{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7A6SPW2SMR23UZMBWZTQYSVNMP","short_pith_number":"pith:7A6SPW2S","canonical_record":{"source":{"id":"1204.1709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-08T04:44:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"58a067f0c3fba244893abb1a5769df92b078ec42342c9a52dc4fdb25efef7223","abstract_canon_sha256":"a62afdd9268090ba2cbe8009296b036bb6f7bed340ab5c8aa53b47509b5bc0f5"},"schema_version":"1.0"},"canonical_sha256":"f83d27db526475ba6581b6670c4aad63f136d44955cb52f27502f0113336e253","source":{"kind":"arxiv","id":"1204.1709","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1709","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1709v1","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1709","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"7A6SPW2SMR23","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7A6SPW2SMR23UZMB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7A6SPW2S","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7A6SPW2SMR23UZMBWZTQYSVNMP","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-08T04:44:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"58a067f0c3fba244893abb1a5769df92b078ec42342c9a52dc4fdb25efef7223","abstract_canon_sha256":"a62afdd9268090ba2cbe8009296b036bb6f7bed340ab5c8aa53b47509b5bc0f5"},"schema_version":"1.0"},"canonical_sha256":"f83d27db526475ba6581b6670c4aad63f136d44955cb52f27502f0113336e253","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:23.348469Z","signature_b64":"P+/fETX/8QSHTCmJH2akTqPjO3Yhf+fxeAi2AStkIThM6YdMd7sJMuLW1kLbp2DXjinF2wrAmPm+xcFDLIFBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f83d27db526475ba6581b6670c4aad63f136d44955cb52f27502f0113336e253","last_reissued_at":"2026-05-18T03:58:23.347910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:23.347910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1709","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":"2026-05-18T03:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oya8CSBnA/+bKb31/MupnranAg1kEuevE8VLe9WEEfLqWGJzBt3uKU1tWboS55/FNqLwdyS6TwSF5aKsp4x9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:57:27.440924Z"},"content_sha256":"f6b0c5d974c4c5fe2969f31d80ea31f343b38a539ecaf5a9289c839177a4ea05","schema_version":"1.0","event_id":"sha256:f6b0c5d974c4c5fe2969f31d80ea31f343b38a539ecaf5a9289c839177a4ea05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7A6SPW2SMR23UZMBWZTQYSVNMP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient-based estimation of Manning's friction coefficient from noisy data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.NA","authors_text":"Bangti Jin, Hany Radwan, Matthias Gehre, Nathan Collier, Victor M. Calo","submitted_at":"2012-04-08T04:44:40Z","abstract_excerpt":"We study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1709","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":"2026-05-18T03:58:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BO/3KJdAc9GlnL1y+ai+GZZD0ujQ6VRAANWgChvC2BMdltsZMaYIT5tdCHkfd7AMgVnP0imBaDjWUGjb1kCOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:57:27.441261Z"},"content_sha256":"1daa23ff8a132d6c6c6cef80a495913ac595de8916a486b13ff1aeb2aacb5a31","schema_version":"1.0","event_id":"sha256:1daa23ff8a132d6c6c6cef80a495913ac595de8916a486b13ff1aeb2aacb5a31"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/bundle.json","state_url":"https://pith.science/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/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":"2026-05-31T09:57:27Z","links":{"resolver":"https://pith.science/pith/7A6SPW2SMR23UZMBWZTQYSVNMP","bundle":"https://pith.science/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/bundle.json","state":"https://pith.science/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7A6SPW2SMR23UZMBWZTQYSVNMP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7A6SPW2SMR23UZMBWZTQYSVNMP","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":"a62afdd9268090ba2cbe8009296b036bb6f7bed340ab5c8aa53b47509b5bc0f5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-08T04:44:40Z","title_canon_sha256":"58a067f0c3fba244893abb1a5769df92b078ec42342c9a52dc4fdb25efef7223"},"schema_version":"1.0","source":{"id":"1204.1709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1709","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1709v1","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1709","created_at":"2026-05-18T03:58:23Z"},{"alias_kind":"pith_short_12","alias_value":"7A6SPW2SMR23","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7A6SPW2SMR23UZMB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7A6SPW2S","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:1daa23ff8a132d6c6c6cef80a495913ac595de8916a486b13ff1aeb2aacb5a31","target":"graph","created_at":"2026-05-18T03:58:23Z","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 study the numerical recovery of Manning's roughness coefficient for the diffusive wave approximation of the shallow water equation. We describe a conjugate gradient method for the numerical inversion. Numerical results for one-dimensional model are presented to illustrate the feasibility of the approach. Also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory.","authors_text":"Bangti Jin, Hany Radwan, Matthias Gehre, Nathan Collier, Victor M. Calo","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-08T04:44:40Z","title":"Gradient-based estimation of Manning's friction coefficient from noisy data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1709","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:f6b0c5d974c4c5fe2969f31d80ea31f343b38a539ecaf5a9289c839177a4ea05","target":"record","created_at":"2026-05-18T03:58:23Z","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":"a62afdd9268090ba2cbe8009296b036bb6f7bed340ab5c8aa53b47509b5bc0f5","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-04-08T04:44:40Z","title_canon_sha256":"58a067f0c3fba244893abb1a5769df92b078ec42342c9a52dc4fdb25efef7223"},"schema_version":"1.0","source":{"id":"1204.1709","kind":"arxiv","version":1}},"canonical_sha256":"f83d27db526475ba6581b6670c4aad63f136d44955cb52f27502f0113336e253","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f83d27db526475ba6581b6670c4aad63f136d44955cb52f27502f0113336e253","first_computed_at":"2026-05-18T03:58:23.347910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:23.347910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P+/fETX/8QSHTCmJH2akTqPjO3Yhf+fxeAi2AStkIThM6YdMd7sJMuLW1kLbp2DXjinF2wrAmPm+xcFDLIFBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:23.348469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6b0c5d974c4c5fe2969f31d80ea31f343b38a539ecaf5a9289c839177a4ea05","sha256:1daa23ff8a132d6c6c6cef80a495913ac595de8916a486b13ff1aeb2aacb5a31"],"state_sha256":"37b5c2944302e2c15f58c5d92adfc75eedeae0f7026c549b46aecbe7d9ff24cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72GEfapbDnGYef/E1ECTub3sj2WBiCIjonjj8MNx5AAHWxVpCNJeZXIEjjvWLV9JqTlUQZw9SfCNA/3LPYafDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:57:27.443174Z","bundle_sha256":"5b6244cf661143859b78ced37922d75de483be64bd2e0dbdb91c2cb7e941a7b3"}}