{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XZ4EJJPDF24P5IYBAUOKB5SDNI","short_pith_number":"pith:XZ4EJJPD","canonical_record":{"source":{"id":"1709.04201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T09:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"bfe6166738de16ebedee1709bee3a56f1d0b1ec7c62e5cd0beea9b41af263edc","abstract_canon_sha256":"f71f812ff379bf67f010a8d574b2dd043c4d2d9e8b3bda15c63da011d68f981b"},"schema_version":"1.0"},"canonical_sha256":"be7844a5e32eb8fea301051ca0f6436a01d7529d8b38362df9000350e2a9122d","source":{"kind":"arxiv","id":"1709.04201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04201","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04201v1","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04201","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"XZ4EJJPDF24P","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XZ4EJJPDF24P5IYB","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XZ4EJJPD","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XZ4EJJPDF24P5IYBAUOKB5SDNI","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T09:09:58Z","cross_cats_sorted":[],"title_canon_sha256":"bfe6166738de16ebedee1709bee3a56f1d0b1ec7c62e5cd0beea9b41af263edc","abstract_canon_sha256":"f71f812ff379bf67f010a8d574b2dd043c4d2d9e8b3bda15c63da011d68f981b"},"schema_version":"1.0"},"canonical_sha256":"be7844a5e32eb8fea301051ca0f6436a01d7529d8b38362df9000350e2a9122d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:15.107573Z","signature_b64":"yDZVnL+wXdURsTBCEfvCXn/iCvMuqQXgxKxpwnaHn/HP5WJ5dsp6spOOY8CvoV8fnk7FdDMaq0BeuS0597/IAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be7844a5e32eb8fea301051ca0f6436a01d7529d8b38362df9000350e2a9122d","last_reissued_at":"2026-05-18T00:35:15.106932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:15.106932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04201","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":"2026-05-18T00:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o/5y3+EYj/gk2qvqxEIwvxRXLpRYa057zp+Q0ujavhftTGzf/ighYMSFW/iyL9cqE7/BoWr29tNq5Iv/dAjeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:15:17.722071Z"},"content_sha256":"d0bce4c3dcb59b8f0ad7e99eece72b072763e381622e02a1f41f62b43cdb5ce4","schema_version":"1.0","event_id":"sha256:d0bce4c3dcb59b8f0ad7e99eece72b072763e381622e02a1f41f62b43cdb5ce4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XZ4EJJPDF24P5IYBAUOKB5SDNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"L^$\\infty$ estimates for the jko scheme in parabolic-elliptic keller-segel systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Santambrogio (LM-Orsay), Jos\\'e-Antonio Carrillo","submitted_at":"2017-09-13T09:09:58Z","abstract_excerpt":"We prove L^$\\infty$ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial L^$\\infty$ norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04201","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":"2026-05-18T00:35:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qV0AJhk6QMKR2w4Ukb4Rnb8Uuti3/50VOPrTqvMahODTmGZ/eGjEySx8r0hLL70VYbY1tJu7UDsc5a4Eif+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:15:17.722445Z"},"content_sha256":"cdadac3c61c5209a4355ce9e65b636db8e1045206a68ef8fba425020ee805b19","schema_version":"1.0","event_id":"sha256:cdadac3c61c5209a4355ce9e65b636db8e1045206a68ef8fba425020ee805b19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/bundle.json","state_url":"https://pith.science/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/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":"2026-05-30T23:15:17Z","links":{"resolver":"https://pith.science/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI","bundle":"https://pith.science/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/bundle.json","state":"https://pith.science/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZ4EJJPDF24P5IYBAUOKB5SDNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XZ4EJJPDF24P5IYBAUOKB5SDNI","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":"f71f812ff379bf67f010a8d574b2dd043c4d2d9e8b3bda15c63da011d68f981b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T09:09:58Z","title_canon_sha256":"bfe6166738de16ebedee1709bee3a56f1d0b1ec7c62e5cd0beea9b41af263edc"},"schema_version":"1.0","source":{"id":"1709.04201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04201","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04201v1","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04201","created_at":"2026-05-18T00:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"XZ4EJJPDF24P","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XZ4EJJPDF24P5IYB","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XZ4EJJPD","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:cdadac3c61c5209a4355ce9e65b636db8e1045206a68ef8fba425020ee805b19","target":"graph","created_at":"2026-05-18T00:35:15Z","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 prove L^$\\infty$ estimates on the densities that are obtained via the JKO scheme for a general form of a parabolic-elliptic Keller-Segel type system, with arbitrary diffusion, arbitrary mass, and in arbitrary dimension. Of course, such an estimate blows up in finite time, a time proportional to the inverse of the initial L^$\\infty$ norm. This estimate can be used to prove short-time well-posedness for a number of equations of this form regardless of the mass of the initial data. The time of existence of the constructed solutions coincides with the maximal time of existence of Lagrangian sol","authors_text":"Filippo Santambrogio (LM-Orsay), Jos\\'e-Antonio Carrillo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T09:09:58Z","title":"L^$\\infty$ estimates for the jko scheme in parabolic-elliptic keller-segel systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04201","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:d0bce4c3dcb59b8f0ad7e99eece72b072763e381622e02a1f41f62b43cdb5ce4","target":"record","created_at":"2026-05-18T00:35:15Z","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":"f71f812ff379bf67f010a8d574b2dd043c4d2d9e8b3bda15c63da011d68f981b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-13T09:09:58Z","title_canon_sha256":"bfe6166738de16ebedee1709bee3a56f1d0b1ec7c62e5cd0beea9b41af263edc"},"schema_version":"1.0","source":{"id":"1709.04201","kind":"arxiv","version":1}},"canonical_sha256":"be7844a5e32eb8fea301051ca0f6436a01d7529d8b38362df9000350e2a9122d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be7844a5e32eb8fea301051ca0f6436a01d7529d8b38362df9000350e2a9122d","first_computed_at":"2026-05-18T00:35:15.106932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:15.106932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yDZVnL+wXdURsTBCEfvCXn/iCvMuqQXgxKxpwnaHn/HP5WJ5dsp6spOOY8CvoV8fnk7FdDMaq0BeuS0597/IAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:15.107573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0bce4c3dcb59b8f0ad7e99eece72b072763e381622e02a1f41f62b43cdb5ce4","sha256:cdadac3c61c5209a4355ce9e65b636db8e1045206a68ef8fba425020ee805b19"],"state_sha256":"e93cb9ddb40c5727dc20ed794a069bbe103fae8e716fe37ea80d14b2c0280512"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OFPlFHsK2FWQqZ2wjfx3/xD1TGeR9g7c30Np370HQ4sLS4TG3Vp9OlVDRK7uKzMsSBVYKmtiqLEdkn2qtPNgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:15:17.724693Z","bundle_sha256":"d4f15314ec1ee9628e5437b163efe5874bd48a853e924771b270235f7e6b20cf"}}