{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZJ62G2MD3COC4LETIY4WQM6NW4","short_pith_number":"pith:ZJ62G2MD","canonical_record":{"source":{"id":"1811.07524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T06:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"a65f471c1ab6352ceca9330240462e1d30ed7ff8ee0f17ab59b1d0bff21bab8e","abstract_canon_sha256":"f7119d3efd7910a017ccf95bc283c5b3112dc315814211ac474ad08dc2a5544e"},"schema_version":"1.0"},"canonical_sha256":"ca7da36983d89c2e2c9346396833cdb732df7a8e3639c4e8f9fdda88425e8710","source":{"kind":"arxiv","id":"1811.07524","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07524","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07524v1","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07524","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ62G2MD3COC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ62G2MD3COC4LET","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ62G2MD","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZJ62G2MD3COC4LETIY4WQM6NW4","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T06:57:59Z","cross_cats_sorted":[],"title_canon_sha256":"a65f471c1ab6352ceca9330240462e1d30ed7ff8ee0f17ab59b1d0bff21bab8e","abstract_canon_sha256":"f7119d3efd7910a017ccf95bc283c5b3112dc315814211ac474ad08dc2a5544e"},"schema_version":"1.0"},"canonical_sha256":"ca7da36983d89c2e2c9346396833cdb732df7a8e3639c4e8f9fdda88425e8710","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:24.218735Z","signature_b64":"f9c1crNbqaep2AOIZ6xB+1vYBUnZ5mcDLtlQzPIs4fJDYTNa0Y+XXLkjPJ0WhL41ihuwxdTgxGBJSWQGclmlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca7da36983d89c2e2c9346396833cdb732df7a8e3639c4e8f9fdda88425e8710","last_reissued_at":"2026-05-18T00:00:24.218043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:24.218043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07524","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":"2026-05-18T00:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIT4Zvegqt7EOrIyQ8mtDFwwp/G3UuXUozCqBwsHCrQ85y5efABSMjIz9cdS4UF1riO5jeeNu3/mTeuJk0cUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:14:01.832473Z"},"content_sha256":"bd2ee99343b7b0c06e9b58010e3e6962d4cce57b588978f8702751ebafb7a4de","schema_version":"1.0","event_id":"sha256:bd2ee99343b7b0c06e9b58010e3e6962d4cce57b588978f8702751ebafb7a4de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZJ62G2MD3COC4LETIY4WQM6NW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The cardiac bidomain model and homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Erik Grandelius, Kenneth H. Karlsen","submitted_at":"2018-11-19T06:57:59Z","abstract_excerpt":"We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07524","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":"2026-05-18T00:00:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4inATpDshPQQ0q8UM5KFf1MmsXK9kcs4DMvotA3B032vkXE/aMvoz6oka8W2HxOusD8tEULT8gvIrlAnP0bcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:14:01.832818Z"},"content_sha256":"54454b509c3142703bb08f845f6849fb5cc2d905ccaf16acc58aa68c734aef0c","schema_version":"1.0","event_id":"sha256:54454b509c3142703bb08f845f6849fb5cc2d905ccaf16acc58aa68c734aef0c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/bundle.json","state_url":"https://pith.science/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/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":"2026-06-09T15:14:01Z","links":{"resolver":"https://pith.science/pith/ZJ62G2MD3COC4LETIY4WQM6NW4","bundle":"https://pith.science/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/bundle.json","state":"https://pith.science/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZJ62G2MD3COC4LETIY4WQM6NW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZJ62G2MD3COC4LETIY4WQM6NW4","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":"f7119d3efd7910a017ccf95bc283c5b3112dc315814211ac474ad08dc2a5544e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T06:57:59Z","title_canon_sha256":"a65f471c1ab6352ceca9330240462e1d30ed7ff8ee0f17ab59b1d0bff21bab8e"},"schema_version":"1.0","source":{"id":"1811.07524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07524","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07524v1","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07524","created_at":"2026-05-18T00:00:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZJ62G2MD3COC","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZJ62G2MD3COC4LET","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZJ62G2MD","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:54454b509c3142703bb08f845f6849fb5cc2d905ccaf16acc58aa68c734aef0c","target":"graph","created_at":"2026-05-18T00:00:24Z","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 provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface.","authors_text":"Erik Grandelius, Kenneth H. Karlsen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T06:57:59Z","title":"The cardiac bidomain model and homogenization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07524","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:bd2ee99343b7b0c06e9b58010e3e6962d4cce57b588978f8702751ebafb7a4de","target":"record","created_at":"2026-05-18T00:00:24Z","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":"f7119d3efd7910a017ccf95bc283c5b3112dc315814211ac474ad08dc2a5544e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T06:57:59Z","title_canon_sha256":"a65f471c1ab6352ceca9330240462e1d30ed7ff8ee0f17ab59b1d0bff21bab8e"},"schema_version":"1.0","source":{"id":"1811.07524","kind":"arxiv","version":1}},"canonical_sha256":"ca7da36983d89c2e2c9346396833cdb732df7a8e3639c4e8f9fdda88425e8710","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca7da36983d89c2e2c9346396833cdb732df7a8e3639c4e8f9fdda88425e8710","first_computed_at":"2026-05-18T00:00:24.218043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:24.218043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9c1crNbqaep2AOIZ6xB+1vYBUnZ5mcDLtlQzPIs4fJDYTNa0Y+XXLkjPJ0WhL41ihuwxdTgxGBJSWQGclmlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:24.218735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd2ee99343b7b0c06e9b58010e3e6962d4cce57b588978f8702751ebafb7a4de","sha256:54454b509c3142703bb08f845f6849fb5cc2d905ccaf16acc58aa68c734aef0c"],"state_sha256":"700eddfd8bc7dc57639fd82bff56c599562e950904d1e0afbd5bd6b503227984"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ae7PPPPP/z6sKp8K1Lj0inqslYrnKj4/Zi5bgp7TUyFqyDVIJfZfdT6PBDi8MmV9NOg3jEz5DOrm0BOioNRgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:14:01.834876Z","bundle_sha256":"bf336d5c2f227fa51e83320cee0bcfdd79ad00cf169fb75eaa37769a2c06b279"}}