{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LVOHU2OXTEGGBCGJPRHL4PQHHQ","short_pith_number":"pith:LVOHU2OX","canonical_record":{"source":{"id":"1505.06150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-22T17:08:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1e5bb58363a4cb80b408eafea0318b868cfff9bf8d09ff15c14e2c575613c42e","abstract_canon_sha256":"22629972564b4519bd11398d7b411032fabfb0ad9f918875251809fbe329bed3"},"schema_version":"1.0"},"canonical_sha256":"5d5c7a69d7990c6088c97c4ebe3e073c096ff8e7cf006e19c2b948c3ec145d14","source":{"kind":"arxiv","id":"1505.06150","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06150","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06150v1","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06150","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LVOHU2OXTEGG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LVOHU2OXTEGGBCGJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LVOHU2OX","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LVOHU2OXTEGGBCGJPRHL4PQHHQ","target":"record","payload":{"canonical_record":{"source":{"id":"1505.06150","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-22T17:08:53Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"1e5bb58363a4cb80b408eafea0318b868cfff9bf8d09ff15c14e2c575613c42e","abstract_canon_sha256":"22629972564b4519bd11398d7b411032fabfb0ad9f918875251809fbe329bed3"},"schema_version":"1.0"},"canonical_sha256":"5d5c7a69d7990c6088c97c4ebe3e073c096ff8e7cf006e19c2b948c3ec145d14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:37.647358Z","signature_b64":"mw6cPHE0xfxgrVJAEMqdO3oenEqgLZEDNLUxt/cDE0q//BUPdWux9mTZs7QrMRnmz8LmCualzijHoL05ayiIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d5c7a69d7990c6088c97c4ebe3e073c096ff8e7cf006e19c2b948c3ec145d14","last_reissued_at":"2026-05-17T23:41:37.646667Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:37.646667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.06150","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":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iRMefZINr2iejkcVrE9uwcNtfS7PP9UJ5NLuEXT4xVJ63hn7gTBd+xRvHdOZeLxRh+6PBOY5YGueruCaHoZ6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:41:20.925984Z"},"content_sha256":"eb197b508fdcd37dbddf3cde04dfc7cccbc11a34974ff01258b265debd85e963","schema_version":"1.0","event_id":"sha256:eb197b508fdcd37dbddf3cde04dfc7cccbc11a34974ff01258b265debd85e963"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LVOHU2OXTEGGBCGJPRHL4PQHHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continuity of solutions to space-varying pointwise linear elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Lashi Bandara","submitted_at":"2015-05-22T17:08:53Z","abstract_excerpt":"We consider pointwise linear elliptic equations of the form $\\mathrm{L}_x u_x = \\eta_x$ on a smooth compact manifold where the operators $\\mathrm{L}_x$ are in divergence form with real, bounded, measurable coefficients that vary in the space variable $x$. We establish $\\mathrm{L}^{2}$-continuity of the solutions at $x$ whenever the coefficients of $\\mathrm{L}_x$ are $\\mathrm{L}^{\\infty}$-continuous at $x$ and the initial datum is $\\mathrm{L}^{2}$-continuous at $x$. This is obtained by reducing the continuity of solutions to a homogeneous Kato square root problem. As an application, we consider"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06150","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":"2026-05-17T23:41:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6Xzw3z5/lcAobTawB7Hx2x7i6wpMO2kV3KlE00NlXOB9BOp83pDx6R3/CILVv8PHDYSMDkx4s1EppDX0l9+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:41:20.926348Z"},"content_sha256":"633514d4d0ab9be944bfa3efed9985f9c97a6d6a799f6b0cfa68737eff85c2d6","schema_version":"1.0","event_id":"sha256:633514d4d0ab9be944bfa3efed9985f9c97a6d6a799f6b0cfa68737eff85c2d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/bundle.json","state_url":"https://pith.science/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/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":"2026-05-28T03:41:20Z","links":{"resolver":"https://pith.science/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ","bundle":"https://pith.science/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/bundle.json","state":"https://pith.science/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVOHU2OXTEGGBCGJPRHL4PQHHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LVOHU2OXTEGGBCGJPRHL4PQHHQ","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":"22629972564b4519bd11398d7b411032fabfb0ad9f918875251809fbe329bed3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-22T17:08:53Z","title_canon_sha256":"1e5bb58363a4cb80b408eafea0318b868cfff9bf8d09ff15c14e2c575613c42e"},"schema_version":"1.0","source":{"id":"1505.06150","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06150","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06150v1","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06150","created_at":"2026-05-17T23:41:37Z"},{"alias_kind":"pith_short_12","alias_value":"LVOHU2OXTEGG","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LVOHU2OXTEGGBCGJ","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LVOHU2OX","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:633514d4d0ab9be944bfa3efed9985f9c97a6d6a799f6b0cfa68737eff85c2d6","target":"graph","created_at":"2026-05-17T23:41:37Z","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 pointwise linear elliptic equations of the form $\\mathrm{L}_x u_x = \\eta_x$ on a smooth compact manifold where the operators $\\mathrm{L}_x$ are in divergence form with real, bounded, measurable coefficients that vary in the space variable $x$. We establish $\\mathrm{L}^{2}$-continuity of the solutions at $x$ whenever the coefficients of $\\mathrm{L}_x$ are $\\mathrm{L}^{\\infty}$-continuous at $x$ and the initial datum is $\\mathrm{L}^{2}$-continuous at $x$. This is obtained by reducing the continuity of solutions to a homogeneous Kato square root problem. As an application, we consider","authors_text":"Lashi Bandara","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-22T17:08:53Z","title":"Continuity of solutions to space-varying pointwise linear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06150","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:eb197b508fdcd37dbddf3cde04dfc7cccbc11a34974ff01258b265debd85e963","target":"record","created_at":"2026-05-17T23:41:37Z","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":"22629972564b4519bd11398d7b411032fabfb0ad9f918875251809fbe329bed3","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-22T17:08:53Z","title_canon_sha256":"1e5bb58363a4cb80b408eafea0318b868cfff9bf8d09ff15c14e2c575613c42e"},"schema_version":"1.0","source":{"id":"1505.06150","kind":"arxiv","version":1}},"canonical_sha256":"5d5c7a69d7990c6088c97c4ebe3e073c096ff8e7cf006e19c2b948c3ec145d14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d5c7a69d7990c6088c97c4ebe3e073c096ff8e7cf006e19c2b948c3ec145d14","first_computed_at":"2026-05-17T23:41:37.646667Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:37.646667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mw6cPHE0xfxgrVJAEMqdO3oenEqgLZEDNLUxt/cDE0q//BUPdWux9mTZs7QrMRnmz8LmCualzijHoL05ayiIDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:37.647358Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06150","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb197b508fdcd37dbddf3cde04dfc7cccbc11a34974ff01258b265debd85e963","sha256:633514d4d0ab9be944bfa3efed9985f9c97a6d6a799f6b0cfa68737eff85c2d6"],"state_sha256":"2d0149e62c990437afb2cb99fa669a661490ca07f25d240c70d832eb65f78a3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvqCBgS6ocpDrrwlqatJSokKz/yh1R86f4pR/ZVV5j7nQeNByXj7p5rmpODqF6YlTEWQUEKo0f5dIKSguGSvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:41:20.928412Z","bundle_sha256":"43962436b79f5957550c66aba600f089b9e8fc15c33c5d252865ec59d26dc8e9"}}