{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6XF4NLNVDVVTQOUBHLDIF45VOG","short_pith_number":"pith:6XF4NLNV","canonical_record":{"source":{"id":"1111.2398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T06:01:33Z","cross_cats_sorted":[],"title_canon_sha256":"e876116b95ad2cf9bc5531b3cf4824b410d22f05708908b35200af04f6772006","abstract_canon_sha256":"933058532face42fa77a8bf12085490c02e6a0ab00bbc76abad7e03727e01e05"},"schema_version":"1.0"},"canonical_sha256":"f5cbc6adb51d6b383a813ac682f3b571ac3b9574f555e67425087bceaae73a0b","source":{"kind":"arxiv","id":"1111.2398","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2398","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2398v1","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2398","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"6XF4NLNVDVVT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6XF4NLNVDVVTQOUB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6XF4NLNV","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6XF4NLNVDVVTQOUBHLDIF45VOG","target":"record","payload":{"canonical_record":{"source":{"id":"1111.2398","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T06:01:33Z","cross_cats_sorted":[],"title_canon_sha256":"e876116b95ad2cf9bc5531b3cf4824b410d22f05708908b35200af04f6772006","abstract_canon_sha256":"933058532face42fa77a8bf12085490c02e6a0ab00bbc76abad7e03727e01e05"},"schema_version":"1.0"},"canonical_sha256":"f5cbc6adb51d6b383a813ac682f3b571ac3b9574f555e67425087bceaae73a0b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:42.793104Z","signature_b64":"K3UmdV6H60+M9fKLJUC9Z+TAuxtpk51ztKwM4HiUk9nvYth63EhBWRhrMsK3vCBHjRm3z11qEQGJdr0g8v2SBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5cbc6adb51d6b383a813ac682f3b571ac3b9574f555e67425087bceaae73a0b","last_reissued_at":"2026-05-18T01:59:42.792482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:42.792482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.2398","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":"2026-05-18T01:59:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hxtg96Vo4QKLSDCbgcA8yvlX19RVPToEH/Wg1zXGTFxAanwbGW/jxS/ews3xC+w18INfwOAyHuTPP8b/aP2BDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:11:35.994120Z"},"content_sha256":"c804370914fee76aa38536ca6598d9b16a1c1f6b816ad817db59cb0355782a76","schema_version":"1.0","event_id":"sha256:c804370914fee76aa38536ca6598d9b16a1c1f6b816ad817db59cb0355782a76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6XF4NLNVDVVTQOUBHLDIF45VOG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The viscosity Method for the Homogenization of soft inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ki-Ahm Lee, Minha Yoo","submitted_at":"2011-11-10T06:01:33Z","abstract_excerpt":"In this paper, we consider periodic soft inclusions $T_{\\epsilon}$ with periodicity $\\epsilon$, where the solution, $u_{\\epsilon}$, satisfies semi-linear elliptic equations of non-divergence in $\\Omega_{\\epsilon}=\\Omega\\setminus \\bar{T}_\\epsilon$ with a Neumann data on $\\partial T^{\\mathfrak a}$ . The difficulty lies in the non-divergence structure of the operator where the standard energy method based on the divergence theorem can not be applied. The main object is developing a viscosity method to find the homogenized equation satisfied by the limit of $u_{\\epsilon}$, called as $u$, as $\\epsi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2398","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":"2026-05-18T01:59:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ogFIiT+5zDXwNdu8zR4kKwmAxjLxomUI+7YtyjGo6HKg4O+breMeC/O1h0MKS28B7xUdJcTTlfSeqPlQmkJDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:11:35.994823Z"},"content_sha256":"eb6ccafc61e4a884a94fc4a9e8ac7584771cb83d282b38ad5b568f9394abb3e2","schema_version":"1.0","event_id":"sha256:eb6ccafc61e4a884a94fc4a9e8ac7584771cb83d282b38ad5b568f9394abb3e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/bundle.json","state_url":"https://pith.science/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/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":"2026-06-07T14:11:35Z","links":{"resolver":"https://pith.science/pith/6XF4NLNVDVVTQOUBHLDIF45VOG","bundle":"https://pith.science/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/bundle.json","state":"https://pith.science/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XF4NLNVDVVTQOUBHLDIF45VOG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6XF4NLNVDVVTQOUBHLDIF45VOG","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":"933058532face42fa77a8bf12085490c02e6a0ab00bbc76abad7e03727e01e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T06:01:33Z","title_canon_sha256":"e876116b95ad2cf9bc5531b3cf4824b410d22f05708908b35200af04f6772006"},"schema_version":"1.0","source":{"id":"1111.2398","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2398","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2398v1","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2398","created_at":"2026-05-18T01:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"6XF4NLNVDVVT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6XF4NLNVDVVTQOUB","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6XF4NLNV","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:eb6ccafc61e4a884a94fc4a9e8ac7584771cb83d282b38ad5b568f9394abb3e2","target":"graph","created_at":"2026-05-18T01:59:42Z","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 consider periodic soft inclusions $T_{\\epsilon}$ with periodicity $\\epsilon$, where the solution, $u_{\\epsilon}$, satisfies semi-linear elliptic equations of non-divergence in $\\Omega_{\\epsilon}=\\Omega\\setminus \\bar{T}_\\epsilon$ with a Neumann data on $\\partial T^{\\mathfrak a}$ . The difficulty lies in the non-divergence structure of the operator where the standard energy method based on the divergence theorem can not be applied. The main object is developing a viscosity method to find the homogenized equation satisfied by the limit of $u_{\\epsilon}$, called as $u$, as $\\epsi","authors_text":"Ki-Ahm Lee, Minha Yoo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T06:01:33Z","title":"The viscosity Method for the Homogenization of soft inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2398","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:c804370914fee76aa38536ca6598d9b16a1c1f6b816ad817db59cb0355782a76","target":"record","created_at":"2026-05-18T01:59:42Z","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":"933058532face42fa77a8bf12085490c02e6a0ab00bbc76abad7e03727e01e05","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-10T06:01:33Z","title_canon_sha256":"e876116b95ad2cf9bc5531b3cf4824b410d22f05708908b35200af04f6772006"},"schema_version":"1.0","source":{"id":"1111.2398","kind":"arxiv","version":1}},"canonical_sha256":"f5cbc6adb51d6b383a813ac682f3b571ac3b9574f555e67425087bceaae73a0b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5cbc6adb51d6b383a813ac682f3b571ac3b9574f555e67425087bceaae73a0b","first_computed_at":"2026-05-18T01:59:42.792482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:42.792482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3UmdV6H60+M9fKLJUC9Z+TAuxtpk51ztKwM4HiUk9nvYth63EhBWRhrMsK3vCBHjRm3z11qEQGJdr0g8v2SBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:42.793104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2398","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c804370914fee76aa38536ca6598d9b16a1c1f6b816ad817db59cb0355782a76","sha256:eb6ccafc61e4a884a94fc4a9e8ac7584771cb83d282b38ad5b568f9394abb3e2"],"state_sha256":"9dbdad00cceaa18df2e89f0ca79a0c3225bf340ff8d97d6b4bec698bf99f23e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fz65lMGc0EHoVg/rv1vWFFfTAb9q1SZ2lbtLs+EgXJIQYzNHIhqNIGHJwTbWE59uFBattdX4ENxgdHerKsxhCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:11:35.998747Z","bundle_sha256":"b8209c36c0f6ec03af4fc05ba5f26825ec6bcd6b5828c47c022be34950279fe4"}}