{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HRPGZD3RLZUNJWQOHACJ2B2UNW","short_pith_number":"pith:HRPGZD3R","canonical_record":{"source":{"id":"1306.3178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-13T18:04:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52c3378d5ffe63b4c349811fdc1b6badd457d4c01e07e20d0805fd5568abcce3","abstract_canon_sha256":"306ff5fd7cfb51f46c74b4db2143fc395eaaa92bd9a7f389134675b3c59b0521"},"schema_version":"1.0"},"canonical_sha256":"3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666","source":{"kind":"arxiv","id":"1306.3178","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3178","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3178v2","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3178","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"HRPGZD3RLZUN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HRPGZD3RLZUNJWQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HRPGZD3R","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HRPGZD3RLZUNJWQOHACJ2B2UNW","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3178","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-13T18:04:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"52c3378d5ffe63b4c349811fdc1b6badd457d4c01e07e20d0805fd5568abcce3","abstract_canon_sha256":"306ff5fd7cfb51f46c74b4db2143fc395eaaa92bd9a7f389134675b3c59b0521"},"schema_version":"1.0"},"canonical_sha256":"3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:59.902532Z","signature_b64":"magNxis/rrx+/KyHUTNj2LP+hykjErnTJDzqp6hq6tp+X92gvC05XZ/2AvgXait3KNyCIbAQidVFBMdWqpNJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666","last_reissued_at":"2026-05-18T02:56:59.902138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:59.902138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3178","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":"2026-05-18T02:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1b6fOQsCn6oiiCkgxfuZxGyXqz8MCMaQmhgiZZcYHSnfSothbeWvTgWJv1TRSsf3I/FQ9V2Q0sA41TXZPeCSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:34:40.751216Z"},"content_sha256":"011bac49c5ae2f76bcf7b4aa16c8fdc54bda4320056d5dd5bef15ea9dd56568b","schema_version":"1.0","event_id":"sha256:011bac49c5ae2f76bcf7b4aa16c8fdc54bda4320056d5dd5bef15ea9dd56568b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HRPGZD3RLZUNJWQOHACJ2B2UNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Sobolev norms and localization on the Fourier side for the solutions to some evolution equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Sergey A. Denisov","submitted_at":"2013-06-13T18:04:05Z","abstract_excerpt":"Some evolution equations with rough time-dependent potential are studied in the case of one-dimensional torus. We show that the solution has higher regularity for the generic values of the coupling constant. The asymptotics for large time and the localization on the Fourier side are studied."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3178","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":"2026-05-18T02:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5IEuuOYj0mUXtFqxCEvShLBBVf6ELfeIzK15KSGDSAJCRfiaKPsExhHbrTmxRhUvvysrU5aWjb0QHjvy6V8JDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:34:40.751578Z"},"content_sha256":"43373641d029efd26e305db03cdf39fe573cfbadbc276ba8af4f6b941742121b","schema_version":"1.0","event_id":"sha256:43373641d029efd26e305db03cdf39fe573cfbadbc276ba8af4f6b941742121b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/bundle.json","state_url":"https://pith.science/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/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":"2026-06-03T21:34:40Z","links":{"resolver":"https://pith.science/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW","bundle":"https://pith.science/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/bundle.json","state":"https://pith.science/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRPGZD3RLZUNJWQOHACJ2B2UNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HRPGZD3RLZUNJWQOHACJ2B2UNW","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":"306ff5fd7cfb51f46c74b4db2143fc395eaaa92bd9a7f389134675b3c59b0521","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-13T18:04:05Z","title_canon_sha256":"52c3378d5ffe63b4c349811fdc1b6badd457d4c01e07e20d0805fd5568abcce3"},"schema_version":"1.0","source":{"id":"1306.3178","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3178","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3178v2","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3178","created_at":"2026-05-18T02:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"HRPGZD3RLZUN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HRPGZD3RLZUNJWQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HRPGZD3R","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:43373641d029efd26e305db03cdf39fe573cfbadbc276ba8af4f6b941742121b","target":"graph","created_at":"2026-05-18T02:56:59Z","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":"Some evolution equations with rough time-dependent potential are studied in the case of one-dimensional torus. We show that the solution has higher regularity for the generic values of the coupling constant. The asymptotics for large time and the localization on the Fourier side are studied.","authors_text":"Sergey A. Denisov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-13T18:04:05Z","title":"The Sobolev norms and localization on the Fourier side for the solutions to some evolution equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3178","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":"sha256:011bac49c5ae2f76bcf7b4aa16c8fdc54bda4320056d5dd5bef15ea9dd56568b","target":"record","created_at":"2026-05-18T02:56:59Z","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":"306ff5fd7cfb51f46c74b4db2143fc395eaaa92bd9a7f389134675b3c59b0521","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-13T18:04:05Z","title_canon_sha256":"52c3378d5ffe63b4c349811fdc1b6badd457d4c01e07e20d0805fd5568abcce3"},"schema_version":"1.0","source":{"id":"1306.3178","kind":"arxiv","version":2}},"canonical_sha256":"3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c5e6c8f715e68d4da0e38049d07546d8f9e9a1152f505393bca690112621666","first_computed_at":"2026-05-18T02:56:59.902138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:59.902138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"magNxis/rrx+/KyHUTNj2LP+hykjErnTJDzqp6hq6tp+X92gvC05XZ/2AvgXait3KNyCIbAQidVFBMdWqpNJCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:59.902532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3178","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:011bac49c5ae2f76bcf7b4aa16c8fdc54bda4320056d5dd5bef15ea9dd56568b","sha256:43373641d029efd26e305db03cdf39fe573cfbadbc276ba8af4f6b941742121b"],"state_sha256":"5c0df92cc87819b8904981a68bea86439d0e22e9e78e808754c26a3aad4a9968"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fFeLE1mWgvS/olJA3B2oonpZLNMxREOqHf2VcezI3ad6hxy/OZb9QJxPIJtneqnYGl13JVgwq5Y2zOIHI40nDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:34:40.753596Z","bundle_sha256":"3d5ab0f00392206049044064bf7036d607c8a16c2e09ccecd65b388dd19c2b14"}}