{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:73H6KLMF7E4ZN5HWTDMSPAFEZM","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":"07396a9d969ead03cb4ea3c1c0eadfd88dc5fa81c8b9a4082e26eef7599f605a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T12:43:26Z","title_canon_sha256":"8476aa1df1daeaa96e3ade8806ea54d5d0f8471016861f231e457c3f8986aa7f"},"schema_version":"1.0","source":{"id":"2606.10793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.10793","created_at":"2026-06-10T01:10:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.10793v1","created_at":"2026-06-10T01:10:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10793","created_at":"2026-06-10T01:10:40Z"},{"alias_kind":"pith_short_12","alias_value":"73H6KLMF7E4Z","created_at":"2026-06-10T01:10:40Z"},{"alias_kind":"pith_short_16","alias_value":"73H6KLMF7E4ZN5HW","created_at":"2026-06-10T01:10:40Z"},{"alias_kind":"pith_short_8","alias_value":"73H6KLMF","created_at":"2026-06-10T01:10:40Z"}],"graph_snapshots":[{"event_id":"sha256:3eb510a4f81488fd72d6a360bb2ea513609e8216202c37233479d55b41660f95","target":"graph","created_at":"2026-06-10T01:10:40Z","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/2606.10793/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a one-sided degenerate Cahn-Hilliard equation with anisotropic traction flux, arising as a reduced continuum description of mechanically biased cell interactions in digit-forming organoids. The equation combines a one-sided degenerate mobility with a density-weighted anisotropic higher-order transport term. This traction term is not generated by the variational derivative of the Cahn-Hilliard energy and therefore produces sign-indefinite contributions in the energy balance. For nonnegative initial data, we prove the global-in-time existence of nonnegative weak solutions. The proof com","authors_text":"Marvin Fritz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T12:43:26Z","title":"Global weak solutions of a one-sided degenerate Cahn-Hilliard model for traction-driven digit morphogenesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10793","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":"sha256:08e28eb113d5b3b84475b1a474e99f575aaa7de9bdd65032b74acf4971fd3ed3","target":"record","created_at":"2026-06-10T01:10:40Z","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":"07396a9d969ead03cb4ea3c1c0eadfd88dc5fa81c8b9a4082e26eef7599f605a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-09T12:43:26Z","title_canon_sha256":"8476aa1df1daeaa96e3ade8806ea54d5d0f8471016861f231e457c3f8986aa7f"},"schema_version":"1.0","source":{"id":"2606.10793","kind":"arxiv","version":1}},"canonical_sha256":"fecfe52d85f93996f4f698d92780a4cb04a1b5ddc264a23d0bab8e4100c66fa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fecfe52d85f93996f4f698d92780a4cb04a1b5ddc264a23d0bab8e4100c66fa0","first_computed_at":"2026-06-10T01:10:40.888404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:10:40.888404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OnZeOhEpHNXtMpz5wB3qir5RJ2P6R19i2S7SXYa1ox/O8rg4iWLYDZjLJEj1xeMu194n680DkbVU6eN3tqOeCg==","signature_status":"signed_v1","signed_at":"2026-06-10T01:10:40.889286Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.10793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08e28eb113d5b3b84475b1a474e99f575aaa7de9bdd65032b74acf4971fd3ed3","sha256:3eb510a4f81488fd72d6a360bb2ea513609e8216202c37233479d55b41660f95"],"state_sha256":"ac7eb101993fca74560ce07ae5108e8b32e17e8079efd76f4c17cd6d3a1ec5a9"}