{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Y5O3ZN3AIL43JCNATRPYBKJKRR","short_pith_number":"pith:Y5O3ZN3A","canonical_record":{"source":{"id":"1806.10859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:56:50Z","cross_cats_sorted":[],"title_canon_sha256":"f350ad2564261a427fe3258cbcd8711d95c28f7f3181e87d1fc5a55bebdd3e34","abstract_canon_sha256":"0e36a07e9605601e488a4e5553093e1d10e1a3d4e42bce0eec612ef41dc1bcfe"},"schema_version":"1.0"},"canonical_sha256":"c75dbcb76042f9b489a09c5f80a92a8c6d23efd221df934a57872e0cd56c9556","source":{"kind":"arxiv","id":"1806.10859","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10859","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10859v3","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10859","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_12","alias_value":"Y5O3ZN3AIL43","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_16","alias_value":"Y5O3ZN3AIL43JCNA","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_8","alias_value":"Y5O3ZN3A","created_at":"2026-07-05T00:46:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Y5O3ZN3AIL43JCNATRPYBKJKRR","target":"record","payload":{"canonical_record":{"source":{"id":"1806.10859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:56:50Z","cross_cats_sorted":[],"title_canon_sha256":"f350ad2564261a427fe3258cbcd8711d95c28f7f3181e87d1fc5a55bebdd3e34","abstract_canon_sha256":"0e36a07e9605601e488a4e5553093e1d10e1a3d4e42bce0eec612ef41dc1bcfe"},"schema_version":"1.0"},"canonical_sha256":"c75dbcb76042f9b489a09c5f80a92a8c6d23efd221df934a57872e0cd56c9556","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:46:29.300655Z","signature_b64":"BNpIiZVQwrQZWH8tzaTNQqxwwgpUqFngNLs54sLCz9z6mjVQxuwBpLWin8DfZtrLE0h1x8T//cawR4kJ2YaZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c75dbcb76042f9b489a09c5f80a92a8c6d23efd221df934a57872e0cd56c9556","last_reissued_at":"2026-07-05T00:46:29.300126Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:46:29.300126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.10859","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:46:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tFyBmA1PhzizgffyPjRlHtNFHWrgn1I0Tz7Ddd4mnFx2PY3C8LHRT68K2MfVa4L0LRIsA1mS0dHcRRq/ljTrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:09:04.837491Z"},"content_sha256":"08e6abaeaf5e735736bb0d7c21b37ea57dcc239d220ee7503af0236e9bc88811","schema_version":"1.0","event_id":"sha256:08e6abaeaf5e735736bb0d7c21b37ea57dcc239d220ee7503af0236e9bc88811"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Y5O3ZN3AIL43JCNATRPYBKJKRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Adrian Muntean, Martin Lind, Omar Richardson","submitted_at":"2018-06-28T09:56:50Z","abstract_excerpt":"In this paper, we study the numerical approximation of a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow in cementitious-based materials. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates for the semidiscrete case. We complement our analysis with simulat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10859","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1806.10859/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:46:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTxzu1o+pIDE4M9lvxPTkJuiHpE4AuiB12x/59qNcTvjMHlN/rbvf0lbneC2zb6XAAcH10coOZ0jJKF+RalDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T18:09:04.837982Z"},"content_sha256":"ae7b993ed18ad5faaaa0322b682ad8705b71fc37b02ab3e7faa26d5a755f6d1d","schema_version":"1.0","event_id":"sha256:ae7b993ed18ad5faaaa0322b682ad8705b71fc37b02ab3e7faa26d5a755f6d1d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/bundle.json","state_url":"https://pith.science/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/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":"2026-08-03T18:09:04Z","links":{"resolver":"https://pith.science/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR","bundle":"https://pith.science/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/bundle.json","state":"https://pith.science/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5O3ZN3AIL43JCNATRPYBKJKRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y5O3ZN3AIL43JCNATRPYBKJKRR","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":"0e36a07e9605601e488a4e5553093e1d10e1a3d4e42bce0eec612ef41dc1bcfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:56:50Z","title_canon_sha256":"f350ad2564261a427fe3258cbcd8711d95c28f7f3181e87d1fc5a55bebdd3e34"},"schema_version":"1.0","source":{"id":"1806.10859","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10859","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10859v3","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10859","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_12","alias_value":"Y5O3ZN3AIL43","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_16","alias_value":"Y5O3ZN3AIL43JCNA","created_at":"2026-07-05T00:46:29Z"},{"alias_kind":"pith_short_8","alias_value":"Y5O3ZN3A","created_at":"2026-07-05T00:46:29Z"}],"graph_snapshots":[{"event_id":"sha256:ae7b993ed18ad5faaaa0322b682ad8705b71fc37b02ab3e7faa26d5a755f6d1d","target":"graph","created_at":"2026-07-05T00:46:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1806.10859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the numerical approximation of a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow in cementitious-based materials. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates for the semidiscrete case. We complement our analysis with simulat","authors_text":"Adrian Muntean, Martin Lind, Omar Richardson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:56:50Z","title":"A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10859","kind":"arxiv","version":3},"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":"sha256:08e6abaeaf5e735736bb0d7c21b37ea57dcc239d220ee7503af0236e9bc88811","target":"record","created_at":"2026-07-05T00:46:29Z","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":"0e36a07e9605601e488a4e5553093e1d10e1a3d4e42bce0eec612ef41dc1bcfe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-28T09:56:50Z","title_canon_sha256":"f350ad2564261a427fe3258cbcd8711d95c28f7f3181e87d1fc5a55bebdd3e34"},"schema_version":"1.0","source":{"id":"1806.10859","kind":"arxiv","version":3}},"canonical_sha256":"c75dbcb76042f9b489a09c5f80a92a8c6d23efd221df934a57872e0cd56c9556","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c75dbcb76042f9b489a09c5f80a92a8c6d23efd221df934a57872e0cd56c9556","first_computed_at":"2026-07-05T00:46:29.300126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:46:29.300126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNpIiZVQwrQZWH8tzaTNQqxwwgpUqFngNLs54sLCz9z6mjVQxuwBpLWin8DfZtrLE0h1x8T//cawR4kJ2YaZDA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:46:29.300655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10859","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08e6abaeaf5e735736bb0d7c21b37ea57dcc239d220ee7503af0236e9bc88811","sha256:ae7b993ed18ad5faaaa0322b682ad8705b71fc37b02ab3e7faa26d5a755f6d1d"],"state_sha256":"d8a30684e8d25e2afec058c3a700cb5ff240bf376a99c58aedcf5d83b255c154"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZdxLd5FgvP7zyTzh8hQqocamBq8RvMBpZtn/N078oPIjBpX5xdTrxudiKvaHBoOQ0C9JAI9mhWrkxbPyS7mBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T18:09:04.841373Z","bundle_sha256":"26983a76a67b612aec5c866e199f97aad3b36d4bde025d7108c625da63c8b5d9"}}