{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GESYFM2VBUK7NIYILMUVMVWNF7","short_pith_number":"pith:GESYFM2V","canonical_record":{"source":{"id":"1707.02016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-07T01:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"ba544eb35821788966d32aba4a009cbfd76727ae6c3341b27406cca3eaf957a9","abstract_canon_sha256":"9c0ac0d46acce92165a5d1ea91cc6c25f813027d4038ce5eaf5ba2b5e4adb5b7"},"schema_version":"1.0"},"canonical_sha256":"312582b3550d15f6a3085b295656cd2fdb23740c838ecca415f5780746884759","source":{"kind":"arxiv","id":"1707.02016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02016","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02016v1","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02016","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"GESYFM2VBUK7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GESYFM2VBUK7NIYI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GESYFM2V","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GESYFM2VBUK7NIYILMUVMVWNF7","target":"record","payload":{"canonical_record":{"source":{"id":"1707.02016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-07T01:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"ba544eb35821788966d32aba4a009cbfd76727ae6c3341b27406cca3eaf957a9","abstract_canon_sha256":"9c0ac0d46acce92165a5d1ea91cc6c25f813027d4038ce5eaf5ba2b5e4adb5b7"},"schema_version":"1.0"},"canonical_sha256":"312582b3550d15f6a3085b295656cd2fdb23740c838ecca415f5780746884759","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:45.468787Z","signature_b64":"XP86FmLRxwKzix/u8v1A6AyejmQk2bcjuq1yZPyPSUJ6tmv5ye7DQxFhuG7px79vq/2oE5SYFSdecu3hQaSHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"312582b3550d15f6a3085b295656cd2fdb23740c838ecca415f5780746884759","last_reissued_at":"2026-05-18T00:40:45.468083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:45.468083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.02016","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":"2026-05-18T00:40:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBY+a9hcW+u1nV66+ySqxlSsAzqcf1tmxvI4RO+l88pw8rdu6BF4Gs2SSv+JMrXGX9i2fBDhcqE7i6ZUmbv5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:18:29.157182Z"},"content_sha256":"b92232de1c66479303bb97b03380d3313aced3c0d6889dc67784cf6ca23aee7a","schema_version":"1.0","event_id":"sha256:b92232de1c66479303bb97b03380d3313aced3c0d6889dc67784cf6ca23aee7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GESYFM2VBUK7NIYILMUVMVWNF7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic stability of the stationary Navier-Stokes flows in Besov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jayson Cunanan, Takahiro Okabe, Yohei Tsutsui","submitted_at":"2017-07-07T01:33:38Z","abstract_excerpt":"We discuss the asymptotic stability of stationary solutions to the incompressible Navier-Stokes equations on the whole space in Besov spaces with positive smoothness and low integrability. A critical estimate for the semigroup generated by the Laplacian with a perturbation is main ingredient of the argument."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02016","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":"2026-05-18T00:40:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5wU3Qnzpocj44mq5jIiXYyik0pN9/NHu3VieGOoGfZbSBP5FXK/OfNJFmLjIxPme2/zfNI2hxcc7SZhQLtgVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:18:29.157845Z"},"content_sha256":"7f33868b457e6cefdab469d5feb94422ee1653fdf255f5a283b0163ed4739626","schema_version":"1.0","event_id":"sha256:7f33868b457e6cefdab469d5feb94422ee1653fdf255f5a283b0163ed4739626"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GESYFM2VBUK7NIYILMUVMVWNF7/bundle.json","state_url":"https://pith.science/pith/GESYFM2VBUK7NIYILMUVMVWNF7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GESYFM2VBUK7NIYILMUVMVWNF7/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":"2026-06-05T01:18:29Z","links":{"resolver":"https://pith.science/pith/GESYFM2VBUK7NIYILMUVMVWNF7","bundle":"https://pith.science/pith/GESYFM2VBUK7NIYILMUVMVWNF7/bundle.json","state":"https://pith.science/pith/GESYFM2VBUK7NIYILMUVMVWNF7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GESYFM2VBUK7NIYILMUVMVWNF7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GESYFM2VBUK7NIYILMUVMVWNF7","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":"9c0ac0d46acce92165a5d1ea91cc6c25f813027d4038ce5eaf5ba2b5e4adb5b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-07T01:33:38Z","title_canon_sha256":"ba544eb35821788966d32aba4a009cbfd76727ae6c3341b27406cca3eaf957a9"},"schema_version":"1.0","source":{"id":"1707.02016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.02016","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"1707.02016v1","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.02016","created_at":"2026-05-18T00:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"GESYFM2VBUK7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GESYFM2VBUK7NIYI","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GESYFM2V","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:7f33868b457e6cefdab469d5feb94422ee1653fdf255f5a283b0163ed4739626","target":"graph","created_at":"2026-05-18T00:40:45Z","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 discuss the asymptotic stability of stationary solutions to the incompressible Navier-Stokes equations on the whole space in Besov spaces with positive smoothness and low integrability. A critical estimate for the semigroup generated by the Laplacian with a perturbation is main ingredient of the argument.","authors_text":"Jayson Cunanan, Takahiro Okabe, Yohei Tsutsui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-07T01:33:38Z","title":"Asymptotic stability of the stationary Navier-Stokes flows in Besov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.02016","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:b92232de1c66479303bb97b03380d3313aced3c0d6889dc67784cf6ca23aee7a","target":"record","created_at":"2026-05-18T00:40:45Z","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":"9c0ac0d46acce92165a5d1ea91cc6c25f813027d4038ce5eaf5ba2b5e4adb5b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-07T01:33:38Z","title_canon_sha256":"ba544eb35821788966d32aba4a009cbfd76727ae6c3341b27406cca3eaf957a9"},"schema_version":"1.0","source":{"id":"1707.02016","kind":"arxiv","version":1}},"canonical_sha256":"312582b3550d15f6a3085b295656cd2fdb23740c838ecca415f5780746884759","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"312582b3550d15f6a3085b295656cd2fdb23740c838ecca415f5780746884759","first_computed_at":"2026-05-18T00:40:45.468083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:45.468083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XP86FmLRxwKzix/u8v1A6AyejmQk2bcjuq1yZPyPSUJ6tmv5ye7DQxFhuG7px79vq/2oE5SYFSdecu3hQaSHCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:45.468787Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.02016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b92232de1c66479303bb97b03380d3313aced3c0d6889dc67784cf6ca23aee7a","sha256:7f33868b457e6cefdab469d5feb94422ee1653fdf255f5a283b0163ed4739626"],"state_sha256":"73806a7d766b136ae9e965fd9ed6c2ec9deaaf8134625eb3a2ed5439841bf250"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lCNSnn43d6KmBgY4hDx6T8Y5Oh+BoaBbDumaNOxaMiwf6OWVOF7Rwc8qO5NO1oecwI8bkh6pGFBg7YNpNki3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:18:29.161522Z","bundle_sha256":"158a5fa56a501b6258942aec091261fa1d686306dd5d192f603bb51436396526"}}