{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","short_pith_number":"pith:CKZCYBVI","canonical_record":{"source":{"id":"2607.27711","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-30T05:45:40Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"157b0412ddf32196e8ee120b99a98235dd0aabcdfbebe7699ab5a417ff9215da","abstract_canon_sha256":"aee2a127a233e4eb8924f1899d2e610a81250c7d488df480e073ebe7d47e04fd"},"schema_version":"1.0"},"canonical_sha256":"12b22c06a847039f28f254a1e19a5f1941e10631edbe816e778fc04dbefe1d6f","source":{"kind":"arxiv","id":"2607.27711","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27711","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27711v1","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27711","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"CKZCYBVII4BZ","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_16","alias_value":"CKZCYBVII4BZ6KHS","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_8","alias_value":"CKZCYBVI","created_at":"2026-07-31T01:29:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27711","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-30T05:45:40Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"157b0412ddf32196e8ee120b99a98235dd0aabcdfbebe7699ab5a417ff9215da","abstract_canon_sha256":"aee2a127a233e4eb8924f1899d2e610a81250c7d488df480e073ebe7d47e04fd"},"schema_version":"1.0"},"canonical_sha256":"12b22c06a847039f28f254a1e19a5f1941e10631edbe816e778fc04dbefe1d6f","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b22c06a847039f28f254a1e19a5f1941e10631edbe816e778fc04dbefe1d6f","last_reissued_at":"2026-07-31T01:29:59.313652Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:29:59.313652Z"},"source_kind":"arxiv","source_id":"2607.27711","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":"2026-07-31T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9gPOUS/cMyE27/8qLDDXUbbhEd2n855dIr0se6SlP9l5wbL39F/IlMiIqqOG7uAZM6wEamD8v3OBVYv0muzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.015604Z"},"content_sha256":"28f33b79a3e138aa1c0c5f4f46a02e7ef174bbf1d2ad8b41eb3d84cf7b981e42","schema_version":"1.0","event_id":"sha256:28f33b79a3e138aa1c0c5f4f46a02e7ef174bbf1d2ad8b41eb3d84cf7b981e42"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contraction Maps Generated by Inverse Mean Curvature Flow","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Bang-Xian Han, Zhuo-Nan Zhu","submitted_at":"2026-07-30T05:45:40Z","abstract_excerpt":"We use inverse mean curvature flow to construct normalized-area-preserving Lipschitz contractions, in an approach analogous in spirit to the heat-flow construction of Kim and E. Milman. This yields contractions from the round sphere onto closed strictly convex hypersurfaces in the sphere, and from the flat disk onto strictly convex free-boundary hypersurfaces in the Euclidean ball.\n  In dimension two, this proves E. Milman's contraction conjecture for Riemannian two-spheres and gives an analogous intrinsic result for nonnegatively curved disks whose boundary has geodesic curvature one. These m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27711","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.27711/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-31T01:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGHxFEVKLINmSo3FsaOOgE22uJHaKip5vFgE4Xo3ptB0lPcFifjzT+7ViVLRaVZSrLT3/SgdGcMcwK7cnvCkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.016108Z"},"content_sha256":"69ac9d30d5f5b71807492d5624bea9f53186b2392305bdebdcada9291afe7901","schema_version":"1.0","event_id":"sha256:69ac9d30d5f5b71807492d5624bea9f53186b2392305bdebdcada9291afe7901"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00205-018-1282-9) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"R. Kupferman, C. Maor, and A. Shachar,Reshetnyak rigidity for Riemannian mani- folds, Arch. Ration. Mech. Anal.231(2019), no. 1, 367–408, doi:10.1007/s00205-018- 1282-9","arxiv_id":"2607.27711","detector":"doi_compliance","evidence":{"ref_index":17,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s00205-018-","reconstructed_doi":"10.1007/s00205-018-1282-9"},"severity":"advisory","ref_index":17,"audited_at":"2026-08-01T03:01:58.485036Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00205-018-1282-9","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"a493de515ad68a4d8d519582080ef9494de8bfb437cb38ba88f3afeca87ca10a","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14965,"payload_sha256":"7ac9f23f5692575087fc92569af84c34a2b3d229ad6a062cd8040c3aced77e58","signature_b64":"Os31cLv81Uer4IykQu0n5hp8Uscu8mXs1GkZsBuw+KyFQWL4kgbP+W7Rru4zV6IOyq5WzkyQEQe1kDS7RcOQBQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oerVhuO+NCRNby7Bjfqnqhz10Q1QlHdsQ3foGi2zwJmHrl13uhRmLuAOQ5cZTV/HkA+BSj8E82v/Am8VWegoAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.020370Z"},"content_sha256":"990877f5c493aae311da20ac3d2b11862b12f16e79bd742a8d95f63770560983","schema_version":"1.0","event_id":"sha256:990877f5c493aae311da20ac3d2b11862b12f16e79bd742a8d95f63770560983"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00526-021-02173-5) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"T. K¨ orber,A free boundary isometric embedding problem in the unit ball, Calc. Var. Par- tial Differential Equations61(2022), no. 2, Article No. 50, 36 pp., doi:10.1007/s00526- 021-02173-5","arxiv_id":"2607.27711","detector":"doi_compliance","evidence":{"ref_index":16,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s00526-","reconstructed_doi":"10.1007/s00526-021-02173-5"},"severity":"advisory","ref_index":16,"audited_at":"2026-08-01T03:01:58.485036Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00526-021-02173-5","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"e8d6416edf30be1f450a4a82cc0daad8dd41f4d4f78c1cd927c09a1b6fbacc4f","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14964,"payload_sha256":"897c7052e34ba0986b6d7ff4dadffa93c35d227bf7a1dd7921ffe6089fb43707","signature_b64":"myHVU5/l0V2ig6qy3DXYzQOp+/vzRp0wPvDaZSVDHTjy50IRaOw+E7nOJYDLuT9WRXsrGjGEX88ESXvq7uiLAg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdEPzzlf15dnj38/CzJ9vZHKPabYpta/0r0PhAqDy3lifqDzAOPcvlzOt874H1Y/xhv/rRynBkVhcT6hXi2aAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.020798Z"},"content_sha256":"c3df28d5317ce474ae0dc14f5cafa586dc985386c482226e7b762115766b6b12","schema_version":"1.0","event_id":"sha256:c3df28d5317ce474ae0dc14f5cafa586dc985386c482226e7b762115766b6b12"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00208-011-0749-x) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Y.-H. Kim and E. Milman,A generalization of Caffarelli’s contraction theorem via (reverse) heat flow, Math. Ann.354(2012), no. 3, 827–862, doi:10.1007/s00208-011- 0749-x","arxiv_id":"2607.27711","detector":"doi_compliance","evidence":{"ref_index":14,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s00208-011-","reconstructed_doi":"10.1007/s00208-011-0749-x"},"severity":"advisory","ref_index":14,"audited_at":"2026-08-01T03:01:58.485036Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00208-011-0749-x","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"35a20edb6ac501c9111478b1f1a70c2dabdc4fcab2dd1f721ac153b3876a4b71","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14963,"payload_sha256":"61e1a9684391eb322b0b3c363240a8db132a696ee04ab2203e1531ef27c664b9","signature_b64":"1GsQpyDOjZVw5PN0JYolU6jmwlrgeVZ3l665th6h8eE126xXQrodYsQGRbmTILCqBmBQd7HQHUUlgqJ7DKHPDg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NpA9rgMBkrWkgMgsj8+Jq5fLasqYgstDNKbXAMd/kYeXmtPFfVcwqDqTq3VE+UxkDzSIJ9YIhy75gDm1NBIHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.021191Z"},"content_sha256":"a48c1324416562c90f787647d57054b753bc3c24b7aa3dde5ffa8024edbc1195","schema_version":"1.0","event_id":"sha256:a48c1324416562c90f787647d57054b753bc3c24b7aa3dde5ffa8024edbc1195"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11118-025-10243-y) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"V. Gimeno i Garcia and F. Gonz´ alez-Ib´ a˜ nez,Evolution of the torsional rigidity under geometric flows, Potential Anal.64(2026), Article No. 29, doi:10.1007/s11118-025- 10243-y","arxiv_id":"2607.27711","detector":"doi_compliance","evidence":{"ref_index":11,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11118-025-","reconstructed_doi":"10.1007/s11118-025-10243-y"},"severity":"advisory","ref_index":11,"audited_at":"2026-08-01T03:01:58.485036Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11118-025-10243-y","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"b15df8aeab89a85c48969571849f3053a87f7b275741abaeddc9a5389501b9ab","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14962,"payload_sha256":"b06db523923aa15280450d14cb7a995122c1d25b5064711000b25a46acf57560","signature_b64":"TSvElHZUxC2Sxgrz9hlaOc4/CJ+QQAFVUyYw4lZdvV5nxLvFVNA09V8/8uB0dX0gkRJX3Wkn029JYjsIY+V3Bw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBK8Pcaw8toBOyUDCKSwarNcXIcCo33oi6JF90oXnFqwKCoBZGDdEeI9UoZfRCBMKaAQUGcUp0kQ8r7iF3kvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.021627Z"},"content_sha256":"cf743258740aa65b462369e1076edd06591df0243d409b969ffeecce836300a4","schema_version":"1.0","event_id":"sha256:cf743258740aa65b462369e1076edd06591df0243d409b969ffeecce836300a4"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/978-0-8176-4583-0) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"M. Gromov,Metric Structures for Riemannian and Non-Riemannian Spaces, Modern Birkh¨ auser Classics, Birkh¨ auser Boston, Boston, MA, 2007, doi:10.1007/978-0-8176- 4583-0","arxiv_id":"2607.27711","detector":"doi_compliance","evidence":{"ref_index":10,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/978-0-8176-","reconstructed_doi":"10.1007/978-0-8176-4583-0"},"severity":"advisory","ref_index":10,"audited_at":"2026-08-01T03:01:58.485036Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/978-0-8176-4583-0","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"18f23dbbcee9825a3e858b4c45afe8f74037c647d8caada6095952dc5cb2aad8","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":14961,"payload_sha256":"b456a104f3b9d2c16a65513245cf5456a048ff4403bba5b1b749f200ada884d1","signature_b64":"+HXgloVxKDFP4/pK6O7TYHM/5t2EQj8EV7T/OrKkk0FuFFLbUVhbeQ5Jn/wwZYnenGH2vg792/6oo0huQvKKBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-01T03:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X5dzMF3zgYuqWCUSNUUrzkHAmWa12XmsS8NCFfn3P7OkOQ7Iyf0G5T6qpLLSmI6rycaHzGrvRHnASRq5gdkbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T13:49:36.022003Z"},"content_sha256":"43d3df4edf3386b52fdc1334ba5fe0000904ea7383e0743e4cf204292ae87ea8","schema_version":"1.0","event_id":"sha256:43d3df4edf3386b52fdc1334ba5fe0000904ea7383e0743e4cf204292ae87ea8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/bundle.json","state_url":"https://pith.science/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/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":"2026-08-21T13:49:36Z","links":{"resolver":"https://pith.science/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF","bundle":"https://pith.science/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/bundle.json","state":"https://pith.science/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKZCYBVII4BZ6KHSKSQ6DGS7DF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CKZCYBVII4BZ6KHSKSQ6DGS7DF","merge_version":"pith-open-graph-merge-v1","event_count":7,"valid_event_count":7,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aee2a127a233e4eb8924f1899d2e610a81250c7d488df480e073ebe7d47e04fd","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-30T05:45:40Z","title_canon_sha256":"157b0412ddf32196e8ee120b99a98235dd0aabcdfbebe7699ab5a417ff9215da"},"schema_version":"1.0","source":{"id":"2607.27711","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27711","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27711v1","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27711","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"CKZCYBVII4BZ","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_16","alias_value":"CKZCYBVII4BZ6KHS","created_at":"2026-07-31T01:29:59Z"},{"alias_kind":"pith_short_8","alias_value":"CKZCYBVI","created_at":"2026-07-31T01:29:59Z"}],"graph_snapshots":[{"event_id":"sha256:69ac9d30d5f5b71807492d5624bea9f53186b2392305bdebdcada9291afe7901","target":"graph","created_at":"2026-07-31T01:29:59Z","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/2607.27711/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use inverse mean curvature flow to construct normalized-area-preserving Lipschitz contractions, in an approach analogous in spirit to the heat-flow construction of Kim and E. Milman. This yields contractions from the round sphere onto closed strictly convex hypersurfaces in the sphere, and from the flat disk onto strictly convex free-boundary hypersurfaces in the Euclidean ball.\n  In dimension two, this proves E. Milman's contraction conjecture for Riemannian two-spheres and gives an analogous intrinsic result for nonnegatively curved disks whose boundary has geodesic curvature one. These m","authors_text":"Bang-Xian Han, Zhuo-Nan Zhu","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-30T05:45:40Z","title":"Contraction Maps Generated by Inverse Mean Curvature Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27711","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":"sha256:28f33b79a3e138aa1c0c5f4f46a02e7ef174bbf1d2ad8b41eb3d84cf7b981e42","target":"record","created_at":"2026-07-31T01:29:59Z","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":"aee2a127a233e4eb8924f1899d2e610a81250c7d488df480e073ebe7d47e04fd","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-30T05:45:40Z","title_canon_sha256":"157b0412ddf32196e8ee120b99a98235dd0aabcdfbebe7699ab5a417ff9215da"},"schema_version":"1.0","source":{"id":"2607.27711","kind":"arxiv","version":1}},"canonical_sha256":"12b22c06a847039f28f254a1e19a5f1941e10631edbe816e778fc04dbefe1d6f","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b22c06a847039f28f254a1e19a5f1941e10631edbe816e778fc04dbefe1d6f","first_computed_at":"2026-07-31T01:29:59.313652Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:29:59.313652Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27711","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:43d3df4edf3386b52fdc1334ba5fe0000904ea7383e0743e4cf204292ae87ea8","sha256:990877f5c493aae311da20ac3d2b11862b12f16e79bd742a8d95f63770560983","sha256:a48c1324416562c90f787647d57054b753bc3c24b7aa3dde5ffa8024edbc1195","sha256:c3df28d5317ce474ae0dc14f5cafa586dc985386c482226e7b762115766b6b12","sha256:cf743258740aa65b462369e1076edd06591df0243d409b969ffeecce836300a4"]}],"invalid_events":[],"applied_event_ids":["sha256:28f33b79a3e138aa1c0c5f4f46a02e7ef174bbf1d2ad8b41eb3d84cf7b981e42","sha256:69ac9d30d5f5b71807492d5624bea9f53186b2392305bdebdcada9291afe7901"],"state_sha256":"bdc4ccf8ec953edf657e7f62cdfe22fc417fdac198636e29b218d96e6a7b297c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sG1I9aC5B3pDMsRbZnOBj3FAU52V9PgV3p1N+uLCVj5lfz7iooK2OCl88Gb4XY7xcWeVFRRj27uN1lWfoVjKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T13:49:36.027206Z","bundle_sha256":"90cbe30871abea0145eaf6b11e93b625997319a31f54daa8def0a2af11f9b977"}}