{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LKB5AOHFI4VDMITZYUABWRTX2N","short_pith_number":"pith:LKB5AOHF","canonical_record":{"source":{"id":"1207.1293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"a9c072f259553e7c85e7e13d9631355256a88024fd73fec6ebb5e4bad042b48a","abstract_canon_sha256":"79480f54e57f860d9003d9f6d8cefe9bae59d0f131ffe80835bc59b4b892cc3b"},"schema_version":"1.0"},"canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","source":{"kind":"arxiv","id":"1207.1293","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1293","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1293v1","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1293","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"LKB5AOHFI4VD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKB5AOHFI4VDMITZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKB5AOHF","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LKB5AOHFI4VDMITZYUABWRTX2N","target":"record","payload":{"canonical_record":{"source":{"id":"1207.1293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"a9c072f259553e7c85e7e13d9631355256a88024fd73fec6ebb5e4bad042b48a","abstract_canon_sha256":"79480f54e57f860d9003d9f6d8cefe9bae59d0f131ffe80835bc59b4b892cc3b"},"schema_version":"1.0"},"canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:51:46.409287Z","signature_b64":"sDxEh72vTZTswyfq2lAm5bYC2h8ecDvnZ0wrRxLLqkZLLp+piPQOnnBDBel00AH/oro6dm0xEqI4jmpzRezyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","last_reissued_at":"2026-05-18T03:51:46.408446Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:51:46.408446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.1293","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":"2026-05-18T03:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tcd0XKx4q8ngkKoVErHvXnu1TMvcIk9Bd4JRHQKeKIEXr+TwvQ55ZhPNBHXhC7On78Kdghb8zwS4czaJbu4ADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:32:55.377849Z"},"content_sha256":"210903a5fd8bf531e50b88fb6df5ff17c73d99027c40e809dd6e897d2186d184","schema_version":"1.0","event_id":"sha256:210903a5fd8bf531e50b88fb6df5ff17c73d99027c40e809dd6e897d2186d184"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LKB5AOHFI4VDMITZYUABWRTX2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On improvement of summability properties in nonautonomous Kolmogorov equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2012-07-05T16:00:06Z","abstract_excerpt":"Under suitable conditions, we obtain some characterization of supercontractivity, ultraboundedness and ultracontractivity of the evolution operator $G(t,s)$ associated to a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\\times\\R^d$, where $I$ is a right-halfline. For this purpose, we establish an Harnack type estimate for $G(t,s)$ and a family of logarithmic Sobolev inequalities with respect to the unique tight evolution system of measures $\\{\\mu_t: t \\in I\\}$ associated to $G(t,s)$. Sufficient conditions for the supercontractivity, ultrabounde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1293","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":"2026-05-18T03:51:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZ2FzDzg8whtN9Qx7DU61qszecy45psmDTdtW0iJMmwonL8gcP15VXEAu7Uptp/4wbqATuePjk5ogUBEHsH3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:32:55.378205Z"},"content_sha256":"dbb049b44434d8c0cea0477e4e1e74c822e7a93a5510e8fe523204372ea94457","schema_version":"1.0","event_id":"sha256:dbb049b44434d8c0cea0477e4e1e74c822e7a93a5510e8fe523204372ea94457"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/bundle.json","state_url":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LKB5AOHFI4VDMITZYUABWRTX2N/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":"2026-06-25T19:32:55Z","links":{"resolver":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N","bundle":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/bundle.json","state":"https://pith.science/pith/LKB5AOHFI4VDMITZYUABWRTX2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LKB5AOHFI4VDMITZYUABWRTX2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LKB5AOHFI4VDMITZYUABWRTX2N","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":"79480f54e57f860d9003d9f6d8cefe9bae59d0f131ffe80835bc59b4b892cc3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","title_canon_sha256":"a9c072f259553e7c85e7e13d9631355256a88024fd73fec6ebb5e4bad042b48a"},"schema_version":"1.0","source":{"id":"1207.1293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.1293","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"arxiv_version","alias_value":"1207.1293v1","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.1293","created_at":"2026-05-18T03:51:46Z"},{"alias_kind":"pith_short_12","alias_value":"LKB5AOHFI4VD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LKB5AOHFI4VDMITZ","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LKB5AOHF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:dbb049b44434d8c0cea0477e4e1e74c822e7a93a5510e8fe523204372ea94457","target":"graph","created_at":"2026-05-18T03:51:46Z","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":"Under suitable conditions, we obtain some characterization of supercontractivity, ultraboundedness and ultracontractivity of the evolution operator $G(t,s)$ associated to a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $I\\times\\R^d$, where $I$ is a right-halfline. For this purpose, we establish an Harnack type estimate for $G(t,s)$ and a family of logarithmic Sobolev inequalities with respect to the unique tight evolution system of measures $\\{\\mu_t: t \\in I\\}$ associated to $G(t,s)$. Sufficient conditions for the supercontractivity, ultrabounde","authors_text":"Luca Lorenzi, Luciana Angiuli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","title":"On improvement of summability properties in nonautonomous Kolmogorov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1293","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":"sha256:210903a5fd8bf531e50b88fb6df5ff17c73d99027c40e809dd6e897d2186d184","target":"record","created_at":"2026-05-18T03:51:46Z","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":"79480f54e57f860d9003d9f6d8cefe9bae59d0f131ffe80835bc59b4b892cc3b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-05T16:00:06Z","title_canon_sha256":"a9c072f259553e7c85e7e13d9631355256a88024fd73fec6ebb5e4bad042b48a"},"schema_version":"1.0","source":{"id":"1207.1293","kind":"arxiv","version":1}},"canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a83d038e5472a362279c5001b4677d34eb12f088f878dfde1b3c818217e01d2","first_computed_at":"2026-05-18T03:51:46.408446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:51:46.408446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDxEh72vTZTswyfq2lAm5bYC2h8ecDvnZ0wrRxLLqkZLLp+piPQOnnBDBel00AH/oro6dm0xEqI4jmpzRezyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:51:46.409287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.1293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:210903a5fd8bf531e50b88fb6df5ff17c73d99027c40e809dd6e897d2186d184","sha256:dbb049b44434d8c0cea0477e4e1e74c822e7a93a5510e8fe523204372ea94457"],"state_sha256":"b44500a25b107101232f1b14040aca065be6668e884e5b83924cbc02f53171ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veZKaufvXe9j79yhgWa2u32NgBsAqxSsjcUBPyNJVk8cXWAgjFTjrutFEJQX7BQlHcQZo3FrAVYizYH7HwPaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:32:55.380142Z","bundle_sha256":"d1b3735b641f3cc3e3e8ef1aeb4df97f637238519fe8d07ae7066f06b7bd2c26"}}