{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ABR42I3X7S6FDMMNJJKU7EXPVJ","short_pith_number":"pith:ABR42I3X","canonical_record":{"source":{"id":"1210.3254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T14:30:30Z","cross_cats_sorted":[],"title_canon_sha256":"979f0164f7fb52b99e18845788a110ae1c8acbeef6ec5d28b4fdb6bfcd9f5dfe","abstract_canon_sha256":"d3d94782a7db302076365c8c2515fb43c0fcb85b8829aa1f6bf2a9b42ebae3e2"},"schema_version":"1.0"},"canonical_sha256":"0063cd2377fcbc51b18d4a554f92efaa690af74a8c799b21b437be4ff24cd06d","source":{"kind":"arxiv","id":"1210.3254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3254","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3254v1","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3254","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"ABR42I3X7S6F","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABR42I3X7S6FDMMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABR42I3X","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ABR42I3X7S6FDMMNJJKU7EXPVJ","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T14:30:30Z","cross_cats_sorted":[],"title_canon_sha256":"979f0164f7fb52b99e18845788a110ae1c8acbeef6ec5d28b4fdb6bfcd9f5dfe","abstract_canon_sha256":"d3d94782a7db302076365c8c2515fb43c0fcb85b8829aa1f6bf2a9b42ebae3e2"},"schema_version":"1.0"},"canonical_sha256":"0063cd2377fcbc51b18d4a554f92efaa690af74a8c799b21b437be4ff24cd06d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:10.975144Z","signature_b64":"+PD3cHcZf0m0IUvaXodn/UwJhv3dYpstPfdsad/SWrTDtR27yoGZaEZto8KwUlZemi6zXW/673Nv8U+evuZzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0063cd2377fcbc51b18d4a554f92efaa690af74a8c799b21b437be4ff24cd06d","last_reissued_at":"2026-05-18T02:20:10.974511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:10.974511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3254","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":"2026-05-18T02:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J0qFpKFozTzkj1KEScHRpf6r0I6hz7izAHcGQ+SQr0lFKpBmAc45I2co33rwc3e9t4+JnLiJYHzXxNr1UePrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:18:36.245741Z"},"content_sha256":"0f7c4e44d8fc8073a8fddf4fc8e19195c33f1a40929fa41d2061a8ddf5a7dd79","schema_version":"1.0","event_id":"sha256:0f7c4e44d8fc8073a8fddf4fc8e19195c33f1a40929fa41d2061a8ddf5a7dd79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ABR42I3X7S6FDMMNJJKU7EXPVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reduced limit for semilinear boundary value problems with measure data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Moshe Marcus, Mousomi Bhakta","submitted_at":"2012-10-11T14:30:30Z","abstract_excerpt":"We study boundary value problems for semilinear elliptic equations of the form $-\\Delta u+g\\circ u=\\mu$ in a smooth bounded domain $\\Omega\\subset R^N$. Let $\\{\\mu_n\\}$ and $\\{\\tau_n\\}$ be sequences of measure in $\\Omega$ and $\\partial \\Omega$ respectively. Assume that there exists a solution $u_n$ of the equation with $\\mu=\\mu_n$ subject to boundary data $\\tau_n$. Further assume that the sequences of measures converge in a weak sense to $\\mu$ and $\\tau$ respectively and $\\{u_n\\}$ converges to $u$ in $L^1(\\Omega)$. In general $u$ is not a solution of the boundary value problem with data $(\\mu,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3254","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":"2026-05-18T02:20:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GxY4GMlmWNZlDBEjMsP/l4TrPm6UymkaOerBJeGrhcNGHLZOuO8rBQms6JPiTh2/ubtLqmlCuPrs35//jAoqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:18:36.246270Z"},"content_sha256":"3e054a12161787fb8cb49458cfd5a1952c830eb634c90827610809338c4ac6b8","schema_version":"1.0","event_id":"sha256:3e054a12161787fb8cb49458cfd5a1952c830eb634c90827610809338c4ac6b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/bundle.json","state_url":"https://pith.science/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/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":"2026-05-27T11:18:36Z","links":{"resolver":"https://pith.science/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ","bundle":"https://pith.science/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/bundle.json","state":"https://pith.science/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ABR42I3X7S6FDMMNJJKU7EXPVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ABR42I3X7S6FDMMNJJKU7EXPVJ","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":"d3d94782a7db302076365c8c2515fb43c0fcb85b8829aa1f6bf2a9b42ebae3e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T14:30:30Z","title_canon_sha256":"979f0164f7fb52b99e18845788a110ae1c8acbeef6ec5d28b4fdb6bfcd9f5dfe"},"schema_version":"1.0","source":{"id":"1210.3254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3254","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3254v1","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3254","created_at":"2026-05-18T02:20:10Z"},{"alias_kind":"pith_short_12","alias_value":"ABR42I3X7S6F","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"ABR42I3X7S6FDMMN","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"ABR42I3X","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:3e054a12161787fb8cb49458cfd5a1952c830eb634c90827610809338c4ac6b8","target":"graph","created_at":"2026-05-18T02:20:10Z","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 study boundary value problems for semilinear elliptic equations of the form $-\\Delta u+g\\circ u=\\mu$ in a smooth bounded domain $\\Omega\\subset R^N$. Let $\\{\\mu_n\\}$ and $\\{\\tau_n\\}$ be sequences of measure in $\\Omega$ and $\\partial \\Omega$ respectively. Assume that there exists a solution $u_n$ of the equation with $\\mu=\\mu_n$ subject to boundary data $\\tau_n$. Further assume that the sequences of measures converge in a weak sense to $\\mu$ and $\\tau$ respectively and $\\{u_n\\}$ converges to $u$ in $L^1(\\Omega)$. In general $u$ is not a solution of the boundary value problem with data $(\\mu,\\","authors_text":"Moshe Marcus, Mousomi Bhakta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T14:30:30Z","title":"Reduced limit for semilinear boundary value problems with measure data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3254","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":"sha256:0f7c4e44d8fc8073a8fddf4fc8e19195c33f1a40929fa41d2061a8ddf5a7dd79","target":"record","created_at":"2026-05-18T02:20:10Z","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":"d3d94782a7db302076365c8c2515fb43c0fcb85b8829aa1f6bf2a9b42ebae3e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T14:30:30Z","title_canon_sha256":"979f0164f7fb52b99e18845788a110ae1c8acbeef6ec5d28b4fdb6bfcd9f5dfe"},"schema_version":"1.0","source":{"id":"1210.3254","kind":"arxiv","version":1}},"canonical_sha256":"0063cd2377fcbc51b18d4a554f92efaa690af74a8c799b21b437be4ff24cd06d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0063cd2377fcbc51b18d4a554f92efaa690af74a8c799b21b437be4ff24cd06d","first_computed_at":"2026-05-18T02:20:10.974511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:10.974511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+PD3cHcZf0m0IUvaXodn/UwJhv3dYpstPfdsad/SWrTDtR27yoGZaEZto8KwUlZemi6zXW/673Nv8U+evuZzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:10.975144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f7c4e44d8fc8073a8fddf4fc8e19195c33f1a40929fa41d2061a8ddf5a7dd79","sha256:3e054a12161787fb8cb49458cfd5a1952c830eb634c90827610809338c4ac6b8"],"state_sha256":"52b8346df8e5f47fb9787f0ffe634910582ca4f29cf8312157df0b84dd63df18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tzXHSpW73iaKTQg8/SVighdm8zpjsBpJdlJJOLYhiGks0DTTqKBMY4q3B5m6f1xWXDQ+DXeP4rbCDWIryWUiDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:18:36.249772Z","bundle_sha256":"fbc1779c08e2d640e1ee3deeb0d1446784a840a172864251c8997a7365281abb"}}