{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:CRV7OW52H56VBEWWQHF4WILIK7","short_pith_number":"pith:CRV7OW52","canonical_record":{"source":{"id":"funct-an/9303004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"funct-an","submitted_at":"1993-03-26T11:23:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3df1b907a0f8fbeab3c06b983e1474fe6ee6e90563948e54ed1b972b36482a5d","abstract_canon_sha256":"81d82d66bbd5ec05234ec15f188679baf0dc99ba9feb23318acd22aec8514edc"},"schema_version":"1.0"},"canonical_sha256":"146bf75bba3f7d5092d681cbcb216857e72cd89cb14d97a7bf61b7587f0be329","source":{"kind":"arxiv","id":"funct-an/9303004","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"funct-an/9303004","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"funct-an/9303004v1","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.funct-an/9303004","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"CRV7OW52H56V","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CRV7OW52H56VBEWW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CRV7OW52","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:CRV7OW52H56VBEWWQHF4WILIK7","target":"record","payload":{"canonical_record":{"source":{"id":"funct-an/9303004","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"funct-an","submitted_at":"1993-03-26T11:23:54Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3df1b907a0f8fbeab3c06b983e1474fe6ee6e90563948e54ed1b972b36482a5d","abstract_canon_sha256":"81d82d66bbd5ec05234ec15f188679baf0dc99ba9feb23318acd22aec8514edc"},"schema_version":"1.0"},"canonical_sha256":"146bf75bba3f7d5092d681cbcb216857e72cd89cb14d97a7bf61b7587f0be329","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:48.419739Z","signature_b64":"KgmUgnPdmmaZyZGb2WCvD1YGrScAZTF7ZcL51eAg6Q2da4j2vKTt5sHKQc8FZiUnv6SUiUXp49DELnZCsfMiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"146bf75bba3f7d5092d681cbcb216857e72cd89cb14d97a7bf61b7587f0be329","last_reissued_at":"2026-05-18T01:06:48.419236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:48.419236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"funct-an/9303004","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":"2026-05-18T01:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBuR92AsvcapIUbm+k9saDWIMI7o7QG+CkFMI0xSk15Ozdja4HQ9UMSw5UxnhV3YL9h8NYzGYUf7Z0DgoRYhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:01:00.998022Z"},"content_sha256":"144c14acce5ed590e0c47f3a159244f7484e1ac4e2517d0e10f47c7a5dae2313","schema_version":"1.0","event_id":"sha256:144c14acce5ed590e0c47f3a159244f7484e1ac4e2517d0e10f47c7a5dae2313"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:CRV7OW52H56VBEWWQHF4WILIK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation of Relaxed Dirichlet Problems by Boundary Value problems in perforated domains","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"funct-an","authors_text":"Annalisa Malusa, Gianni Dal Maso","submitted_at":"1993-03-26T11:23:54Z","abstract_excerpt":"Given an elliptic operator~$L$ on a bounded domain~$\\Omega \\subseteq {\\bf R}^n$, and a positive Radon measure~$\\mu$ on~$\\Omega$, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains~$\\Omega_h \\subseteq \\Omega$ with the following property: for every~$f\\in H^{-1}(\\Omega)$ the sequence~$u_h$ of the solutions of the Dirichlet problems~$L\\, u_h=f$ in~$\\Omega_h$, $u_h=0$ on~$\\partial \\Omega_h$, extended to 0 in~$\\Omega \\setminus \\Omega_h$, converges to the solution of the \\lq\\lq relaxed Dirichlet problem\\rq\\rq\\ $L\\,u+\\mu u=f$ in~$\\Omega$, $u=0$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9303004","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":"2026-05-18T01:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LixGP01WvyR3eh0LiqjRAswLlzeaRxUKFLB0hHHr2Tl+mXhEPfOYuM+/XiGPrWF+dlX70YEnjOvnFikQwpTRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:01:00.999013Z"},"content_sha256":"29368dd5222ba4c0e437aba59d9d48e46ed82a8ad0f76f748d5c65cde8f856da","schema_version":"1.0","event_id":"sha256:29368dd5222ba4c0e437aba59d9d48e46ed82a8ad0f76f748d5c65cde8f856da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRV7OW52H56VBEWWQHF4WILIK7/bundle.json","state_url":"https://pith.science/pith/CRV7OW52H56VBEWWQHF4WILIK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRV7OW52H56VBEWWQHF4WILIK7/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":"2026-05-31T11:01:01Z","links":{"resolver":"https://pith.science/pith/CRV7OW52H56VBEWWQHF4WILIK7","bundle":"https://pith.science/pith/CRV7OW52H56VBEWWQHF4WILIK7/bundle.json","state":"https://pith.science/pith/CRV7OW52H56VBEWWQHF4WILIK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRV7OW52H56VBEWWQHF4WILIK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:CRV7OW52H56VBEWWQHF4WILIK7","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":"81d82d66bbd5ec05234ec15f188679baf0dc99ba9feb23318acd22aec8514edc","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"funct-an","submitted_at":"1993-03-26T11:23:54Z","title_canon_sha256":"3df1b907a0f8fbeab3c06b983e1474fe6ee6e90563948e54ed1b972b36482a5d"},"schema_version":"1.0","source":{"id":"funct-an/9303004","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"funct-an/9303004","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"funct-an/9303004v1","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.funct-an/9303004","created_at":"2026-05-18T01:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"CRV7OW52H56V","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CRV7OW52H56VBEWW","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CRV7OW52","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:29368dd5222ba4c0e437aba59d9d48e46ed82a8ad0f76f748d5c65cde8f856da","target":"graph","created_at":"2026-05-18T01:06:48Z","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":"Given an elliptic operator~$L$ on a bounded domain~$\\Omega \\subseteq {\\bf R}^n$, and a positive Radon measure~$\\mu$ on~$\\Omega$, not charging polar sets, we discuss an explicit approximation procedure which leads to a sequence of domains~$\\Omega_h \\subseteq \\Omega$ with the following property: for every~$f\\in H^{-1}(\\Omega)$ the sequence~$u_h$ of the solutions of the Dirichlet problems~$L\\, u_h=f$ in~$\\Omega_h$, $u_h=0$ on~$\\partial \\Omega_h$, extended to 0 in~$\\Omega \\setminus \\Omega_h$, converges to the solution of the \\lq\\lq relaxed Dirichlet problem\\rq\\rq\\ $L\\,u+\\mu u=f$ in~$\\Omega$, $u=0$","authors_text":"Annalisa Malusa, Gianni Dal Maso","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"funct-an","submitted_at":"1993-03-26T11:23:54Z","title":"Approximation of Relaxed Dirichlet Problems by Boundary Value problems in perforated domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"funct-an/9303004","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":"sha256:144c14acce5ed590e0c47f3a159244f7484e1ac4e2517d0e10f47c7a5dae2313","target":"record","created_at":"2026-05-18T01:06:48Z","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":"81d82d66bbd5ec05234ec15f188679baf0dc99ba9feb23318acd22aec8514edc","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"funct-an","submitted_at":"1993-03-26T11:23:54Z","title_canon_sha256":"3df1b907a0f8fbeab3c06b983e1474fe6ee6e90563948e54ed1b972b36482a5d"},"schema_version":"1.0","source":{"id":"funct-an/9303004","kind":"arxiv","version":1}},"canonical_sha256":"146bf75bba3f7d5092d681cbcb216857e72cd89cb14d97a7bf61b7587f0be329","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"146bf75bba3f7d5092d681cbcb216857e72cd89cb14d97a7bf61b7587f0be329","first_computed_at":"2026-05-18T01:06:48.419236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:48.419236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KgmUgnPdmmaZyZGb2WCvD1YGrScAZTF7ZcL51eAg6Q2da4j2vKTt5sHKQc8FZiUnv6SUiUXp49DELnZCsfMiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:48.419739Z","signed_message":"canonical_sha256_bytes"},"source_id":"funct-an/9303004","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:144c14acce5ed590e0c47f3a159244f7484e1ac4e2517d0e10f47c7a5dae2313","sha256:29368dd5222ba4c0e437aba59d9d48e46ed82a8ad0f76f748d5c65cde8f856da"],"state_sha256":"0be0b75cd1ae1677e67972d7823b953f0c7210950f784c6f8e552382591f8bc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Apok0CxVy3uZxwF1395SEvjfKE3r/V4sexMtds8PrzGG1QeAyTzTvnaPqbMKWbj8Gmvdkc/wp2Ce1hH+/HUUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:01:01.003870Z","bundle_sha256":"2f8c7a0ce345c7180d4f5c38792b59144f3eb119892e0e965eb59da7dc2bc54b"}}