{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q5RGAS4WWHRQKF2KABQOHFXCNI","short_pith_number":"pith:Q5RGAS4W","canonical_record":{"source":{"id":"1512.03735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T13:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"f71cda2300e3ba88ece243b8b719bd6a5678b18cf7a3d874e753e1abbf3c3d0f","abstract_canon_sha256":"e170a2fe1d8746eee625ab49c93f7e7be139d6a83dec510680c386ba7fc32257"},"schema_version":"1.0"},"canonical_sha256":"8762604b96b1e305174a0060e396e26a12dba5bfa83aba2e7d73f5693ccb03b1","source":{"kind":"arxiv","id":"1512.03735","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03735","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03735v1","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03735","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"Q5RGAS4WWHRQ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5RGAS4WWHRQKF2K","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5RGAS4W","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q5RGAS4WWHRQKF2KABQOHFXCNI","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03735","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T13:40:01Z","cross_cats_sorted":[],"title_canon_sha256":"f71cda2300e3ba88ece243b8b719bd6a5678b18cf7a3d874e753e1abbf3c3d0f","abstract_canon_sha256":"e170a2fe1d8746eee625ab49c93f7e7be139d6a83dec510680c386ba7fc32257"},"schema_version":"1.0"},"canonical_sha256":"8762604b96b1e305174a0060e396e26a12dba5bfa83aba2e7d73f5693ccb03b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:11.270215Z","signature_b64":"xeE0FK0mUGiA0DbmXbosEgykWZqrS8feebjG0odtWDkXghnOQs5OCxYPqix5BRNwkvDFacwrKCH4021N99BRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8762604b96b1e305174a0060e396e26a12dba5bfa83aba2e7d73f5693ccb03b1","last_reissued_at":"2026-05-18T01:19:11.269548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:11.269548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03735","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":"2026-05-18T01:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HXMkQ+llG7QI9wOSMLN2gqwy6+QViKe0QjRNUNmS/C2XGfY7keJ7iD/eJN+WaR1zWJj5WSOJtGM5lJVhIPjrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:18.247800Z"},"content_sha256":"92fe6baab227f5bd49f16cfd8b488c56f26023025d036253d1c103b7d0a85ac3","schema_version":"1.0","event_id":"sha256:92fe6baab227f5bd49f16cfd8b488c56f26023025d036253d1c103b7d0a85ac3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q5RGAS4WWHRQKF2KABQOHFXCNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrian Muntean, Vo Anh Khoa","submitted_at":"2015-12-09T13:40:01Z","abstract_excerpt":"In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03735","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":"2026-05-18T01:19:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vbxfIjfwjlVpnJMKx6fEjkbWdWDUgPQSSR172DpDN0uVbdvQyhtjFzw/nGiX9BhwUZmMyiPR4gxK/QrkDTOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:37:18.248151Z"},"content_sha256":"ba19ca288b5683f3d41ff39bd7c8f1600826861e8b58651bc892ba2699ab551b","schema_version":"1.0","event_id":"sha256:ba19ca288b5683f3d41ff39bd7c8f1600826861e8b58651bc892ba2699ab551b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/bundle.json","state_url":"https://pith.science/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/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":"2026-05-31T03:37:18Z","links":{"resolver":"https://pith.science/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI","bundle":"https://pith.science/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/bundle.json","state":"https://pith.science/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5RGAS4WWHRQKF2KABQOHFXCNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q5RGAS4WWHRQKF2KABQOHFXCNI","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":"e170a2fe1d8746eee625ab49c93f7e7be139d6a83dec510680c386ba7fc32257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T13:40:01Z","title_canon_sha256":"f71cda2300e3ba88ece243b8b719bd6a5678b18cf7a3d874e753e1abbf3c3d0f"},"schema_version":"1.0","source":{"id":"1512.03735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03735","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03735v1","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03735","created_at":"2026-05-18T01:19:11Z"},{"alias_kind":"pith_short_12","alias_value":"Q5RGAS4WWHRQ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5RGAS4WWHRQKF2K","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5RGAS4W","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:ba19ca288b5683f3d41ff39bd7c8f1600826861e8b58651bc892ba2699ab551b","target":"graph","created_at":"2026-05-18T01:19:11Z","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 study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then","authors_text":"Adrian Muntean, Vo Anh Khoa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T13:40:01Z","title":"Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03735","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":"sha256:92fe6baab227f5bd49f16cfd8b488c56f26023025d036253d1c103b7d0a85ac3","target":"record","created_at":"2026-05-18T01:19:11Z","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":"e170a2fe1d8746eee625ab49c93f7e7be139d6a83dec510680c386ba7fc32257","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-09T13:40:01Z","title_canon_sha256":"f71cda2300e3ba88ece243b8b719bd6a5678b18cf7a3d874e753e1abbf3c3d0f"},"schema_version":"1.0","source":{"id":"1512.03735","kind":"arxiv","version":1}},"canonical_sha256":"8762604b96b1e305174a0060e396e26a12dba5bfa83aba2e7d73f5693ccb03b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8762604b96b1e305174a0060e396e26a12dba5bfa83aba2e7d73f5693ccb03b1","first_computed_at":"2026-05-18T01:19:11.269548Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:11.269548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xeE0FK0mUGiA0DbmXbosEgykWZqrS8feebjG0odtWDkXghnOQs5OCxYPqix5BRNwkvDFacwrKCH4021N99BRBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:11.270215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92fe6baab227f5bd49f16cfd8b488c56f26023025d036253d1c103b7d0a85ac3","sha256:ba19ca288b5683f3d41ff39bd7c8f1600826861e8b58651bc892ba2699ab551b"],"state_sha256":"ef86d2a8183a5505de632c0af2b74e0cc4c5fd869a66ba7c183380a1b1d5fda9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULFdNimUfOyHgdiRoSKBBaTK+mYAsEUM51MhmpjUfrzKGTpxVCjAU2+Dj/d0nDrMRcNwI4dNxWfj2t0nVtaTCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:37:18.250580Z","bundle_sha256":"a3e347176f2df7e3d5dd9d5fc25d238434cfedd643885a95ae6a894b3241cecf"}}