{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7GNEADKXYRAJKBSBSX54YOG7H7","short_pith_number":"pith:7GNEADKX","canonical_record":{"source":{"id":"1711.08741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-23T15:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"864d204896f23eb7ac44be78efa9452344d1cfcd09cfd2e57dda568ec2fc7aae","abstract_canon_sha256":"9663f78b5001b8231cc3cee649e8936d90488b45da5b0b2c93d51471d4f5bfe7"},"schema_version":"1.0"},"canonical_sha256":"f99a400d57c44095064195fbcc38df3fedb9374e95e59cd57cab034a04d56dfd","source":{"kind":"arxiv","id":"1711.08741","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08741","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08741v2","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08741","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"7GNEADKXYRAJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7GNEADKXYRAJKBSB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7GNEADKX","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7GNEADKXYRAJKBSBSX54YOG7H7","target":"record","payload":{"canonical_record":{"source":{"id":"1711.08741","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-23T15:37:22Z","cross_cats_sorted":[],"title_canon_sha256":"864d204896f23eb7ac44be78efa9452344d1cfcd09cfd2e57dda568ec2fc7aae","abstract_canon_sha256":"9663f78b5001b8231cc3cee649e8936d90488b45da5b0b2c93d51471d4f5bfe7"},"schema_version":"1.0"},"canonical_sha256":"f99a400d57c44095064195fbcc38df3fedb9374e95e59cd57cab034a04d56dfd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:41.498136Z","signature_b64":"pQ/gbiFRfe4PbpY/TiAXAg7N0Zhxh6KihmTzs+NSEeeOvY0k/WqhVHmzWVLKyJsvSckqah2vyPkUGaHCGy1vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f99a400d57c44095064195fbcc38df3fedb9374e95e59cd57cab034a04d56dfd","last_reissued_at":"2026-05-18T00:19:41.497472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:41.497472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.08741","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":"2026-05-18T00:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRvbyJKSuLJAeKTQlRc3Wuy2ifKohLX+buTC4tZ+o07W5GAbv2o7O//WY/5CFxWAldgk6/dIgEYc6MA68W6wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:02:21.637773Z"},"content_sha256":"359a521b9461527e59828430123dd32f2c2087f150411cf6bffde75ad1aea299","schema_version":"1.0","event_id":"sha256:359a521b9461527e59828430123dd32f2c2087f150411cf6bffde75ad1aea299"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7GNEADKXYRAJKBSBSX54YOG7H7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remark on the strong solvability of the Navier-Stokes equations in the weak $L^n$ space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Takahiro Okabe, Yohei Tsutsui","submitted_at":"2017-11-23T15:37:22Z","abstract_excerpt":"The initial value problem of the incompressible Navier-Stokes equations with non-zero forces in $L^{n,\\infty}(\\mathbb{R}^n)$ is investigated. Even though the Stokes semigroup is not strongly continuous on $L^{n,\\infty}(\\mathbb{R}^n)$, with the qualitative condition for the external forces, it is clarified that the mild solution of the Naiver-Stokes equations satisfies the differential equations in the topology of $L^{n,\\infty}(\\mathbb{R}^n)$. Inspired by the conditions for the forces, we characterize the maximal complete subspace in $L^{n,\\infty}(\\mathbb{R}^n)$ where the Stokes semigroup is st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08741","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":"2026-05-18T00:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8lDPdwHnqjrnSmqRyibu6Z5pvY2aDrVcq0l93cUS3WE3veXMDiT9p+dmF7ZU8hgl2OPrKbyUzTOWhmCfJjgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:02:21.638160Z"},"content_sha256":"a61960d9018f6fc60bef6320f7ce20f703950525b854febc352927232794a7dc","schema_version":"1.0","event_id":"sha256:a61960d9018f6fc60bef6320f7ce20f703950525b854febc352927232794a7dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7GNEADKXYRAJKBSBSX54YOG7H7/bundle.json","state_url":"https://pith.science/pith/7GNEADKXYRAJKBSBSX54YOG7H7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7GNEADKXYRAJKBSBSX54YOG7H7/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":"2026-06-04T19:02:21Z","links":{"resolver":"https://pith.science/pith/7GNEADKXYRAJKBSBSX54YOG7H7","bundle":"https://pith.science/pith/7GNEADKXYRAJKBSBSX54YOG7H7/bundle.json","state":"https://pith.science/pith/7GNEADKXYRAJKBSBSX54YOG7H7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7GNEADKXYRAJKBSBSX54YOG7H7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7GNEADKXYRAJKBSBSX54YOG7H7","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":"9663f78b5001b8231cc3cee649e8936d90488b45da5b0b2c93d51471d4f5bfe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-23T15:37:22Z","title_canon_sha256":"864d204896f23eb7ac44be78efa9452344d1cfcd09cfd2e57dda568ec2fc7aae"},"schema_version":"1.0","source":{"id":"1711.08741","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.08741","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1711.08741v2","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08741","created_at":"2026-05-18T00:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"7GNEADKXYRAJ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7GNEADKXYRAJKBSB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7GNEADKX","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:a61960d9018f6fc60bef6320f7ce20f703950525b854febc352927232794a7dc","target":"graph","created_at":"2026-05-18T00:19:41Z","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 initial value problem of the incompressible Navier-Stokes equations with non-zero forces in $L^{n,\\infty}(\\mathbb{R}^n)$ is investigated. Even though the Stokes semigroup is not strongly continuous on $L^{n,\\infty}(\\mathbb{R}^n)$, with the qualitative condition for the external forces, it is clarified that the mild solution of the Naiver-Stokes equations satisfies the differential equations in the topology of $L^{n,\\infty}(\\mathbb{R}^n)$. Inspired by the conditions for the forces, we characterize the maximal complete subspace in $L^{n,\\infty}(\\mathbb{R}^n)$ where the Stokes semigroup is st","authors_text":"Takahiro Okabe, Yohei Tsutsui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-23T15:37:22Z","title":"Remark on the strong solvability of the Navier-Stokes equations in the weak $L^n$ space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08741","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":"sha256:359a521b9461527e59828430123dd32f2c2087f150411cf6bffde75ad1aea299","target":"record","created_at":"2026-05-18T00:19:41Z","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":"9663f78b5001b8231cc3cee649e8936d90488b45da5b0b2c93d51471d4f5bfe7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-23T15:37:22Z","title_canon_sha256":"864d204896f23eb7ac44be78efa9452344d1cfcd09cfd2e57dda568ec2fc7aae"},"schema_version":"1.0","source":{"id":"1711.08741","kind":"arxiv","version":2}},"canonical_sha256":"f99a400d57c44095064195fbcc38df3fedb9374e95e59cd57cab034a04d56dfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f99a400d57c44095064195fbcc38df3fedb9374e95e59cd57cab034a04d56dfd","first_computed_at":"2026-05-18T00:19:41.497472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:41.497472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pQ/gbiFRfe4PbpY/TiAXAg7N0Zhxh6KihmTzs+NSEeeOvY0k/WqhVHmzWVLKyJsvSckqah2vyPkUGaHCGy1vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:41.498136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.08741","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:359a521b9461527e59828430123dd32f2c2087f150411cf6bffde75ad1aea299","sha256:a61960d9018f6fc60bef6320f7ce20f703950525b854febc352927232794a7dc"],"state_sha256":"c7ccaa5956745e9b81162ce2983b33c93e9e60b0187e2f1608800f10b1bc9fea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5nF2HDE1ESqV0YrjDQz1yWbwcN6QARk3yNmYYExiyyVYFmlo3wYqYAMG6b0iaNeuGij5s1OKo8PQ4HOr180Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:02:21.640060Z","bundle_sha256":"c43fb82ca1c89403cee6de6d6807e8ee736ae553eea3a58b0c8731cc37f841df"}}