{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EPRG7G7I2GNWZSL3OX3FMTSV23","short_pith_number":"pith:EPRG7G7I","canonical_record":{"source":{"id":"1301.2488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-11T13:10:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0283083fa3f155d3c54dbbc0dac76056a826cc51e934adf6804506e04bda7581","abstract_canon_sha256":"9074e8d7d9caefcaea3c1b4bc7841859b75b2595e3b6526108fa9b209d500ce8"},"schema_version":"1.0"},"canonical_sha256":"23e26f9be8d19b6cc97b75f6564e55d6d08e31d661630dc11ac1d35efcf58736","source":{"kind":"arxiv","id":"1301.2488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2488","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2488v1","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2488","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"EPRG7G7I2GNW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EPRG7G7I2GNWZSL3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EPRG7G7I","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EPRG7G7I2GNWZSL3OX3FMTSV23","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-11T13:10:38Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"0283083fa3f155d3c54dbbc0dac76056a826cc51e934adf6804506e04bda7581","abstract_canon_sha256":"9074e8d7d9caefcaea3c1b4bc7841859b75b2595e3b6526108fa9b209d500ce8"},"schema_version":"1.0"},"canonical_sha256":"23e26f9be8d19b6cc97b75f6564e55d6d08e31d661630dc11ac1d35efcf58736","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:47.178644Z","signature_b64":"CXfj7qiHcoaYtDeeXguYMeSxf18uytfdP5gqIWhz2FmCAnLAvEFc++Fi30NrYJqDiN4M0YggzzV/8NuIK3mbDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e26f9be8d19b6cc97b75f6564e55d6d08e31d661630dc11ac1d35efcf58736","last_reissued_at":"2026-05-18T02:48:47.178143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:47.178143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2488","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":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9HJuwy+hsxbTye0Og1W6poZe0576xcLShR6WemiJsCuCNt9+P2FkQE1Yn9UcgMS55pop0DxbP2TpuZEMKXQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:32:53.853369Z"},"content_sha256":"1c496e14c062c3c262a9f98e03c4dad8fb97733c98255040f82c660861d7bdee","schema_version":"1.0","event_id":"sha256:1c496e14c062c3c262a9f98e03c4dad8fb97733c98255040f82c660861d7bdee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EPRG7G7I2GNWZSL3OX3FMTSV23","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"Heiko Berninger, Kathrin Smetana, Mario Ohlberger, Oliver Sander","submitted_at":"2013-01-11T13:10:38Z","abstract_excerpt":"We analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differential equations (ODE's) on parts of the domain boundary, and with nonlinear outflow conditions of Signorini's type. The coupling of the partial differential equation (PDE) and the ODE's is given by nonlinear Robin boundary conditions. This article provides two major new contributions regarding these infiltration conditions. First, an existence result for the continuous coupled problem is established with the help of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2488","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":"2026-05-18T02:48:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPzkBxgvQqS7dOEZc3e5xFp8mtW9o1auQ2yhbmBWy18CWup+SRZPm/yox/UMkL2BXGRx6PFckV7QyiXji9EABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:32:53.853789Z"},"content_sha256":"a7d99c88174b1aee92d250e654bb49916d02191bce0f1ddfe70be132a1973d13","schema_version":"1.0","event_id":"sha256:a7d99c88174b1aee92d250e654bb49916d02191bce0f1ddfe70be132a1973d13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/bundle.json","state_url":"https://pith.science/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/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":"2026-05-30T16:32:53Z","links":{"resolver":"https://pith.science/pith/EPRG7G7I2GNWZSL3OX3FMTSV23","bundle":"https://pith.science/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/bundle.json","state":"https://pith.science/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPRG7G7I2GNWZSL3OX3FMTSV23/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EPRG7G7I2GNWZSL3OX3FMTSV23","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":"9074e8d7d9caefcaea3c1b4bc7841859b75b2595e3b6526108fa9b209d500ce8","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-11T13:10:38Z","title_canon_sha256":"0283083fa3f155d3c54dbbc0dac76056a826cc51e934adf6804506e04bda7581"},"schema_version":"1.0","source":{"id":"1301.2488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2488","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2488v1","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2488","created_at":"2026-05-18T02:48:47Z"},{"alias_kind":"pith_short_12","alias_value":"EPRG7G7I2GNW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EPRG7G7I2GNWZSL3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EPRG7G7I","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:a7d99c88174b1aee92d250e654bb49916d02191bce0f1ddfe70be132a1973d13","target":"graph","created_at":"2026-05-18T02:48:47Z","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 analytically and numerically analyze groundwater flow in a homogeneous soil described by the Richards equation, coupled to surface water represented by a set of ordinary differential equations (ODE's) on parts of the domain boundary, and with nonlinear outflow conditions of Signorini's type. The coupling of the partial differential equation (PDE) and the ODE's is given by nonlinear Robin boundary conditions. This article provides two major new contributions regarding these infiltration conditions. First, an existence result for the continuous coupled problem is established with the help of ","authors_text":"Heiko Berninger, Kathrin Smetana, Mario Ohlberger, Oliver Sander","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-11T13:10:38Z","title":"Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2488","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":"sha256:1c496e14c062c3c262a9f98e03c4dad8fb97733c98255040f82c660861d7bdee","target":"record","created_at":"2026-05-18T02:48:47Z","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":"9074e8d7d9caefcaea3c1b4bc7841859b75b2595e3b6526108fa9b209d500ce8","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-11T13:10:38Z","title_canon_sha256":"0283083fa3f155d3c54dbbc0dac76056a826cc51e934adf6804506e04bda7581"},"schema_version":"1.0","source":{"id":"1301.2488","kind":"arxiv","version":1}},"canonical_sha256":"23e26f9be8d19b6cc97b75f6564e55d6d08e31d661630dc11ac1d35efcf58736","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23e26f9be8d19b6cc97b75f6564e55d6d08e31d661630dc11ac1d35efcf58736","first_computed_at":"2026-05-18T02:48:47.178143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:47.178143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CXfj7qiHcoaYtDeeXguYMeSxf18uytfdP5gqIWhz2FmCAnLAvEFc++Fi30NrYJqDiN4M0YggzzV/8NuIK3mbDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:47.178644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c496e14c062c3c262a9f98e03c4dad8fb97733c98255040f82c660861d7bdee","sha256:a7d99c88174b1aee92d250e654bb49916d02191bce0f1ddfe70be132a1973d13"],"state_sha256":"a05f33cc2e621d244d8284e9238665f9a277906a1610f28ab60cff92cd0ab2af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NqHT1QP55bvHQGGOkm/HwJle1jnUvSpDsXaR99HJDzKsIzmRwp2iBbhdlLa7HxGi87L8egpTV0G14VLDP0RpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:32:53.856659Z","bundle_sha256":"c0e492939240fc095179533d15417f6b476196f761134e3a183f37bb5f70c398"}}