{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LFD7IOCHY5PKGMXL3BAI55MNOW","short_pith_number":"pith:LFD7IOCH","canonical_record":{"source":{"id":"1812.10246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T06:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"2029e9d3c0d2b5576c7a8e60ad6787660dc7233ea7354e66a4d044452b9fb820","abstract_canon_sha256":"ed8cec4b6a888e2936b0da9b2af0a3746deab3503b65a00113daba88a1fa8064"},"schema_version":"1.0"},"canonical_sha256":"5947f43847c75ea332ebd8408ef58d758f66685e7e30eddd5acbafe3f0474cb9","source":{"kind":"arxiv","id":"1812.10246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10246","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10246v1","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10246","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"LFD7IOCHY5PK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LFD7IOCHY5PKGMXL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LFD7IOCH","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LFD7IOCHY5PKGMXL3BAI55MNOW","target":"record","payload":{"canonical_record":{"source":{"id":"1812.10246","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T06:57:16Z","cross_cats_sorted":[],"title_canon_sha256":"2029e9d3c0d2b5576c7a8e60ad6787660dc7233ea7354e66a4d044452b9fb820","abstract_canon_sha256":"ed8cec4b6a888e2936b0da9b2af0a3746deab3503b65a00113daba88a1fa8064"},"schema_version":"1.0"},"canonical_sha256":"5947f43847c75ea332ebd8408ef58d758f66685e7e30eddd5acbafe3f0474cb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:24.678691Z","signature_b64":"iZzrGMM/U6L7hV0Oh7o2gZcRqas8EAt4iusrsBsiTxX3zKOFlzZpa8UusqGpDFYkITlW9Q1jQGoZlNQUX1cjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5947f43847c75ea332ebd8408ef58d758f66685e7e30eddd5acbafe3f0474cb9","last_reissued_at":"2026-05-17T23:57:24.678153Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:24.678153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.10246","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":"2026-05-17T23:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ej8DNFdlbVSYgQ83Hk1EdgGPacbitEqX5F+A99IiTVSWe5Tsgh2sKZsZ4FJS1MCWYjhgVL3TT+P8JwCbLUZcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:57.598060Z"},"content_sha256":"2e7673945520f4e6f1a9b4fdc6dbeed2347474d2c739e7a6621fc7919d27368e","schema_version":"1.0","event_id":"sha256:2e7673945520f4e6f1a9b4fdc6dbeed2347474d2c739e7a6621fc7919d27368e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LFD7IOCHY5PKGMXL3BAI55MNOW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Space like strong unique continuation for sublinear parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnid Banerjee, Ramesh Manna","submitted_at":"2018-12-26T06:57:16Z","abstract_excerpt":"In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established by Ruland in [Ru] for analogous elliptic sublinear equations. Similar to that in [Ru], this is accomplished via a new $L^{2}-L^{2}$ type Carleman estimate for a class of sublinear parabolic operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10246","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":"2026-05-17T23:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNPM/hAysExzP/ZXIGSwCND89C6mO4k9k+NmS7qVaUEzS9csdZcQf5QAo9e4swi3OIsn2+zn+za+1Eqym8dQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:54:57.598418Z"},"content_sha256":"83ba699fcd355f09aa1a84dc30547ef70b02c690ee014978a483d7bb273c2367","schema_version":"1.0","event_id":"sha256:83ba699fcd355f09aa1a84dc30547ef70b02c690ee014978a483d7bb273c2367"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/bundle.json","state_url":"https://pith.science/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/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":"2026-06-27T02:54:57Z","links":{"resolver":"https://pith.science/pith/LFD7IOCHY5PKGMXL3BAI55MNOW","bundle":"https://pith.science/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/bundle.json","state":"https://pith.science/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFD7IOCHY5PKGMXL3BAI55MNOW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LFD7IOCHY5PKGMXL3BAI55MNOW","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":"ed8cec4b6a888e2936b0da9b2af0a3746deab3503b65a00113daba88a1fa8064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T06:57:16Z","title_canon_sha256":"2029e9d3c0d2b5576c7a8e60ad6787660dc7233ea7354e66a4d044452b9fb820"},"schema_version":"1.0","source":{"id":"1812.10246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.10246","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1812.10246v1","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10246","created_at":"2026-05-17T23:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"LFD7IOCHY5PK","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LFD7IOCHY5PKGMXL","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LFD7IOCH","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:83ba699fcd355f09aa1a84dc30547ef70b02c690ee014978a483d7bb273c2367","target":"graph","created_at":"2026-05-17T23:57:24Z","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":"In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established by Ruland in [Ru] for analogous elliptic sublinear equations. Similar to that in [Ru], this is accomplished via a new $L^{2}-L^{2}$ type Carleman estimate for a class of sublinear parabolic operators.","authors_text":"Agnid Banerjee, Ramesh Manna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T06:57:16Z","title":"Space like strong unique continuation for sublinear parabolic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10246","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":"sha256:2e7673945520f4e6f1a9b4fdc6dbeed2347474d2c739e7a6621fc7919d27368e","target":"record","created_at":"2026-05-17T23:57:24Z","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":"ed8cec4b6a888e2936b0da9b2af0a3746deab3503b65a00113daba88a1fa8064","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-12-26T06:57:16Z","title_canon_sha256":"2029e9d3c0d2b5576c7a8e60ad6787660dc7233ea7354e66a4d044452b9fb820"},"schema_version":"1.0","source":{"id":"1812.10246","kind":"arxiv","version":1}},"canonical_sha256":"5947f43847c75ea332ebd8408ef58d758f66685e7e30eddd5acbafe3f0474cb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5947f43847c75ea332ebd8408ef58d758f66685e7e30eddd5acbafe3f0474cb9","first_computed_at":"2026-05-17T23:57:24.678153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:24.678153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZzrGMM/U6L7hV0Oh7o2gZcRqas8EAt4iusrsBsiTxX3zKOFlzZpa8UusqGpDFYkITlW9Q1jQGoZlNQUX1cjCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:24.678691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.10246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e7673945520f4e6f1a9b4fdc6dbeed2347474d2c739e7a6621fc7919d27368e","sha256:83ba699fcd355f09aa1a84dc30547ef70b02c690ee014978a483d7bb273c2367"],"state_sha256":"8b608f6a6d618e08487cea68c20d1ec6933a7d8750236e935dace40ade9696bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkP4C+Fc63Fg+nIGopKRjhAf75vsRGtbHz+UvIqZvuFiySVvMz3gPcIKA1qyA3AJXIpMYvxlk2WQxyFy3YrbBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:54:57.600475Z","bundle_sha256":"662377561cc63d9f442a7a7bc4305c567412e4cdf0c51e0fded35e5ae844f969"}}