{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LHNR34645K7XZBCXGONRPI3Q2J","short_pith_number":"pith:LHNR3464","canonical_record":{"source":{"id":"1712.02963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-08T06:45:45Z","cross_cats_sorted":[],"title_canon_sha256":"8c26e92315a3611abd375a4a7939b8181a48d81ee9d14e91db3ae78b4fcd1063","abstract_canon_sha256":"d8a85d4840ae31ca1498b2c74c5b3802a711276caab97be93da7797fc70198ed"},"schema_version":"1.0"},"canonical_sha256":"59db1df3dceabf7c8457339b17a370d2746d982209d0a09431cec7279c096519","source":{"kind":"arxiv","id":"1712.02963","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02963","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02963v2","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02963","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"LHNR34645K7X","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LHNR34645K7XZBCX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LHNR3464","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LHNR34645K7XZBCXGONRPI3Q2J","target":"record","payload":{"canonical_record":{"source":{"id":"1712.02963","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-08T06:45:45Z","cross_cats_sorted":[],"title_canon_sha256":"8c26e92315a3611abd375a4a7939b8181a48d81ee9d14e91db3ae78b4fcd1063","abstract_canon_sha256":"d8a85d4840ae31ca1498b2c74c5b3802a711276caab97be93da7797fc70198ed"},"schema_version":"1.0"},"canonical_sha256":"59db1df3dceabf7c8457339b17a370d2746d982209d0a09431cec7279c096519","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:50.171165Z","signature_b64":"eucoiwFPYaE3vtA162rT6JsZBpKUYMdN3y/DZcj3yfCZwNUWRk/ZpJSCYsQ14Rv2RsuMMycza50IYKOT+MlNCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59db1df3dceabf7c8457339b17a370d2746d982209d0a09431cec7279c096519","last_reissued_at":"2026-05-18T00:11:50.170630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:50.170630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.02963","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":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mg12EaXb3bhlul5bvl7tZm1XbrH+oRw8n/HGf77Pzbqenw0xaEMLT2XaIxDQA9CRgFio7wqGWuZTYtqx26XAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:58:33.844637Z"},"content_sha256":"d73a82cb1908be23e629691de19b392dcd53e96f73a835d123f682989a6c0e89","schema_version":"1.0","event_id":"sha256:d73a82cb1908be23e629691de19b392dcd53e96f73a835d123f682989a6c0e89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LHNR34645K7XZBCXGONRPI3Q2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the heat kernel of a class of fourth order operators in two dimensions: sharp Gaussian estimates and short time asymptotics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gerassimos Barbatis, Panagiotis Branikas","submitted_at":"2017-12-08T06:45:45Z","abstract_excerpt":"We consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\\infty}$ coefficients we obtain Gaussian estimates with best constants, while for operators with constant coefficients we obtain short time asymptotic estimates. The novelty of this work is that we do not assume that the associated symbol is strongly convex. The short time asymptotics reveal a behavior which is qualitatively different from that of the strongly convex case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02963","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":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGA4LtlTRULOWCEA/f4s3ZQKafFNT+C55ldXZH1KIcTh2qOAIvTANyo9NxqqFU0PkVcJFG8L8WKw3EhbnqLhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:58:33.844982Z"},"content_sha256":"0ab18ccafce448c8d29dbe05e7658e2864fe7cae375405bd0c0c8140e11ff883","schema_version":"1.0","event_id":"sha256:0ab18ccafce448c8d29dbe05e7658e2864fe7cae375405bd0c0c8140e11ff883"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LHNR34645K7XZBCXGONRPI3Q2J/bundle.json","state_url":"https://pith.science/pith/LHNR34645K7XZBCXGONRPI3Q2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LHNR34645K7XZBCXGONRPI3Q2J/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":"2026-06-25T23:58:33Z","links":{"resolver":"https://pith.science/pith/LHNR34645K7XZBCXGONRPI3Q2J","bundle":"https://pith.science/pith/LHNR34645K7XZBCXGONRPI3Q2J/bundle.json","state":"https://pith.science/pith/LHNR34645K7XZBCXGONRPI3Q2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LHNR34645K7XZBCXGONRPI3Q2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LHNR34645K7XZBCXGONRPI3Q2J","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":"d8a85d4840ae31ca1498b2c74c5b3802a711276caab97be93da7797fc70198ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-08T06:45:45Z","title_canon_sha256":"8c26e92315a3611abd375a4a7939b8181a48d81ee9d14e91db3ae78b4fcd1063"},"schema_version":"1.0","source":{"id":"1712.02963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.02963","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1712.02963v2","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.02963","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"LHNR34645K7X","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LHNR34645K7XZBCX","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LHNR3464","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:0ab18ccafce448c8d29dbe05e7658e2864fe7cae375405bd0c0c8140e11ff883","target":"graph","created_at":"2026-05-18T00:11:50Z","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 consider a class of fourth order uniformly elliptic operators in planar Euclidean domains and study the associated heat kernel. For operators with $L^{\\infty}$ coefficients we obtain Gaussian estimates with best constants, while for operators with constant coefficients we obtain short time asymptotic estimates. The novelty of this work is that we do not assume that the associated symbol is strongly convex. The short time asymptotics reveal a behavior which is qualitatively different from that of the strongly convex case.","authors_text":"Gerassimos Barbatis, Panagiotis Branikas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-08T06:45:45Z","title":"On the heat kernel of a class of fourth order operators in two dimensions: sharp Gaussian estimates and short time asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02963","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:d73a82cb1908be23e629691de19b392dcd53e96f73a835d123f682989a6c0e89","target":"record","created_at":"2026-05-18T00:11:50Z","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":"d8a85d4840ae31ca1498b2c74c5b3802a711276caab97be93da7797fc70198ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-08T06:45:45Z","title_canon_sha256":"8c26e92315a3611abd375a4a7939b8181a48d81ee9d14e91db3ae78b4fcd1063"},"schema_version":"1.0","source":{"id":"1712.02963","kind":"arxiv","version":2}},"canonical_sha256":"59db1df3dceabf7c8457339b17a370d2746d982209d0a09431cec7279c096519","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59db1df3dceabf7c8457339b17a370d2746d982209d0a09431cec7279c096519","first_computed_at":"2026-05-18T00:11:50.170630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:50.170630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eucoiwFPYaE3vtA162rT6JsZBpKUYMdN3y/DZcj3yfCZwNUWRk/ZpJSCYsQ14Rv2RsuMMycza50IYKOT+MlNCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:50.171165Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.02963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d73a82cb1908be23e629691de19b392dcd53e96f73a835d123f682989a6c0e89","sha256:0ab18ccafce448c8d29dbe05e7658e2864fe7cae375405bd0c0c8140e11ff883"],"state_sha256":"b332cff06d4147bba1410646aa8bddd0aa37703681f5690b12c9513c15ad16c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+41hwKuGJNS680D7HzF5K9WzDdYvbgNrTMIT+1jqrsXPisc0IoOBPCO6My1rrODvkCYwon0XrXE0lcapamUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:58:33.846953Z","bundle_sha256":"649b98a2f8ba66f5e9b9ddfbdcb17103b581d653cc14d0b3e1b50cfe67d17cba"}}