{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BJXZVOMKQ6GI255ZR7HP7OUOPO","short_pith_number":"pith:BJXZVOMK","canonical_record":{"source":{"id":"1610.08933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T19:05:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cb8e04cac9d0647647486fdb854651f592cee13b1468b7ff3a03f23e8a30c1f5","abstract_canon_sha256":"6daea360fb343d94447b25d27efe7824437ec0b30c1bdbf87ac846223da7bc9a"},"schema_version":"1.0"},"canonical_sha256":"0a6f9ab98a878c8d77b98fceffba8e7b80fb97fba671eb3ad0d259c89436bb40","source":{"kind":"arxiv","id":"1610.08933","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08933","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08933v3","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08933","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"BJXZVOMKQ6GI","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BJXZVOMKQ6GI255Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BJXZVOMK","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BJXZVOMKQ6GI255ZR7HP7OUOPO","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08933","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T19:05:13Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cb8e04cac9d0647647486fdb854651f592cee13b1468b7ff3a03f23e8a30c1f5","abstract_canon_sha256":"6daea360fb343d94447b25d27efe7824437ec0b30c1bdbf87ac846223da7bc9a"},"schema_version":"1.0"},"canonical_sha256":"0a6f9ab98a878c8d77b98fceffba8e7b80fb97fba671eb3ad0d259c89436bb40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:41.964734Z","signature_b64":"WkGYwlSSSaXg0hXA4VPbozb91rW2hdEaYsWiTyOpnDRxa3Cj9cpc7LbKtcDrd312vGLK/6RiIzdNFq2+CCS7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a6f9ab98a878c8d77b98fceffba8e7b80fb97fba671eb3ad0d259c89436bb40","last_reissued_at":"2026-05-18T00:31:41.963960Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:41.963960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08933","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":"2026-05-18T00:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OvLdSlBWqK2/ATKskPEunrfHd5B4kaFGXyZ3SwPAPRbVynNgAz8ZelGKU+2bXFDsMdKiRNekwKjpI63uqMD7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:58:20.405525Z"},"content_sha256":"e4f9c33626d3076e536daeec0ea420d0bfc0ba34df357854148902c644007fc7","schema_version":"1.0","event_id":"sha256:e4f9c33626d3076e536daeec0ea420d0bfc0ba34df357854148902c644007fc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BJXZVOMKQ6GI255ZR7HP7OUOPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behavior of flows by powers of the Gaussian curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Kyeongsu Choi, Panagiota Daskalopoulos, Simon Brendle","submitted_at":"2016-10-27T19:05:13Z","abstract_excerpt":"We consider a one-parameter family of strictly convex hypersurfaces in $\\mathbb{R}^{n+1}$ moving with speed $- K^\\alpha \\nu$, where $\\nu$ denotes the outward-pointing unit normal vector and $\\alpha \\geq \\frac{1}{n+2}$. For $\\alpha > \\frac{1}{n+2}$, we show that the flow converges to a round sphere after rescaling. In the affine invariant case $\\alpha=\\frac{1}{n+2}$, our arguments give an alternative proof of the fact that the flow converges to an ellipsoid after rescaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08933","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":"2026-05-18T00:31:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rj9zXRGU+7TKeXnU9bWxkQ6Bx0qUwpVryu/8c/YExLs3NFl9+xCE+dLG+dMN2vpi6wMn8jWiyz4LNRORp0HHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:58:20.406202Z"},"content_sha256":"932372c2ec6757ea98429ed981f3e5d6e56378ef0c9ee541db2d5b1d782670a4","schema_version":"1.0","event_id":"sha256:932372c2ec6757ea98429ed981f3e5d6e56378ef0c9ee541db2d5b1d782670a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/bundle.json","state_url":"https://pith.science/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/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":"2026-06-06T20:58:20Z","links":{"resolver":"https://pith.science/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO","bundle":"https://pith.science/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/bundle.json","state":"https://pith.science/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJXZVOMKQ6GI255ZR7HP7OUOPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BJXZVOMKQ6GI255ZR7HP7OUOPO","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":"6daea360fb343d94447b25d27efe7824437ec0b30c1bdbf87ac846223da7bc9a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T19:05:13Z","title_canon_sha256":"cb8e04cac9d0647647486fdb854651f592cee13b1468b7ff3a03f23e8a30c1f5"},"schema_version":"1.0","source":{"id":"1610.08933","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08933","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08933v3","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08933","created_at":"2026-05-18T00:31:41Z"},{"alias_kind":"pith_short_12","alias_value":"BJXZVOMKQ6GI","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BJXZVOMKQ6GI255Z","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BJXZVOMK","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:932372c2ec6757ea98429ed981f3e5d6e56378ef0c9ee541db2d5b1d782670a4","target":"graph","created_at":"2026-05-18T00:31:41Z","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 consider a one-parameter family of strictly convex hypersurfaces in $\\mathbb{R}^{n+1}$ moving with speed $- K^\\alpha \\nu$, where $\\nu$ denotes the outward-pointing unit normal vector and $\\alpha \\geq \\frac{1}{n+2}$. For $\\alpha > \\frac{1}{n+2}$, we show that the flow converges to a round sphere after rescaling. In the affine invariant case $\\alpha=\\frac{1}{n+2}$, our arguments give an alternative proof of the fact that the flow converges to an ellipsoid after rescaling.","authors_text":"Kyeongsu Choi, Panagiota Daskalopoulos, Simon Brendle","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T19:05:13Z","title":"Asymptotic behavior of flows by powers of the Gaussian curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08933","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:e4f9c33626d3076e536daeec0ea420d0bfc0ba34df357854148902c644007fc7","target":"record","created_at":"2026-05-18T00:31:41Z","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":"6daea360fb343d94447b25d27efe7824437ec0b30c1bdbf87ac846223da7bc9a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-27T19:05:13Z","title_canon_sha256":"cb8e04cac9d0647647486fdb854651f592cee13b1468b7ff3a03f23e8a30c1f5"},"schema_version":"1.0","source":{"id":"1610.08933","kind":"arxiv","version":3}},"canonical_sha256":"0a6f9ab98a878c8d77b98fceffba8e7b80fb97fba671eb3ad0d259c89436bb40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6f9ab98a878c8d77b98fceffba8e7b80fb97fba671eb3ad0d259c89436bb40","first_computed_at":"2026-05-18T00:31:41.963960Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:41.963960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WkGYwlSSSaXg0hXA4VPbozb91rW2hdEaYsWiTyOpnDRxa3Cj9cpc7LbKtcDrd312vGLK/6RiIzdNFq2+CCS7CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:41.964734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08933","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4f9c33626d3076e536daeec0ea420d0bfc0ba34df357854148902c644007fc7","sha256:932372c2ec6757ea98429ed981f3e5d6e56378ef0c9ee541db2d5b1d782670a4"],"state_sha256":"67bcfca5a4d81c8e34fd12bbb59d4b947b553802d3c1d3fe445973924c126af5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lG/BYPBW9DjzeWwWylqZA9ef2hwdcNGDzavQb5d6V0wKkYOLpdjLuxn1/jPwsaTugWwa2lJBdIbxR7O/u+nAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:58:20.410453Z","bundle_sha256":"907621bd05a0af0e9a5626be16cac13a646acd28436a3173eb57634ed9c10621"}}