{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YX3VOAE7KVCHA56TMT5Y67PRZ6","short_pith_number":"pith:YX3VOAE7","canonical_record":{"source":{"id":"1703.07087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T08:07:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d72f0b37154af6a0b76429a9409a2f5ad977b68c90a78090a08d8f547fc87da8","abstract_canon_sha256":"213a03b26f6bb1a1ed7ce327b10b938f392b99e9ce715d03eabb420982a0a8fc"},"schema_version":"1.0"},"canonical_sha256":"c5f757009f55447077d364fb8f7df1cf9e31a6bf037d7599b56eafdb3ef5ba0f","source":{"kind":"arxiv","id":"1703.07087","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07087","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07087v3","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07087","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"pith_short_12","alias_value":"YX3VOAE7KVCH","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YX3VOAE7KVCHA56T","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YX3VOAE7","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YX3VOAE7KVCHA56TMT5Y67PRZ6","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07087","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T08:07:35Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"d72f0b37154af6a0b76429a9409a2f5ad977b68c90a78090a08d8f547fc87da8","abstract_canon_sha256":"213a03b26f6bb1a1ed7ce327b10b938f392b99e9ce715d03eabb420982a0a8fc"},"schema_version":"1.0"},"canonical_sha256":"c5f757009f55447077d364fb8f7df1cf9e31a6bf037d7599b56eafdb3ef5ba0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:22.346469Z","signature_b64":"xzclo1V89EqmSV/IOr/h4gWOgozMZx/xO8ikJdcu62kdzdOYOp4i1XbkRPFA8BVr4gGc+IJswME8jAkxbn+ICQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5f757009f55447077d364fb8f7df1cf9e31a6bf037d7599b56eafdb3ef5ba0f","last_reissued_at":"2026-05-17T23:41:22.345813Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:22.345813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07087","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yuA++N3tT+8ny06VAA81cmbxSyZpYLUgLZfUF5wFKZvCrsFWYFSNNVCQcBhsMyKFBskrq9xFDcNaSEe9NZEEDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:10:46.126413Z"},"content_sha256":"efb6a3f67c406e2a5d073ab47b5ad74cee7425d186be954f135607ab004e47b5","schema_version":"1.0","event_id":"sha256:efb6a3f67c406e2a5d073ab47b5ad74cee7425d186be954f135607ab004e47b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YX3VOAE7KVCHA56TMT5Y67PRZ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Heiko Kr\\\"oner, Julian Scheuer","submitted_at":"2017-03-21T08:07:35Z","abstract_excerpt":"We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07087","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:41:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"drxy9RvtUfp6ow1eZCw3E/3hGMNvYn0HIBU2nJfMM7ETZbaaB2rqmAngahMOJA6GTbSsCdR+d/He7xHjhN3DCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:10:46.126774Z"},"content_sha256":"3406ee1327d9a4920aec547004cd19166b524adb10d3c0aaa0965dc21d662b72","schema_version":"1.0","event_id":"sha256:3406ee1327d9a4920aec547004cd19166b524adb10d3c0aaa0965dc21d662b72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/bundle.json","state_url":"https://pith.science/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/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":"2026-05-30T08:10:46Z","links":{"resolver":"https://pith.science/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6","bundle":"https://pith.science/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/bundle.json","state":"https://pith.science/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YX3VOAE7KVCHA56TMT5Y67PRZ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YX3VOAE7KVCHA56TMT5Y67PRZ6","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":"213a03b26f6bb1a1ed7ce327b10b938f392b99e9ce715d03eabb420982a0a8fc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T08:07:35Z","title_canon_sha256":"d72f0b37154af6a0b76429a9409a2f5ad977b68c90a78090a08d8f547fc87da8"},"schema_version":"1.0","source":{"id":"1703.07087","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07087","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07087v3","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07087","created_at":"2026-05-17T23:41:22Z"},{"alias_kind":"pith_short_12","alias_value":"YX3VOAE7KVCH","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YX3VOAE7KVCHA56T","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YX3VOAE7","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:3406ee1327d9a4920aec547004cd19166b524adb10d3c0aaa0965dc21d662b72","target":"graph","created_at":"2026-05-17T23:41:22Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power","authors_text":"Heiko Kr\\\"oner, Julian Scheuer","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T08:07:35Z","title":"Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07087","kind":"arxiv","version":3},"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:efb6a3f67c406e2a5d073ab47b5ad74cee7425d186be954f135607ab004e47b5","target":"record","created_at":"2026-05-17T23:41:22Z","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":"213a03b26f6bb1a1ed7ce327b10b938f392b99e9ce715d03eabb420982a0a8fc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-21T08:07:35Z","title_canon_sha256":"d72f0b37154af6a0b76429a9409a2f5ad977b68c90a78090a08d8f547fc87da8"},"schema_version":"1.0","source":{"id":"1703.07087","kind":"arxiv","version":3}},"canonical_sha256":"c5f757009f55447077d364fb8f7df1cf9e31a6bf037d7599b56eafdb3ef5ba0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5f757009f55447077d364fb8f7df1cf9e31a6bf037d7599b56eafdb3ef5ba0f","first_computed_at":"2026-05-17T23:41:22.345813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:22.345813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xzclo1V89EqmSV/IOr/h4gWOgozMZx/xO8ikJdcu62kdzdOYOp4i1XbkRPFA8BVr4gGc+IJswME8jAkxbn+ICQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:22.346469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07087","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efb6a3f67c406e2a5d073ab47b5ad74cee7425d186be954f135607ab004e47b5","sha256:3406ee1327d9a4920aec547004cd19166b524adb10d3c0aaa0965dc21d662b72"],"state_sha256":"80162fdca9f74c9ba4dea3cff17111de71285f83bff6dec696eaf7f9621f810e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bm4+2oEh4hny3qJXdR/CzCoqNoora7elaXuDrw03ZMgD/QPFl4LuthF2P/8R42i0xzchNDpqdtI7drH5DIdsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:10:46.128995Z","bundle_sha256":"af1a10341de84b699bcb1950627c1ebd66f844333970825a9092dd0cfc8ef4dd"}}