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Solid tumors are poroelastic solids with a chemo-mechanical feedback on growth.Journal of Elasticity, 129(1–2), 107–","work_id":"2dde1156-f6bb-4f61-81a5-850af1f3d1c9","year":2017},{"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":"f9c588537d43ec5e996f974bc2639712dcca933b1eb351037b2652981e2f0a87"},"source":{"id":"2605.13609","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T17:47:01.391632Z","id":"d21e8d19-fd9a-4c67-9b1d-07ebfd8bab45","model_set":{"reader":"grok-4.3"},"one_line_summary":"Volumetric growth in linear elasticity is cast as a constrained optimization problem that determines the growth tensor at each step while satisfying equilibrium, mass balance, and irreversibility.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Volumetric growth in linear elasticity is determined implicitly by constrained optimization rather than by prescribed evolution laws.","strongest_claim":"Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than prescribed through phenomenological evolution laws.","weakest_assumption":"That a suitable objective functional exists which encodes the physical driving mechanism of growth and that the resulting incremental constrained minimization problem remains well-posed under the stated equilibrium, mass-balance, and irreversibility constraints."}},"verdict_id":"d21e8d19-fd9a-4c67-9b1d-07ebfd8bab45"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:10bc043670eda119f20d57e1af5a2fe8a3079bd388ad0387aaf3626c31b467d1","target":"record","created_at":"2026-05-18T02:44:18Z","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":"f18fb868dda3ade6ce6caa3e3bef197b5dabd00687d19baee79e9c56e23ccaf2","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-05-13T14:43:09Z","title_canon_sha256":"da9e201cdc025ed092239cfa0e167626b2cd25abdcee434fb35dc4e753c7c43f"},"schema_version":"1.0","source":{"id":"2605.13609","kind":"arxiv","version":1}},"canonical_sha256":"e9fe46c6bac81f186c34525850334cd99e3b0d2c76038be210af2fb7216f800d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9fe46c6bac81f186c34525850334cd99e3b0d2c76038be210af2fb7216f800d","first_computed_at":"2026-05-18T02:44:18.076055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:18.076055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F0PvnMXvIodbNLnrNmgFl+RNSc5jBIbyXYA/wtpnO0AW35vXLW6JvtYzJiNM69lM3OlZ54/i0SgI3BppIYbYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:18.076515Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13609","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:22fe20720e6a4a67c6fbe62243ba504e62e41ecd58a98551ce6a2eb914124cdf","sha256:5cacfbbd2e2826880a3d14f272733a0c37c97eec6bdcc340f4f768cd43dd248b"]}],"invalid_events":[],"applied_event_ids":["sha256:10bc043670eda119f20d57e1af5a2fe8a3079bd388ad0387aaf3626c31b467d1","sha256:c768343ea6e57c71796505acb770d8e1c182c2e6c91f301aee227c014e872105"],"state_sha256":"20f5eaed672ca8bf9829ed94f3c0e00feacc18351679a7ba041069b497efa57f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEn3PxJOQcrTupG3iczLc8+O2mVuyzKl0sZGVj25BLFZhNnjeIM92oX6wPDzfqFm6DY2W/WlQr+fB1Sm1JDcCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T03:33:14.277655Z","bundle_sha256":"ea94bc6fea9a319f6ff97db5c1e2a6a88bf01e22fd1c91a02a4c450b4e93954d"}}