{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TWCM63VTF2ORMMHBYWMJ37A7RK","short_pith_number":"pith:TWCM63VT","canonical_record":{"source":{"id":"1706.08246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-26T06:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"4617cab1ce81f841684b542dda1482b36430e9e9337bddd77728dfe23fec1b8f","abstract_canon_sha256":"920d2985966eebe3f30609f769087da2e6aa7f403e0ff0f3f080f79b02f97ae0"},"schema_version":"1.0"},"canonical_sha256":"9d84cf6eb32e9d1630e1c5989dfc1f8a8cb52e08c3433f1a0a19dd5c8472eac1","source":{"kind":"arxiv","id":"1706.08246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08246","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08246v1","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08246","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"TWCM63VTF2OR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWCM63VTF2ORMMHB","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWCM63VT","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TWCM63VTF2ORMMHBYWMJ37A7RK","target":"record","payload":{"canonical_record":{"source":{"id":"1706.08246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-26T06:41:59Z","cross_cats_sorted":[],"title_canon_sha256":"4617cab1ce81f841684b542dda1482b36430e9e9337bddd77728dfe23fec1b8f","abstract_canon_sha256":"920d2985966eebe3f30609f769087da2e6aa7f403e0ff0f3f080f79b02f97ae0"},"schema_version":"1.0"},"canonical_sha256":"9d84cf6eb32e9d1630e1c5989dfc1f8a8cb52e08c3433f1a0a19dd5c8472eac1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:20.276353Z","signature_b64":"Aq4i9zVcBcuWrbp75+mJaCF4RNSUzZzGqjER/hwv1kDO2qbBG2EvGpDxXxB8Age3vxEx7OaqEfiRSgb+akNKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d84cf6eb32e9d1630e1c5989dfc1f8a8cb52e08c3433f1a0a19dd5c8472eac1","last_reissued_at":"2026-05-18T00:09:20.275662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:20.275662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.08246","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":"2026-05-18T00:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HwpitA+7Awd58EqGRINbNt8zoas/NEPPMDD+LQKuNwKtSz6u0PjFFthfulTZN0TMXvuDHUXIcKNkGy/d/MQXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:09:26.114057Z"},"content_sha256":"66655cd602264a9be14479eabdb20a1b72a08c27cd0cac4dd56d8854613b5bb8","schema_version":"1.0","event_id":"sha256:66655cd602264a9be14479eabdb20a1b72a08c27cd0cac4dd56d8854613b5bb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TWCM63VTF2ORMMHBYWMJ37A7RK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eulerian dynamics with a commutator forcing III. Fractional diffusion of order $0<\\alpha<1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Eitan Tadmor, Roman Shvydkoy","submitted_at":"2017-06-26T06:41:59Z","abstract_excerpt":"We continue our study of hydrodynamic models of self-organized evolution of agents with singular interaction kernel $\\phi(x) = |x|^{-(1+\\alpha)}$. Following our works \\cite{ST2017a,ST2017b} which focused on the range $1\\leq \\alpha <2$, and Do et. al. \\cite{DKRT2017} which covered the range $0<\\alpha<1$, in this paper we revisit the latter case and give a short(-er) proof of global in time existence of smooth solutions, together with a full description of their long time dynamics. Specifically, we prove that starting from any initial condition in $(\\rho_0,u_0) \\in H^{2+\\alpha}\\times H^3$, the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08246","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":"2026-05-18T00:09:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47+QwDqYtEm6C78g4Wg0+6aaUIvwqC7Q7/8fxgop0Vt6Khll9UaRZ06/z7kX/foEtSyaZEupjuWz1zsE20C+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:09:26.114462Z"},"content_sha256":"11192f8131e491ba93699c81170cf32727dd5f4cb21c9b3f255d468a073c6ba7","schema_version":"1.0","event_id":"sha256:11192f8131e491ba93699c81170cf32727dd5f4cb21c9b3f255d468a073c6ba7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/bundle.json","state_url":"https://pith.science/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/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":"2026-05-26T11:09:26Z","links":{"resolver":"https://pith.science/pith/TWCM63VTF2ORMMHBYWMJ37A7RK","bundle":"https://pith.science/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/bundle.json","state":"https://pith.science/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWCM63VTF2ORMMHBYWMJ37A7RK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TWCM63VTF2ORMMHBYWMJ37A7RK","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":"920d2985966eebe3f30609f769087da2e6aa7f403e0ff0f3f080f79b02f97ae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-26T06:41:59Z","title_canon_sha256":"4617cab1ce81f841684b542dda1482b36430e9e9337bddd77728dfe23fec1b8f"},"schema_version":"1.0","source":{"id":"1706.08246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.08246","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"arxiv_version","alias_value":"1706.08246v1","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08246","created_at":"2026-05-18T00:09:20Z"},{"alias_kind":"pith_short_12","alias_value":"TWCM63VTF2OR","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TWCM63VTF2ORMMHB","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TWCM63VT","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:11192f8131e491ba93699c81170cf32727dd5f4cb21c9b3f255d468a073c6ba7","target":"graph","created_at":"2026-05-18T00:09:20Z","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 continue our study of hydrodynamic models of self-organized evolution of agents with singular interaction kernel $\\phi(x) = |x|^{-(1+\\alpha)}$. Following our works \\cite{ST2017a,ST2017b} which focused on the range $1\\leq \\alpha <2$, and Do et. al. \\cite{DKRT2017} which covered the range $0<\\alpha<1$, in this paper we revisit the latter case and give a short(-er) proof of global in time existence of smooth solutions, together with a full description of their long time dynamics. Specifically, we prove that starting from any initial condition in $(\\rho_0,u_0) \\in H^{2+\\alpha}\\times H^3$, the s","authors_text":"Eitan Tadmor, Roman Shvydkoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-26T06:41:59Z","title":"Eulerian dynamics with a commutator forcing III. Fractional diffusion of order $0<\\alpha<1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08246","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":"sha256:66655cd602264a9be14479eabdb20a1b72a08c27cd0cac4dd56d8854613b5bb8","target":"record","created_at":"2026-05-18T00:09:20Z","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":"920d2985966eebe3f30609f769087da2e6aa7f403e0ff0f3f080f79b02f97ae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-26T06:41:59Z","title_canon_sha256":"4617cab1ce81f841684b542dda1482b36430e9e9337bddd77728dfe23fec1b8f"},"schema_version":"1.0","source":{"id":"1706.08246","kind":"arxiv","version":1}},"canonical_sha256":"9d84cf6eb32e9d1630e1c5989dfc1f8a8cb52e08c3433f1a0a19dd5c8472eac1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d84cf6eb32e9d1630e1c5989dfc1f8a8cb52e08c3433f1a0a19dd5c8472eac1","first_computed_at":"2026-05-18T00:09:20.275662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:20.275662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aq4i9zVcBcuWrbp75+mJaCF4RNSUzZzGqjER/hwv1kDO2qbBG2EvGpDxXxB8Age3vxEx7OaqEfiRSgb+akNKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:20.276353Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.08246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66655cd602264a9be14479eabdb20a1b72a08c27cd0cac4dd56d8854613b5bb8","sha256:11192f8131e491ba93699c81170cf32727dd5f4cb21c9b3f255d468a073c6ba7"],"state_sha256":"b54544015086bf2201c0bb53319fb97bee0b81b95b3647f2102f861142f0ed9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/b4oYeUYNkHLfGjDUYY5VzFvpXiYfoUG+6nw7g9fckkSW3vjrbX667S+s2ktXUB11Z8+QMCQIWkKNW+rm8WAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:09:26.117063Z","bundle_sha256":"e21db43345dfd5e0ef02d243a02e283af8cf13c0cea5a8c25f6bc75dcf676efc"}}