8e18d317bff65efc8db2bea3246b7ce404ad5d23708"},"schema_version":"1.0","source":{"id":"2204.07320","kind":"arxiv","version":1}},"canonical_sha256":"20cd92662054c0538e5c28b693ce06096cbabd591f560969781a29c4685d9d5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20cd92662054c0538e5c28b693ce06096cbabd591f560969781a29c4685d9d5e","first_computed_at":"2026-07-05T05:16:50.608752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:16:50.608752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wQEtO1wyAqGxEseOpzyQBiyHN6PAOZImta0LaH1765KXp/jJYvPkVSiVw6Y+H9cnFUvc4tqdQ47EmWPkqcKNAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:16:50.609146Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.07320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:556ef14eeba5574274cb132d8384fd582f106e0a92785786bd091480f4823edb","sha256:dca12341d0506e2d6bb2d62cf4b73c8a951f967110bf67a7dae1e0a27f6dea92"],"state_sha256":"69138af4f4700fd06d980bd58513c78edf0c991dea13b34a6eea675169e0624c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n0/Yx5F16zXjExl18/hrVXn4OgSnziNaN4TtwyO+rFc9YeLtQVUoqntvRE02G8HOmjvfsydJujI1v1yIAzbCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-21T04:22:14.838066Z","bundle_sha256":"acdf996c7f3db2e182709794e680d1f0943f62f5bd2cb77364226f4541d5a50f"}}