{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6DUVXIWNXIL2JULPM7LZ4F5VLD","short_pith_number":"pith:6DUVXIWN","canonical_record":{"source":{"id":"1810.10378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-23T06:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"7080ce169c5452561698cd62472783bdfd0e7644eb8946894088cbe020f5c5f4","abstract_canon_sha256":"2c71cdec0786c892dfed42fdcb758a54f0716c3bebcfaac729c3de7d0dc3c8f5"},"schema_version":"1.0"},"canonical_sha256":"f0e95ba2cdba17a4d16f67d79e17b558cd06faf272a81dd37a763feeffbb1c6b","source":{"kind":"arxiv","id":"1810.10378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10378","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10378v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10378","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"6DUVXIWNXIL2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6DUVXIWNXIL2JULP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6DUVXIWN","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6DUVXIWNXIL2JULPM7LZ4F5VLD","target":"record","payload":{"canonical_record":{"source":{"id":"1810.10378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-23T06:26:28Z","cross_cats_sorted":[],"title_canon_sha256":"7080ce169c5452561698cd62472783bdfd0e7644eb8946894088cbe020f5c5f4","abstract_canon_sha256":"2c71cdec0786c892dfed42fdcb758a54f0716c3bebcfaac729c3de7d0dc3c8f5"},"schema_version":"1.0"},"canonical_sha256":"f0e95ba2cdba17a4d16f67d79e17b558cd06faf272a81dd37a763feeffbb1c6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:23.333259Z","signature_b64":"HMspYtzyX2PbHdwDjcTL/fcpqmaeFsuo3XL/Tmth92KQ/RDB33Fkbxpa55HkEkB00YOvu0LI7HyDM/22u/5HDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0e95ba2cdba17a4d16f67d79e17b558cd06faf272a81dd37a763feeffbb1c6b","last_reissued_at":"2026-05-18T00:02:23.332614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:23.332614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.10378","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lx375Sb4/ZvThx763y5z9/AENLYRWi8/QZc+ObU1811G9gCTbPWpx1egp+hqNKjmtNYXHw1TpLmvwsQFzbQzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:12:07.640450Z"},"content_sha256":"a0864e805a0530a18c7d75832d8e565643a9523263d61a671a05e66eb2218f65","schema_version":"1.0","event_id":"sha256:a0864e805a0530a18c7d75832d8e565643a9523263d61a671a05e66eb2218f65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6DUVXIWNXIL2JULPM7LZ4F5VLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On parabolic equations with critical electromagnetic potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ana Primo, Veronica Felli","submitted_at":"2018-10-23T06:26:28Z","abstract_excerpt":"We consider a class of parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique continuation results, and an integral representation formula for solutions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10378","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":"2026-05-18T00:02:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPl3E0ZPQ0XiTEeWq9S3SkemQC431Twd9Dg++wFpFoIlha1hIdKAqXubSoZKXzGTW7OQHcnEM2y8DgQ/CGb2CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:12:07.641127Z"},"content_sha256":"f37b9f75f395787302eeb82b4b86cfe35d93cacc250757f050ea1b12334b7841","schema_version":"1.0","event_id":"sha256:f37b9f75f395787302eeb82b4b86cfe35d93cacc250757f050ea1b12334b7841"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/bundle.json","state_url":"https://pith.science/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/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":"2026-05-27T10:12:07Z","links":{"resolver":"https://pith.science/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD","bundle":"https://pith.science/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/bundle.json","state":"https://pith.science/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DUVXIWNXIL2JULPM7LZ4F5VLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6DUVXIWNXIL2JULPM7LZ4F5VLD","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":"2c71cdec0786c892dfed42fdcb758a54f0716c3bebcfaac729c3de7d0dc3c8f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-23T06:26:28Z","title_canon_sha256":"7080ce169c5452561698cd62472783bdfd0e7644eb8946894088cbe020f5c5f4"},"schema_version":"1.0","source":{"id":"1810.10378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.10378","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"arxiv_version","alias_value":"1810.10378v1","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.10378","created_at":"2026-05-18T00:02:23Z"},{"alias_kind":"pith_short_12","alias_value":"6DUVXIWNXIL2","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6DUVXIWNXIL2JULP","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6DUVXIWN","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:f37b9f75f395787302eeb82b4b86cfe35d93cacc250757f050ea1b12334b7841","target":"graph","created_at":"2026-05-18T00:02:23Z","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 parabolic equations with critical electromagnetic potentials, for which we obtain a classification of local asymptotics, unique continuation results, and an integral representation formula for solutions.","authors_text":"Ana Primo, Veronica Felli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-23T06:26:28Z","title":"On parabolic equations with critical electromagnetic potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.10378","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:a0864e805a0530a18c7d75832d8e565643a9523263d61a671a05e66eb2218f65","target":"record","created_at":"2026-05-18T00:02:23Z","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":"2c71cdec0786c892dfed42fdcb758a54f0716c3bebcfaac729c3de7d0dc3c8f5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-23T06:26:28Z","title_canon_sha256":"7080ce169c5452561698cd62472783bdfd0e7644eb8946894088cbe020f5c5f4"},"schema_version":"1.0","source":{"id":"1810.10378","kind":"arxiv","version":1}},"canonical_sha256":"f0e95ba2cdba17a4d16f67d79e17b558cd06faf272a81dd37a763feeffbb1c6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0e95ba2cdba17a4d16f67d79e17b558cd06faf272a81dd37a763feeffbb1c6b","first_computed_at":"2026-05-18T00:02:23.332614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:23.332614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HMspYtzyX2PbHdwDjcTL/fcpqmaeFsuo3XL/Tmth92KQ/RDB33Fkbxpa55HkEkB00YOvu0LI7HyDM/22u/5HDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:23.333259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.10378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0864e805a0530a18c7d75832d8e565643a9523263d61a671a05e66eb2218f65","sha256:f37b9f75f395787302eeb82b4b86cfe35d93cacc250757f050ea1b12334b7841"],"state_sha256":"94abcc8ed2d1e2906a7ca8479f5e9c61f92921d105d58bb95f2cd0ff069244cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5nTXCxdhjs6Zt3fz+yC6Lqh6O4pHvf+W3VNoK1HqiM4LNOO+aqB4y4N+OljjGGRpKqFLU1glWxYwFwLklfloAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:12:07.644660Z","bundle_sha256":"e66ae183ddb69871bf8e63e727d2e4d2da6bb5d647bdbea359e7b2177fc74d6e"}}