{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FHY7OOYBTNMNFDZTAWLVHBL3MV","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"94abf35e585cde190bbc2403cb87b3aa59e7efc3f9146f7642c4678681b3d017","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T14:36:19Z","title_canon_sha256":"711f8960cd2fc6e9830af1cea4a88b69cd946668407432da9fc4601e48946802"},"schema_version":"1.0","source":{"id":"2605.13602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13602","created_at":"2026-05-18T02:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13602v1","created_at":"2026-05-18T02:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13602","created_at":"2026-05-18T02:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"FHY7OOYBTNMN","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"FHY7OOYBTNMNFDZT","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"FHY7OOYB","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:41db77ce61d195a7f5f4c4d96ff9902191c2aaf7d6657ee20249754410d50f93","target":"graph","created_at":"2026-05-18T02:44:22Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance; growth is modeled as an irreversible surface deposition process subject to a global mass constraint."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"A time-discrete variational model for accretive surface growth minimizes mean compliance subject to a global mass constraint and yields a constrained gradient flow in the continuous-time limit."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step."}],"snapshot_sha256":"1e221625045ca76f0b7c57b73c91972ecad518378a399a9e234f364c243553d5"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a constrained minimization problem. Growth is modeled as an irreversible surface deposition process subject to a global mass constraint, while the driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance.\n  The approach is illustrated on a linearly elastic cantilever beam whose cross-sectional height evolves thro","authors_text":"Marco Picchi Scardaoni, Roberto Paroni, Rohan Abeyaratne","cross_cats":["math.MP"],"headline":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T14:36:19Z","title":"Surface Growth Driven by an Optimality Criterion"},"references":{"count":38,"internal_anchors":0,"resolved_work":38,"sample":[{"cited_arxiv_id":"","doi":"10.1007/s00158-022-","is_internal_anchor":false,"ref_index":1,"title":"Akerson, A., Bourdin, B., Bhattacharya, K. (2022). Optimal design of responsive structures.Structural and Multidisciplinary Optimization, 65. doi:10.1007/s00158-022- 03202-0","work_id":"4c1f754b-9c05-4c10-998d-03fef692c400","year":2022},{"cited_arxiv_id":"","doi":"10.1016/bs.hna.2020.10.004","is_internal_anchor":false,"ref_index":2,"title":"doi:10.1016/bs.hna.2020.10.004 , author =","work_id":"0e516fd2-0f49-4af9-b4b7-7078e4bdb896","year":2021},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Ambrosi, D., Mollica, F. (2002). On the mechanics of a growing tumor.International Journal of Engineering Science, 40(12), 1297–1316","work_id":"6a63b289-777f-45a2-acdb-ae5f7437bdae","year":2002},{"cited_arxiv_id":"","doi":"10.1177/1081286505059739","is_internal_anchor":false,"ref_index":4,"title":"Ambrosi, D., Guana, F. (2007). Stress-modulated growth.Mathematics and Mechanics of Solids, 12(3), 319–342. doi:10.1177/1081286505059739","work_id":"d82252f3-8052-456b-8dbd-d368e29cc640","year":2007},{"cited_arxiv_id":"","doi":"10.1007/978-3-7643-8722-8","is_internal_anchor":false,"ref_index":5,"title":"Gradient Flows: In Metric Spaces and in the Space of Probability Measures","work_id":"66948f4c-bf3b-4a10-a642-af9d3f03c777","year":2005}],"snapshot_sha256":"84172aced24e6736a92474916133dcbe57d786e2eb3b2eed2f695280298a08ce"},"source":{"id":"2605.13602","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T17:52:11.250111Z","id":"25d4f002-77cc-4c3b-9e47-0a6e5f0e9ccc","model_set":{"reader":"grok-4.3"},"one_line_summary":"A time-discrete variational model for accretive surface growth minimizes mean compliance subject to a global mass constraint and yields a constrained gradient flow in the continuous-time limit.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Surface growth is determined by minimizing structural mean compliance subject to a global mass constraint at each discrete step.","strongest_claim":"Through a formal limiting procedure, we derive from the time-discrete formulation a time-continuous limit in the form of a constrained gradient flow.","weakest_assumption":"The driving mechanism is encoded in an objective functional, here taken to be the structural mean compliance; growth is modeled as an irreversible surface deposition process subject to a global mass constraint."}},"verdict_id":"25d4f002-77cc-4c3b-9e47-0a6e5f0e9ccc"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:401982763d9bf89ee2d7061551c39a8547691628ef324a527dd3340df43bff42","target":"record","created_at":"2026-05-18T02:44:22Z","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":"94abf35e585cde190bbc2403cb87b3aa59e7efc3f9146f7642c4678681b3d017","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T14:36:19Z","title_canon_sha256":"711f8960cd2fc6e9830af1cea4a88b69cd946668407432da9fc4601e48946802"},"schema_version":"1.0","source":{"id":"2605.13602","kind":"arxiv","version":1}},"canonical_sha256":"29f1f73b019b58d28f33059753857b654ee86fb0168648c9c1779b0c2b2bf555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29f1f73b019b58d28f33059753857b654ee86fb0168648c9c1779b0c2b2bf555","first_computed_at":"2026-05-18T02:44:22.905695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:22.905695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHyKZR4C/UhMEuJ2HJt5G3ov0J9duvE9jWJEI63sso6yhxFwKlawQpaUKxIoYir5PsdUfPl8r0BH4MxXv//wCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:22.906105Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13602","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:32e9e18c3bbcb0310fb59e31fcf2256ddeabf62e5d394a56fe422c02e1d6d455","sha256:645449abe7f582950aa3be347ae69c95c7e810a00d521942816a6124c4528bf9","sha256:c910afb8a859ce460c0daeca93da27e3a1a6845fa98da1105e9c1a90cfbd9e57","sha256:ff1513a318bd3d4067416d0f6027b24a6e67d58d9ceff0f90e3a0d31a989d4d4"]}],"invalid_events":[],"applied_event_ids":["sha256:401982763d9bf89ee2d7061551c39a8547691628ef324a527dd3340df43bff42","sha256:41db77ce61d195a7f5f4c4d96ff9902191c2aaf7d6657ee20249754410d50f93"],"state_sha256":"42d378c203930b150acc1f74c5e36cc71947a29a9714232519a22d4ce554d597"}