{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7VOPM4XSQAZNHGGOF7DJUAYKAN","short_pith_number":"pith:7VOPM4XS","canonical_record":{"source":{"id":"1005.1994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-12T06:47:51Z","cross_cats_sorted":[],"title_canon_sha256":"003679ec0487cf4c8c1f827db5be8f4600f29c61189aafa2651c418505032d06","abstract_canon_sha256":"f3c858e6a08736db6a6f14f7bb99a2b816785327cea9e2d5b9fff21963d063d3"},"schema_version":"1.0"},"canonical_sha256":"fd5cf672f28032d398ce2fc69a030a03455c3c29f1658abec2a2256c14050fec","source":{"kind":"arxiv","id":"1005.1994","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1994","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1994v2","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1994","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"7VOPM4XSQAZN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7VOPM4XSQAZNHGGO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7VOPM4XS","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7VOPM4XSQAZNHGGOF7DJUAYKAN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1994","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-12T06:47:51Z","cross_cats_sorted":[],"title_canon_sha256":"003679ec0487cf4c8c1f827db5be8f4600f29c61189aafa2651c418505032d06","abstract_canon_sha256":"f3c858e6a08736db6a6f14f7bb99a2b816785327cea9e2d5b9fff21963d063d3"},"schema_version":"1.0"},"canonical_sha256":"fd5cf672f28032d398ce2fc69a030a03455c3c29f1658abec2a2256c14050fec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:08.179862Z","signature_b64":"zJER5VAVZ61+FuZqxCiB/e3x1jbL05FypVm5NzSq3qaRadqGVju3qOJ7rAACp+M9riT06KMfv0DTNbrQscL2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd5cf672f28032d398ce2fc69a030a03455c3c29f1658abec2a2256c14050fec","last_reissued_at":"2026-05-18T04:06:08.179244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:08.179244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1994","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6Px7wL6EW02bAIICyyiDf/LZgOMEcfzjD/+aCmUhnsRCXKXAajbeWGtQBgZpuXWG0j8EHFiaUYO1euFIGiDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:44:40.775308Z"},"content_sha256":"b2c893eebf88658c4da8b412fb3f3704c1c74a95c6fe5fc79bd1435b7e3e99f9","schema_version":"1.0","event_id":"sha256:b2c893eebf88658c4da8b412fb3f3704c1c74a95c6fe5fc79bd1435b7e3e99f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7VOPM4XSQAZNHGGOF7DJUAYKAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast diffusion equations: matching large time asymptotics by relative entropy methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Giuseppe Toscani, Jean Dolbeault (CEREMADE)","submitted_at":"2010-05-12T06:47:51Z","abstract_excerpt":"A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite second moment. The method is based on relative entropy estimates and a time-dependent change of variables which is determined by second moments, and not by the scaling corresponding to the self-similar Barenblatt solutions, as it is usually done."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1994","kind":"arxiv","version":2},"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":"2026-05-18T04:06:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGfSyGoNr7uOi89YM/OF2A+7m4So7aJZtXmTjjUFExFX61RF/H04iqipd9sP512vcdLLgw2Ri8CDQOSEqfy/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:44:40.776049Z"},"content_sha256":"b268fdef411dea34a44e65a9f908310482f64f81032a2d8d9a196a72c6e687a3","schema_version":"1.0","event_id":"sha256:b268fdef411dea34a44e65a9f908310482f64f81032a2d8d9a196a72c6e687a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/bundle.json","state_url":"https://pith.science/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/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":"2026-05-28T17:44:40Z","links":{"resolver":"https://pith.science/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN","bundle":"https://pith.science/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/bundle.json","state":"https://pith.science/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VOPM4XSQAZNHGGOF7DJUAYKAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7VOPM4XSQAZNHGGOF7DJUAYKAN","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":"f3c858e6a08736db6a6f14f7bb99a2b816785327cea9e2d5b9fff21963d063d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-12T06:47:51Z","title_canon_sha256":"003679ec0487cf4c8c1f827db5be8f4600f29c61189aafa2651c418505032d06"},"schema_version":"1.0","source":{"id":"1005.1994","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1994","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1994v2","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1994","created_at":"2026-05-18T04:06:08Z"},{"alias_kind":"pith_short_12","alias_value":"7VOPM4XSQAZN","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"7VOPM4XSQAZNHGGO","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"7VOPM4XS","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:b268fdef411dea34a44e65a9f908310482f64f81032a2d8d9a196a72c6e687a3","target":"graph","created_at":"2026-05-18T04:06:08Z","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":"A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite second moment. The method is based on relative entropy estimates and a time-dependent change of variables which is determined by second moments, and not by the scaling corresponding to the self-similar Barenblatt solutions, as it is usually done.","authors_text":"Giuseppe Toscani, Jean Dolbeault (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-12T06:47:51Z","title":"Fast diffusion equations: matching large time asymptotics by relative entropy methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1994","kind":"arxiv","version":2},"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:b2c893eebf88658c4da8b412fb3f3704c1c74a95c6fe5fc79bd1435b7e3e99f9","target":"record","created_at":"2026-05-18T04:06:08Z","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":"f3c858e6a08736db6a6f14f7bb99a2b816785327cea9e2d5b9fff21963d063d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-12T06:47:51Z","title_canon_sha256":"003679ec0487cf4c8c1f827db5be8f4600f29c61189aafa2651c418505032d06"},"schema_version":"1.0","source":{"id":"1005.1994","kind":"arxiv","version":2}},"canonical_sha256":"fd5cf672f28032d398ce2fc69a030a03455c3c29f1658abec2a2256c14050fec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5cf672f28032d398ce2fc69a030a03455c3c29f1658abec2a2256c14050fec","first_computed_at":"2026-05-18T04:06:08.179244Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:08.179244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zJER5VAVZ61+FuZqxCiB/e3x1jbL05FypVm5NzSq3qaRadqGVju3qOJ7rAACp+M9riT06KMfv0DTNbrQscL2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:08.179862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1994","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2c893eebf88658c4da8b412fb3f3704c1c74a95c6fe5fc79bd1435b7e3e99f9","sha256:b268fdef411dea34a44e65a9f908310482f64f81032a2d8d9a196a72c6e687a3"],"state_sha256":"a89d02d766e207102767765e4e128602634d42630a7550df9e772da07d95fb22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y18BSG8nTLrJaKDdTe+Gi5wb4pyckhZPMXC+9brhT4jqV00bd9PgEIIWszZDG+xRrscEjaC/BGaJc+tCnqrMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:44:40.779938Z","bundle_sha256":"9c16da0d2830bf23ac9e42a6e26c13d8ee5fa056f4e3386d8089d0f471b6d0ff"}}