{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TRTGOIPKU5QQ3D4Y4UUEJ5KF6N","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":"7dded8f7a854697781d8d5485a3c190308c81a03a3e99e6826fb1abdb35a3c4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-25T02:53:21Z","title_canon_sha256":"69581b033273df8b312e0afb527b04c6f853f432c50c59fc3ea1cc2c04734782"},"schema_version":"1.0","source":{"id":"1302.5983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5983","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5983v1","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5983","created_at":"2026-05-18T03:32:32Z"},{"alias_kind":"pith_short_12","alias_value":"TRTGOIPKU5QQ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TRTGOIPKU5QQ3D4Y","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TRTGOIPK","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:dc50d09bbedce7b62e2de972dc7f89dda4d5b596ce655164975771c79a9a1a5b","target":"graph","created_at":"2026-05-18T03:32:32Z","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":"Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation which relates constant mean curvature surfaces and time-invariant pressure distribution graphs constrained by the Darcy-Forchheimer law. We therein established a direct relationship between the CMC graph equation and a certain family of equations which we call $g$-Forchheimer equations. The corresponding results, on fast flows and their geometric interpretati","authors_text":"Akif Ibragimov, Eugenio Aulisa, Magdalena Toda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-25T02:53:21Z","title":"Geometric Methods in the Analysis on Non-linear Flows in Porous Media (Preliminary Version)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5983","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":"sha256:088061ba6b0a52733ea0ff259222ed1766a21126f95cdca7848c7d54cedb26e1","target":"record","created_at":"2026-05-18T03:32:32Z","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":"7dded8f7a854697781d8d5485a3c190308c81a03a3e99e6826fb1abdb35a3c4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-25T02:53:21Z","title_canon_sha256":"69581b033273df8b312e0afb527b04c6f853f432c50c59fc3ea1cc2c04734782"},"schema_version":"1.0","source":{"id":"1302.5983","kind":"arxiv","version":1}},"canonical_sha256":"9c666721eaa7610d8f98e52844f545f3434d8d6ad5a3b3db6a46854532fb955b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c666721eaa7610d8f98e52844f545f3434d8d6ad5a3b3db6a46854532fb955b","first_computed_at":"2026-05-18T03:32:32.978036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:32.978036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ke+ZCI9LkoAp7Vxn4nv0UiBY9IMwM16iqiYujGIISgusNsduCkoWjffS8PbZhatSiTLy8GBmchFQj5smHGjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:32.978665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:088061ba6b0a52733ea0ff259222ed1766a21126f95cdca7848c7d54cedb26e1","sha256:dc50d09bbedce7b62e2de972dc7f89dda4d5b596ce655164975771c79a9a1a5b"],"state_sha256":"ee6cbac6a70cbe5dfd7524be3bd9b2decfe6726425c9cab455c252b74979b6fb"}