{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EY7Q2X7XJHZCP6CICBAX4LZSCR","short_pith_number":"pith:EY7Q2X7X","canonical_record":{"source":{"id":"1607.04582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-15T17:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"08d3968e24f0f955b297975074d708c4863f16dca470d61357f8782dfaea22e9","abstract_canon_sha256":"fc47f0fe843b640fab523991e06325b9d1ebbff2ebae3e78e0b1f4800fd5c801"},"schema_version":"1.0"},"canonical_sha256":"263f0d5ff749f227f84810417e2f321472be26e42e56fa8512bc3e3f685ba618","source":{"kind":"arxiv","id":"1607.04582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04582","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04582v1","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04582","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"EY7Q2X7XJHZC","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EY7Q2X7XJHZCP6CI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EY7Q2X7X","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EY7Q2X7XJHZCP6CICBAX4LZSCR","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-15T17:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"08d3968e24f0f955b297975074d708c4863f16dca470d61357f8782dfaea22e9","abstract_canon_sha256":"fc47f0fe843b640fab523991e06325b9d1ebbff2ebae3e78e0b1f4800fd5c801"},"schema_version":"1.0"},"canonical_sha256":"263f0d5ff749f227f84810417e2f321472be26e42e56fa8512bc3e3f685ba618","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:56.954492Z","signature_b64":"tzDTY5FAk56R4Jc4zez7UiAa+KEVU5q13RxRrCQF3w6widZgfxPQlL+NKvnU1y9uqDOVqzn6ksMmdPTMMqbmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"263f0d5ff749f227f84810417e2f321472be26e42e56fa8512bc3e3f685ba618","last_reissued_at":"2026-05-18T00:28:56.953934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:56.953934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04582","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":"2026-05-18T00:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w+sACs6vZ0aU/5f87RZ9dIavUBfaGKkh9BjASXjQW8TrD6rbrZqi1s8G1Rci5zcIx7fesJq+oF/U3/sRpDojAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:45:52.408351Z"},"content_sha256":"4b10f29946df7514bc74f1a5dc0098d7828238d09508e39962e7daa10aaceca6","schema_version":"1.0","event_id":"sha256:4b10f29946df7514bc74f1a5dc0098d7828238d09508e39962e7daa10aaceca6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EY7Q2X7XJHZCP6CICBAX4LZSCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global mild solutions for the nonautonomous 2D Navier-Stokes equations with impulse effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Everaldo M. Bonotto, Jaqueline G. Mesquita, Ricardo P. Silva","submitted_at":"2016-07-15T17:08:00Z","abstract_excerpt":"The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D Navier-Stokes equations with impulse effects and allowing that the nonlinear terms are explicitly time-dependent. Additionally, we present sufficient conditions to obtain dissipativity (boundedness) for solutions starting in bounded sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04582","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":"2026-05-18T00:28:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0ZC5OdNtXw9aOz2SHBcs4qijnKHdLJZYnrJ6t5sXq0GyzDj7o/JB4p6/CUqu82iH95mVYdlhbYe02SxyRzSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T08:45:52.408695Z"},"content_sha256":"02603e18b9be6e38ba12c615c1c89da210c698dce56fe63138fa59e368a33efb","schema_version":"1.0","event_id":"sha256:02603e18b9be6e38ba12c615c1c89da210c698dce56fe63138fa59e368a33efb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/bundle.json","state_url":"https://pith.science/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/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":"2026-06-26T08:45:52Z","links":{"resolver":"https://pith.science/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR","bundle":"https://pith.science/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/bundle.json","state":"https://pith.science/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EY7Q2X7XJHZCP6CICBAX4LZSCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EY7Q2X7XJHZCP6CICBAX4LZSCR","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":"fc47f0fe843b640fab523991e06325b9d1ebbff2ebae3e78e0b1f4800fd5c801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-15T17:08:00Z","title_canon_sha256":"08d3968e24f0f955b297975074d708c4863f16dca470d61357f8782dfaea22e9"},"schema_version":"1.0","source":{"id":"1607.04582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04582","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04582v1","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04582","created_at":"2026-05-18T00:28:56Z"},{"alias_kind":"pith_short_12","alias_value":"EY7Q2X7XJHZC","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EY7Q2X7XJHZCP6CI","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EY7Q2X7X","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:02603e18b9be6e38ba12c615c1c89da210c698dce56fe63138fa59e368a33efb","target":"graph","created_at":"2026-05-18T00:28:56Z","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":"The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D Navier-Stokes equations with impulse effects and allowing that the nonlinear terms are explicitly time-dependent. Additionally, we present sufficient conditions to obtain dissipativity (boundedness) for solutions starting in bounded sets.","authors_text":"Everaldo M. Bonotto, Jaqueline G. Mesquita, Ricardo P. Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-15T17:08:00Z","title":"Global mild solutions for the nonautonomous 2D Navier-Stokes equations with impulse effects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04582","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":"sha256:4b10f29946df7514bc74f1a5dc0098d7828238d09508e39962e7daa10aaceca6","target":"record","created_at":"2026-05-18T00:28:56Z","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":"fc47f0fe843b640fab523991e06325b9d1ebbff2ebae3e78e0b1f4800fd5c801","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-15T17:08:00Z","title_canon_sha256":"08d3968e24f0f955b297975074d708c4863f16dca470d61357f8782dfaea22e9"},"schema_version":"1.0","source":{"id":"1607.04582","kind":"arxiv","version":1}},"canonical_sha256":"263f0d5ff749f227f84810417e2f321472be26e42e56fa8512bc3e3f685ba618","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"263f0d5ff749f227f84810417e2f321472be26e42e56fa8512bc3e3f685ba618","first_computed_at":"2026-05-18T00:28:56.953934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:56.953934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tzDTY5FAk56R4Jc4zez7UiAa+KEVU5q13RxRrCQF3w6widZgfxPQlL+NKvnU1y9uqDOVqzn6ksMmdPTMMqbmAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:56.954492Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b10f29946df7514bc74f1a5dc0098d7828238d09508e39962e7daa10aaceca6","sha256:02603e18b9be6e38ba12c615c1c89da210c698dce56fe63138fa59e368a33efb"],"state_sha256":"ce7a856675a0a53978ddadd12bbb2d06186937a4cff411dfd2f84963c6225733"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sE7SUMrTPZ/r77TPcvcpvLf65Ba13XObx7sD93dmRYn4vrdt9wuwlH/4ZDlNeTIPzctsYyYENyVXBXSw6HVDBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T08:45:52.410595Z","bundle_sha256":"40c3ab57f5a1623c50075105de3ef3538e1aae3fe0c5ee73809e72eacb328ee7"}}