{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YSL6BA4EMW5PDU4J3AT7Q2AMHP","short_pith_number":"pith:YSL6BA4E","canonical_record":{"source":{"id":"1206.3898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T11:58:54Z","cross_cats_sorted":[],"title_canon_sha256":"46abb6f11ffcbe13c0346d5019073b4ea4cb6e30317f432160811993b6fdbc2c","abstract_canon_sha256":"bce75929176c73151b5dc70511a22d37b4514029e139df9db3dea04527808269"},"schema_version":"1.0"},"canonical_sha256":"c497e0838465baf1d389d827f8680c3be52a68450db85b297048653fe476ce28","source":{"kind":"arxiv","id":"1206.3898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3898","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3898v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3898","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"YSL6BA4EMW5P","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YSL6BA4EMW5PDU4J","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YSL6BA4E","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YSL6BA4EMW5PDU4J3AT7Q2AMHP","target":"record","payload":{"canonical_record":{"source":{"id":"1206.3898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T11:58:54Z","cross_cats_sorted":[],"title_canon_sha256":"46abb6f11ffcbe13c0346d5019073b4ea4cb6e30317f432160811993b6fdbc2c","abstract_canon_sha256":"bce75929176c73151b5dc70511a22d37b4514029e139df9db3dea04527808269"},"schema_version":"1.0"},"canonical_sha256":"c497e0838465baf1d389d827f8680c3be52a68450db85b297048653fe476ce28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:18.442216Z","signature_b64":"6RXd6jWjtkNdCj2sn586ONJ+SMGNBqRm6iJmhB1NCFltO3g+RXX30epaPp51FhXXH3nrIjj0fcRITH1DzQwhCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c497e0838465baf1d389d827f8680c3be52a68450db85b297048653fe476ce28","last_reissued_at":"2026-05-18T03:53:18.441203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:18.441203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.3898","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":"2026-05-18T03:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ch8TGHWLAQAP6I+ZkN00C0VWKceWdeL/mWfL5myuEba0xl3nru00BewLIMhC9kV+H2d+Erbrj473xJx6BVY6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:19:25.351518Z"},"content_sha256":"3c108de16a1671bb454354a66df16d708941797c3dddcc39c270171bcb051937","schema_version":"1.0","event_id":"sha256:3c108de16a1671bb454354a66df16d708941797c3dddcc39c270171bcb051937"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YSL6BA4EMW5PDU4J3AT7Q2AMHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries in low regularity settings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Seungly Oh","submitted_at":"2012-06-18T11:58:54Z","abstract_excerpt":"We show a smoothing effect of near full derivative for low-regularity global-in-time solutions of the periodic Korteweg-de Vries (KdV) equation. The smoothing is given by slightly shifting the space-time Fourier support of the nonlinear solution, which we call \\emph{resonant phase-shift}. More precisely, we show that $[\\mathcal{S}u](t) - e^{-t\\partial_x^3} u(0) \\in H^{-s+1-}$ where $u(0) \\in H^{-s}$ for $0\\leq s <1/2$ where $\\mathcal{S}$ is the resonant phase-shift operator described below. We use the normal form method to obtain the result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3898","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":"2026-05-18T03:53:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+q9lV1bJp3HIyYWtMlFtyAhtNVsvnYM6FsJKwf2+WKzNzTCCB3iK/2J3bPLaNpp50sIzrR3drgeECTh5rvn7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:19:25.351866Z"},"content_sha256":"337a1462c1a49a337fd920cbc77367e052a48e82ecfc4a694b15fade641796d3","schema_version":"1.0","event_id":"sha256:337a1462c1a49a337fd920cbc77367e052a48e82ecfc4a694b15fade641796d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/bundle.json","state_url":"https://pith.science/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/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":"2026-06-22T13:19:25Z","links":{"resolver":"https://pith.science/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP","bundle":"https://pith.science/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/bundle.json","state":"https://pith.science/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSL6BA4EMW5PDU4J3AT7Q2AMHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YSL6BA4EMW5PDU4J3AT7Q2AMHP","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":"bce75929176c73151b5dc70511a22d37b4514029e139df9db3dea04527808269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T11:58:54Z","title_canon_sha256":"46abb6f11ffcbe13c0346d5019073b4ea4cb6e30317f432160811993b6fdbc2c"},"schema_version":"1.0","source":{"id":"1206.3898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3898","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3898v1","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3898","created_at":"2026-05-18T03:53:18Z"},{"alias_kind":"pith_short_12","alias_value":"YSL6BA4EMW5P","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YSL6BA4EMW5PDU4J","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YSL6BA4E","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:337a1462c1a49a337fd920cbc77367e052a48e82ecfc4a694b15fade641796d3","target":"graph","created_at":"2026-05-18T03:53:18Z","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 show a smoothing effect of near full derivative for low-regularity global-in-time solutions of the periodic Korteweg-de Vries (KdV) equation. The smoothing is given by slightly shifting the space-time Fourier support of the nonlinear solution, which we call \\emph{resonant phase-shift}. More precisely, we show that $[\\mathcal{S}u](t) - e^{-t\\partial_x^3} u(0) \\in H^{-s+1-}$ where $u(0) \\in H^{-s}$ for $0\\leq s <1/2$ where $\\mathcal{S}$ is the resonant phase-shift operator described below. We use the normal form method to obtain the result.","authors_text":"Seungly Oh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T11:58:54Z","title":"Resonant phase-shift and global smoothing of the periodic Korteweg-de Vries in low regularity settings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3898","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":"sha256:3c108de16a1671bb454354a66df16d708941797c3dddcc39c270171bcb051937","target":"record","created_at":"2026-05-18T03:53:18Z","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":"bce75929176c73151b5dc70511a22d37b4514029e139df9db3dea04527808269","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-18T11:58:54Z","title_canon_sha256":"46abb6f11ffcbe13c0346d5019073b4ea4cb6e30317f432160811993b6fdbc2c"},"schema_version":"1.0","source":{"id":"1206.3898","kind":"arxiv","version":1}},"canonical_sha256":"c497e0838465baf1d389d827f8680c3be52a68450db85b297048653fe476ce28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c497e0838465baf1d389d827f8680c3be52a68450db85b297048653fe476ce28","first_computed_at":"2026-05-18T03:53:18.441203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:18.441203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6RXd6jWjtkNdCj2sn586ONJ+SMGNBqRm6iJmhB1NCFltO3g+RXX30epaPp51FhXXH3nrIjj0fcRITH1DzQwhCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:18.442216Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c108de16a1671bb454354a66df16d708941797c3dddcc39c270171bcb051937","sha256:337a1462c1a49a337fd920cbc77367e052a48e82ecfc4a694b15fade641796d3"],"state_sha256":"70e6dae9189097a3d0238e161b63c4bbb5d027c63af479843e9e6a706b5981c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ywrXqnMBniSCZ8aH+gQ4EkZ3eVUmwJdjWCW3KT0wAfEL4bgkAgc94BcGcEofB9lYphzoJ/Ts4xwytEPU52tAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:19:25.353857Z","bundle_sha256":"9a8324427571beb325a93eaffcb84d6a9a4e912f6479d9c02c89aad88aec1d0b"}}