{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K67EVLN2YJMB6QWORLPZSMSFEG","short_pith_number":"pith:K67EVLN2","canonical_record":{"source":{"id":"1509.04053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-14T12:20:18Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bc512a76e53037aec6ca644d573ef0c49e8d64c0b9619f11050eeb3247e24fc0","abstract_canon_sha256":"d607d3dd115462405b6fe034ee46ccea003b01dfc3d2d1840bb2c30d8c8442ff"},"schema_version":"1.0"},"canonical_sha256":"57be4aadbac2581f42ce8adf993245219f14bb7cb052400e81fd8a02396fbd71","source":{"kind":"arxiv","id":"1509.04053","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04053","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04053v2","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04053","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"K67EVLN2YJMB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K67EVLN2YJMB6QWO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K67EVLN2","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K67EVLN2YJMB6QWORLPZSMSFEG","target":"record","payload":{"canonical_record":{"source":{"id":"1509.04053","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-14T12:20:18Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"bc512a76e53037aec6ca644d573ef0c49e8d64c0b9619f11050eeb3247e24fc0","abstract_canon_sha256":"d607d3dd115462405b6fe034ee46ccea003b01dfc3d2d1840bb2c30d8c8442ff"},"schema_version":"1.0"},"canonical_sha256":"57be4aadbac2581f42ce8adf993245219f14bb7cb052400e81fd8a02396fbd71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:18.764329Z","signature_b64":"76BxJSot9LXf6g3PMmpX2DnOGpu34+sdQMhVTEPgd0gmNR+y3wu2NLdMprxRoq110l5PXLM9M9GBjOADqhzRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57be4aadbac2581f42ce8adf993245219f14bb7cb052400e81fd8a02396fbd71","last_reissued_at":"2026-05-18T00:43:18.763602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:18.763602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.04053","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":"2026-05-18T00:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4m4TKFj13TyXNb2MRWUuAVYs+maaTLj4UaSwXdoNb15PvAbYg0wBpkpJwSbacRlqofcFKMF0xoqns2LB9OyAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:49:59.506211Z"},"content_sha256":"bb228027e15a2354b6ef56dd7e2422a46eb5daaf51a2f59240722cb4d018b582","schema_version":"1.0","event_id":"sha256:bb228027e15a2354b6ef56dd7e2422a46eb5daaf51a2f59240722cb4d018b582"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K67EVLN2YJMB6QWORLPZSMSFEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analyticity of solutions to parabolic evolutions and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Can Zhang, Luis Escauriaza, Santiago Montaner","submitted_at":"2015-09-14T12:20:18Z","abstract_excerpt":"We find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates to obtain observability inequalities and null-controllability of parabolic evolutions over measurable sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04053","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":"2026-05-18T00:43:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tPl97jWyngccN6iuitEcZM44O8UqeDmGmBx9CQmZEmIzPwdMYVpTdD0ppoY6CT5DWsuiQ8F6YsU/ufLafIR7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:49:59.506601Z"},"content_sha256":"86402d9fe2e4af8add492c983d3cccebe16c16d1381a7f3698f1279ee9e2412d","schema_version":"1.0","event_id":"sha256:86402d9fe2e4af8add492c983d3cccebe16c16d1381a7f3698f1279ee9e2412d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K67EVLN2YJMB6QWORLPZSMSFEG/bundle.json","state_url":"https://pith.science/pith/K67EVLN2YJMB6QWORLPZSMSFEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K67EVLN2YJMB6QWORLPZSMSFEG/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":"2026-06-23T13:49:59Z","links":{"resolver":"https://pith.science/pith/K67EVLN2YJMB6QWORLPZSMSFEG","bundle":"https://pith.science/pith/K67EVLN2YJMB6QWORLPZSMSFEG/bundle.json","state":"https://pith.science/pith/K67EVLN2YJMB6QWORLPZSMSFEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K67EVLN2YJMB6QWORLPZSMSFEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K67EVLN2YJMB6QWORLPZSMSFEG","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":"d607d3dd115462405b6fe034ee46ccea003b01dfc3d2d1840bb2c30d8c8442ff","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-14T12:20:18Z","title_canon_sha256":"bc512a76e53037aec6ca644d573ef0c49e8d64c0b9619f11050eeb3247e24fc0"},"schema_version":"1.0","source":{"id":"1509.04053","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.04053","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1509.04053v2","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.04053","created_at":"2026-05-18T00:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"K67EVLN2YJMB","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K67EVLN2YJMB6QWO","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K67EVLN2","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:86402d9fe2e4af8add492c983d3cccebe16c16d1381a7f3698f1279ee9e2412d","target":"graph","created_at":"2026-05-18T00:43:18Z","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 find new quantitative estimates on the space-time analyticity of solutions to linear parabolic equations with analytic coefficients near the initial time. We apply the estimates to obtain observability inequalities and null-controllability of parabolic evolutions over measurable sets.","authors_text":"Can Zhang, Luis Escauriaza, Santiago Montaner","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-14T12:20:18Z","title":"Analyticity of solutions to parabolic evolutions and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04053","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:bb228027e15a2354b6ef56dd7e2422a46eb5daaf51a2f59240722cb4d018b582","target":"record","created_at":"2026-05-18T00:43:18Z","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":"d607d3dd115462405b6fe034ee46ccea003b01dfc3d2d1840bb2c30d8c8442ff","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-14T12:20:18Z","title_canon_sha256":"bc512a76e53037aec6ca644d573ef0c49e8d64c0b9619f11050eeb3247e24fc0"},"schema_version":"1.0","source":{"id":"1509.04053","kind":"arxiv","version":2}},"canonical_sha256":"57be4aadbac2581f42ce8adf993245219f14bb7cb052400e81fd8a02396fbd71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57be4aadbac2581f42ce8adf993245219f14bb7cb052400e81fd8a02396fbd71","first_computed_at":"2026-05-18T00:43:18.763602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:18.763602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"76BxJSot9LXf6g3PMmpX2DnOGpu34+sdQMhVTEPgd0gmNR+y3wu2NLdMprxRoq110l5PXLM9M9GBjOADqhzRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:18.764329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.04053","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb228027e15a2354b6ef56dd7e2422a46eb5daaf51a2f59240722cb4d018b582","sha256:86402d9fe2e4af8add492c983d3cccebe16c16d1381a7f3698f1279ee9e2412d"],"state_sha256":"456d5fd1a7e3baf2ce35952d9c26194f8f22a889af01c6bf9be9309f28938513"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sfyrxRnjYQZ3E5NcuDrVUVDvIaAduKXgiCzsZcp+vsLQMz47x2zm+WeG4ydG5uvSKdXzxoG3yp8ZImx1EYOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:49:59.508582Z","bundle_sha256":"da66367de3663dc8071ba3449f26a610dedc8eae42c34d001a7280e4c357c499"}}