{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2UMZA27HZ4TW46V7SYZT7UN6KL","short_pith_number":"pith:2UMZA27H","canonical_record":{"source":{"id":"1504.00955","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T23:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"3e86e36fd3aa4e270d32bd9efef935af3ac15fcf83ee23a8ec723cf962a30974","abstract_canon_sha256":"3792114f4947849804dedd4902e24544e477ac2ecd7720613e1c7885f7dfc301"},"schema_version":"1.0"},"canonical_sha256":"d519906be7cf276e7abf96333fd1be52d641397e730433977b9c04c47ba68544","source":{"kind":"arxiv","id":"1504.00955","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00955","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00955v4","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00955","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"2UMZA27HZ4TW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2UMZA27HZ4TW46V7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2UMZA27H","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2UMZA27HZ4TW46V7SYZT7UN6KL","target":"record","payload":{"canonical_record":{"source":{"id":"1504.00955","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T23:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"3e86e36fd3aa4e270d32bd9efef935af3ac15fcf83ee23a8ec723cf962a30974","abstract_canon_sha256":"3792114f4947849804dedd4902e24544e477ac2ecd7720613e1c7885f7dfc301"},"schema_version":"1.0"},"canonical_sha256":"d519906be7cf276e7abf96333fd1be52d641397e730433977b9c04c47ba68544","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:04.706515Z","signature_b64":"adc/SWF+GzCoJFVLG6XxgTIbDIu5PSXHfADBS0So+gancY4xeJ7ikd5P+GLe+XZeumGkNnzq0xYKFSz+BgltBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d519906be7cf276e7abf96333fd1be52d641397e730433977b9c04c47ba68544","last_reissued_at":"2026-05-18T00:56:04.705840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:04.705840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.00955","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2AlAVPpd3DYSRpIVBViEwD7G6Vh1Mg36voyhsNX4s93K3CgBqv+yXW0jrvcTbCihFl0cp0dwlDgqeilfEcPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:47:22.172786Z"},"content_sha256":"28d05885723c4c2025e4648fca7989c185b0ef1c54eff1310e514cd8afddf22a","schema_version":"1.0","event_id":"sha256:28d05885723c4c2025e4648fca7989c185b0ef1c54eff1310e514cd8afddf22a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2UMZA27HZ4TW46V7SYZT7UN6KL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical Keller-Segel meets Burgers on ${\\mathbb S}^1$: large-time smooth solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jan Burczak, Rafael Granero-Belinch\\'on","submitted_at":"2015-04-03T23:12:12Z","abstract_excerpt":"We show that solutions to the parabolic-elliptic Keller-Segel system on ${\\mathbb S}^1$ with critical fractional diffusion $(-\\Delta)^\\frac{1}{2}$ remain smooth for any initial data and any positive time. This disproves, at least in the periodic setting, the large-data-blowup conjecture by Bournaveas and Calvez. As a tool, we show smoothness of solutions to a modified critical Burgers equation via a generalization of the method of moduli of continuity by Kiselev, Nazarov and Shterenberg. over a setting where the considered equation has no scaling. This auxiliary result may be interesting by it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00955","kind":"arxiv","version":4},"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":"2026-05-18T00:56:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oSbbxV4F+t6vCpW9tXukUdVsaAdCMfbTWIk8vJph2zfOwW+VluZFVHecLQkOAlCESSYLMw6jMlhN7oXV+VUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:47:22.173193Z"},"content_sha256":"2cb99f009a1ea3bd5fc6a0c11960170cc7f4fa5ea85307e3a72dc434be47a0fe","schema_version":"1.0","event_id":"sha256:2cb99f009a1ea3bd5fc6a0c11960170cc7f4fa5ea85307e3a72dc434be47a0fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/bundle.json","state_url":"https://pith.science/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/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":"2026-06-11T20:47:22Z","links":{"resolver":"https://pith.science/pith/2UMZA27HZ4TW46V7SYZT7UN6KL","bundle":"https://pith.science/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/bundle.json","state":"https://pith.science/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2UMZA27HZ4TW46V7SYZT7UN6KL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2UMZA27HZ4TW46V7SYZT7UN6KL","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":"3792114f4947849804dedd4902e24544e477ac2ecd7720613e1c7885f7dfc301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T23:12:12Z","title_canon_sha256":"3e86e36fd3aa4e270d32bd9efef935af3ac15fcf83ee23a8ec723cf962a30974"},"schema_version":"1.0","source":{"id":"1504.00955","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.00955","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"arxiv_version","alias_value":"1504.00955v4","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.00955","created_at":"2026-05-18T00:56:04Z"},{"alias_kind":"pith_short_12","alias_value":"2UMZA27HZ4TW","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2UMZA27HZ4TW46V7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2UMZA27H","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:2cb99f009a1ea3bd5fc6a0c11960170cc7f4fa5ea85307e3a72dc434be47a0fe","target":"graph","created_at":"2026-05-18T00:56:04Z","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 show that solutions to the parabolic-elliptic Keller-Segel system on ${\\mathbb S}^1$ with critical fractional diffusion $(-\\Delta)^\\frac{1}{2}$ remain smooth for any initial data and any positive time. This disproves, at least in the periodic setting, the large-data-blowup conjecture by Bournaveas and Calvez. As a tool, we show smoothness of solutions to a modified critical Burgers equation via a generalization of the method of moduli of continuity by Kiselev, Nazarov and Shterenberg. over a setting where the considered equation has no scaling. This auxiliary result may be interesting by it","authors_text":"Jan Burczak, Rafael Granero-Belinch\\'on","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T23:12:12Z","title":"Critical Keller-Segel meets Burgers on ${\\mathbb S}^1$: large-time smooth solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00955","kind":"arxiv","version":4},"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":"sha256:28d05885723c4c2025e4648fca7989c185b0ef1c54eff1310e514cd8afddf22a","target":"record","created_at":"2026-05-18T00:56:04Z","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":"3792114f4947849804dedd4902e24544e477ac2ecd7720613e1c7885f7dfc301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-03T23:12:12Z","title_canon_sha256":"3e86e36fd3aa4e270d32bd9efef935af3ac15fcf83ee23a8ec723cf962a30974"},"schema_version":"1.0","source":{"id":"1504.00955","kind":"arxiv","version":4}},"canonical_sha256":"d519906be7cf276e7abf96333fd1be52d641397e730433977b9c04c47ba68544","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d519906be7cf276e7abf96333fd1be52d641397e730433977b9c04c47ba68544","first_computed_at":"2026-05-18T00:56:04.705840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:04.705840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"adc/SWF+GzCoJFVLG6XxgTIbDIu5PSXHfADBS0So+gancY4xeJ7ikd5P+GLe+XZeumGkNnzq0xYKFSz+BgltBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:04.706515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.00955","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28d05885723c4c2025e4648fca7989c185b0ef1c54eff1310e514cd8afddf22a","sha256:2cb99f009a1ea3bd5fc6a0c11960170cc7f4fa5ea85307e3a72dc434be47a0fe"],"state_sha256":"33a2cd15403be1f79b57b14e7805a09cf1cc13f6cb8314b5d1dd7a6d0603dd8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t388fDzjba4iBmKVCToRzLfTtizWcTngVPH0/HMBr4WKYrIpwWbA37KboWjlrftbSJ1aScLYsvoE74lrqP3eAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:47:22.176413Z","bundle_sha256":"1a0c0a44cf2a84e5f2fd862fdc5cd447221806636be778d4363e3e7252512fb9"}}