{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:V5FVNOV4UZFC36IBS6LVM6LCCI","short_pith_number":"pith:V5FVNOV4","canonical_record":{"source":{"id":"1512.04980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-15T21:46:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"a9675f0173e42c7afa7c471fc09f7119e057b0f8b948b6107f860b822202579e","abstract_canon_sha256":"67053b4ebd8fc5c12ee96bccc73102eb6c55299e0384e033fcc26eb3d6e5e32e"},"schema_version":"1.0"},"canonical_sha256":"af4b56babca64a2df9019797567962121fcfece3ae55ce55dae79bdd2a3c7a3d","source":{"kind":"arxiv","id":"1512.04980","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04980","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04980v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04980","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"V5FVNOV4UZFC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V5FVNOV4UZFC36IB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V5FVNOV4","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:V5FVNOV4UZFC36IBS6LVM6LCCI","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04980","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-15T21:46:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"a9675f0173e42c7afa7c471fc09f7119e057b0f8b948b6107f860b822202579e","abstract_canon_sha256":"67053b4ebd8fc5c12ee96bccc73102eb6c55299e0384e033fcc26eb3d6e5e32e"},"schema_version":"1.0"},"canonical_sha256":"af4b56babca64a2df9019797567962121fcfece3ae55ce55dae79bdd2a3c7a3d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:13.831989Z","signature_b64":"ZOSHbi6Vvlaz0P12hpnE2i1Qok0J6yIZbd8o8yQOIeMrRds31EEb7+bO26DJqA4fwPlANEjrbDh+f91PTKM4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af4b56babca64a2df9019797567962121fcfece3ae55ce55dae79bdd2a3c7a3d","last_reissued_at":"2026-05-18T01:24:13.831483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:13.831483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04980","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":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2rsmTdwIC5Gy5ol5Kg25LzvWaJavL6KE0UkWhwlXfb8CzJdy84jup7/PYmpBIf6p4d1kwdusS+Hx3Wd877yOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:06:27.861015Z"},"content_sha256":"16ae9795d8577bf91cff59436d3767c9af49f59b8752503f3190fedbc4ed6987","schema_version":"1.0","event_id":"sha256:16ae9795d8577bf91cff59436d3767c9af49f59b8752503f3190fedbc4ed6987"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:V5FVNOV4UZFC36IBS6LVM6LCCI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Hao Yin, Peter M. Topping","submitted_at":"2015-12-15T21:46:14Z","abstract_excerpt":"We prove the sharp local L^1 - L^\\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\\infty estimate for p larger than 1. It also has several applications in geometry, providing the missing step in order to pose the Ricci flow with rough initial data in the noncompact case, for example starting with a general noncompact Alexandrov surface, and giving the sharp asymptotics for the contracting cusp Ricci flow, as we show elsewhere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04980","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":"2026-05-18T01:24:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s2Bwhz0wLO5n7TYVlnwp2gIKaQteeNB/XIR0a/CwSiEeS25tdxYCH+e+Fisb2HWQB4Qxkdl/u6h6xM+LOF5HCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:06:27.861371Z"},"content_sha256":"f03aaf9e0c56628003c1c21f003bbc08b13e66a0d8aa0b6d4c992a156324e768","schema_version":"1.0","event_id":"sha256:f03aaf9e0c56628003c1c21f003bbc08b13e66a0d8aa0b6d4c992a156324e768"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/bundle.json","state_url":"https://pith.science/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/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":"2026-06-26T13:06:27Z","links":{"resolver":"https://pith.science/pith/V5FVNOV4UZFC36IBS6LVM6LCCI","bundle":"https://pith.science/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/bundle.json","state":"https://pith.science/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5FVNOV4UZFC36IBS6LVM6LCCI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:V5FVNOV4UZFC36IBS6LVM6LCCI","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":"67053b4ebd8fc5c12ee96bccc73102eb6c55299e0384e033fcc26eb3d6e5e32e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-15T21:46:14Z","title_canon_sha256":"a9675f0173e42c7afa7c471fc09f7119e057b0f8b948b6107f860b822202579e"},"schema_version":"1.0","source":{"id":"1512.04980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04980","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04980v1","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04980","created_at":"2026-05-18T01:24:13Z"},{"alias_kind":"pith_short_12","alias_value":"V5FVNOV4UZFC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"V5FVNOV4UZFC36IB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"V5FVNOV4","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:f03aaf9e0c56628003c1c21f003bbc08b13e66a0d8aa0b6d4c992a156324e768","target":"graph","created_at":"2026-05-18T01:24:13Z","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 the sharp local L^1 - L^\\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\\infty estimate for p larger than 1. It also has several applications in geometry, providing the missing step in order to pose the Ricci flow with rough initial data in the noncompact case, for example starting with a general noncompact Alexandrov surface, and giving the sharp asymptotics for the contracting cusp Ricci flow, as we show elsewhere.","authors_text":"Hao Yin, Peter M. Topping","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-15T21:46:14Z","title":"Sharp decay estimates for the logarithmic fast diffusion equation and the Ricci flow on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04980","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":"sha256:16ae9795d8577bf91cff59436d3767c9af49f59b8752503f3190fedbc4ed6987","target":"record","created_at":"2026-05-18T01:24:13Z","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":"67053b4ebd8fc5c12ee96bccc73102eb6c55299e0384e033fcc26eb3d6e5e32e","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-15T21:46:14Z","title_canon_sha256":"a9675f0173e42c7afa7c471fc09f7119e057b0f8b948b6107f860b822202579e"},"schema_version":"1.0","source":{"id":"1512.04980","kind":"arxiv","version":1}},"canonical_sha256":"af4b56babca64a2df9019797567962121fcfece3ae55ce55dae79bdd2a3c7a3d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af4b56babca64a2df9019797567962121fcfece3ae55ce55dae79bdd2a3c7a3d","first_computed_at":"2026-05-18T01:24:13.831483Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:13.831483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOSHbi6Vvlaz0P12hpnE2i1Qok0J6yIZbd8o8yQOIeMrRds31EEb7+bO26DJqA4fwPlANEjrbDh+f91PTKM4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:13.831989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16ae9795d8577bf91cff59436d3767c9af49f59b8752503f3190fedbc4ed6987","sha256:f03aaf9e0c56628003c1c21f003bbc08b13e66a0d8aa0b6d4c992a156324e768"],"state_sha256":"715b952a9228586fd975d5f13205b9b625d971dab822ecd2bbf80e8e4c0fc1d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KbxrBchlPFikFTIMpetYXwsPW8xHWry6skWdhwtR3PjHlqS5W3FXWyNjFKUguoPKlnhwMxmy+D4kETUHMSzSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:06:27.863305Z","bundle_sha256":"3a17fd1d3d90be0522e0ab5038c2fbe3d98ad605209ce7e5a0de82edb64133bb"}}