{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P7DV4SR45DIQRFQ5JIP3GFKA35","short_pith_number":"pith:P7DV4SR4","canonical_record":{"source":{"id":"1306.0305","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-03T06:44:05Z","cross_cats_sorted":[],"title_canon_sha256":"b5ecfacc42263617d59c285574280f2a458d62c87d87a7d8ca6916deec3c340c","abstract_canon_sha256":"a733c03c1ab18e7e88eb5deac6d98ab1c2f1e24ede5d3e774f6fbc49277ac822"},"schema_version":"1.0"},"canonical_sha256":"7fc75e4a3ce8d108961d4a1fb31540df5a4ba286abc22753f3ff746005a36027","source":{"kind":"arxiv","id":"1306.0305","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0305","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0305v5","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0305","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"P7DV4SR45DIQ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7DV4SR45DIQRFQ5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7DV4SR4","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P7DV4SR45DIQRFQ5JIP3GFKA35","target":"record","payload":{"canonical_record":{"source":{"id":"1306.0305","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-03T06:44:05Z","cross_cats_sorted":[],"title_canon_sha256":"b5ecfacc42263617d59c285574280f2a458d62c87d87a7d8ca6916deec3c340c","abstract_canon_sha256":"a733c03c1ab18e7e88eb5deac6d98ab1c2f1e24ede5d3e774f6fbc49277ac822"},"schema_version":"1.0"},"canonical_sha256":"7fc75e4a3ce8d108961d4a1fb31540df5a4ba286abc22753f3ff746005a36027","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:18.272792Z","signature_b64":"XT32s4V9VIHlLRcyptSGBkGVRK1w3ISEtNvstIMylf+5qFBr4wHYL5ME0+kgktWzQeWRZdZPgVthYSFUm6iMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fc75e4a3ce8d108961d4a1fb31540df5a4ba286abc22753f3ff746005a36027","last_reissued_at":"2026-05-18T02:14:18.272222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:18.272222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.0305","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9aNCe4u+c+V+DMbo+cV5AJRSaoTOzNqdSKCGY/ds+3v500+Im7A/MVbJP9KVCuLh/U9tCjACH+2B+JC1vh8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:59:54.773987Z"},"content_sha256":"e3e37cf74092fd5e9d286fe68a244f9b229226bd2e5ac7f65083bea411820fb1","schema_version":"1.0","event_id":"sha256:e3e37cf74092fd5e9d286fe68a244f9b229226bd2e5ac7f65083bea411820fb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P7DV4SR45DIQRFQ5JIP3GFKA35","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongho Chae","submitted_at":"2013-06-03T06:44:05Z","abstract_excerpt":"We study scenarios of self-similar type blow-up for the incompressible Navier-Stokes and the Euler equations. The previous notions of the discretely (backward) self-similar solution and the asymptotically self-similar solution are generalized to the locally asymptotically discretely self-similar solution. We prove that there exists no such locally asymptotically discretely self-similar blow-up for the 3D Navier-Stokes equations if the blow-up profile is a time periodic function belonging to $C^1(\\Bbb R ; L^3(\\Bbb R^3)\\cap C^2 (\\Bbb R^3))$. For the 3D Euler equations we show that the scenario o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0305","kind":"arxiv","version":5},"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":"2026-05-18T02:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTDYp7DSsdwA1fNfHAnQkBmckl8DLXUmRs3bvn4UVIboN3uhpspvTCVm/97wHdwCJ6C1iQQeuquCXcNXizRcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:59:54.774348Z"},"content_sha256":"01d534f67c686a836384740e0094cbbb012c9145d9febb2bf37a76f3ecaeba79","schema_version":"1.0","event_id":"sha256:01d534f67c686a836384740e0094cbbb012c9145d9febb2bf37a76f3ecaeba79"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/bundle.json","state_url":"https://pith.science/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/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":"2026-05-28T04:59:54Z","links":{"resolver":"https://pith.science/pith/P7DV4SR45DIQRFQ5JIP3GFKA35","bundle":"https://pith.science/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/bundle.json","state":"https://pith.science/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P7DV4SR45DIQRFQ5JIP3GFKA35/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P7DV4SR45DIQRFQ5JIP3GFKA35","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":"a733c03c1ab18e7e88eb5deac6d98ab1c2f1e24ede5d3e774f6fbc49277ac822","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-03T06:44:05Z","title_canon_sha256":"b5ecfacc42263617d59c285574280f2a458d62c87d87a7d8ca6916deec3c340c"},"schema_version":"1.0","source":{"id":"1306.0305","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0305","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0305v5","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0305","created_at":"2026-05-18T02:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"P7DV4SR45DIQ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P7DV4SR45DIQRFQ5","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P7DV4SR4","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:01d534f67c686a836384740e0094cbbb012c9145d9febb2bf37a76f3ecaeba79","target":"graph","created_at":"2026-05-18T02:14:18Z","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 study scenarios of self-similar type blow-up for the incompressible Navier-Stokes and the Euler equations. The previous notions of the discretely (backward) self-similar solution and the asymptotically self-similar solution are generalized to the locally asymptotically discretely self-similar solution. We prove that there exists no such locally asymptotically discretely self-similar blow-up for the 3D Navier-Stokes equations if the blow-up profile is a time periodic function belonging to $C^1(\\Bbb R ; L^3(\\Bbb R^3)\\cap C^2 (\\Bbb R^3))$. For the 3D Euler equations we show that the scenario o","authors_text":"Dongho Chae","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-03T06:44:05Z","title":"Remarks on the asymptotically discretely self-similar solutions of the Navier-Stokes and the Euler equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0305","kind":"arxiv","version":5},"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:e3e37cf74092fd5e9d286fe68a244f9b229226bd2e5ac7f65083bea411820fb1","target":"record","created_at":"2026-05-18T02:14:18Z","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":"a733c03c1ab18e7e88eb5deac6d98ab1c2f1e24ede5d3e774f6fbc49277ac822","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-03T06:44:05Z","title_canon_sha256":"b5ecfacc42263617d59c285574280f2a458d62c87d87a7d8ca6916deec3c340c"},"schema_version":"1.0","source":{"id":"1306.0305","kind":"arxiv","version":5}},"canonical_sha256":"7fc75e4a3ce8d108961d4a1fb31540df5a4ba286abc22753f3ff746005a36027","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fc75e4a3ce8d108961d4a1fb31540df5a4ba286abc22753f3ff746005a36027","first_computed_at":"2026-05-18T02:14:18.272222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:18.272222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XT32s4V9VIHlLRcyptSGBkGVRK1w3ISEtNvstIMylf+5qFBr4wHYL5ME0+kgktWzQeWRZdZPgVthYSFUm6iMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:18.272792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0305","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3e37cf74092fd5e9d286fe68a244f9b229226bd2e5ac7f65083bea411820fb1","sha256:01d534f67c686a836384740e0094cbbb012c9145d9febb2bf37a76f3ecaeba79"],"state_sha256":"f1d50efd49526a31d1de12e62f9c2b015bebc7e1f7fde18050f98079effd45c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wS7zkORxsOFmtpYeN+qPysecRsqhDaN+CzaiT8ES4lMPEAosWe7NSLby0KuzpGm1Fyv+ksL4mYr3BM5ZLWzGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:59:54.776309Z","bundle_sha256":"af2567af69f82c62da3f92b65263926bca35b620fd22488e1b4249f4bc436380"}}