{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KJ4BYNZSGBUAA2RK7FEH6JYY3W","short_pith_number":"pith:KJ4BYNZS","canonical_record":{"source":{"id":"1310.0717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-02T14:33:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dc1a3aa99d8cf2739b993adf59f0d9775972e537ffdfeb0fdb8e8f907b799915","abstract_canon_sha256":"8f950ca2e74c5a4f037eaa9207475dd82fe90350287da25a5c0472c67b9e2046"},"schema_version":"1.0"},"canonical_sha256":"52781c37323068006a2af9487f2718dd9a3b5eb1b09f0bd7afdb9850c5fe0510","source":{"kind":"arxiv","id":"1310.0717","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0717","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0717v2","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0717","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"KJ4BYNZSGBUA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KJ4BYNZSGBUAA2RK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KJ4BYNZS","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KJ4BYNZSGBUAA2RK7FEH6JYY3W","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0717","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-02T14:33:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"dc1a3aa99d8cf2739b993adf59f0d9775972e537ffdfeb0fdb8e8f907b799915","abstract_canon_sha256":"8f950ca2e74c5a4f037eaa9207475dd82fe90350287da25a5c0472c67b9e2046"},"schema_version":"1.0"},"canonical_sha256":"52781c37323068006a2af9487f2718dd9a3b5eb1b09f0bd7afdb9850c5fe0510","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:31.761427Z","signature_b64":"qX0L/ZOMrz61w8gQUI9UNXOvLEDfDvpeW2yA3f56Q6UsOoHE9+QAcSWJmZUSSGUghriUpRoZXu6IvmKwDldsAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52781c37323068006a2af9487f2718dd9a3b5eb1b09f0bd7afdb9850c5fe0510","last_reissued_at":"2026-05-18T03:03:31.760783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:31.760783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0717","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lVuTaDVp0JhB2GGj/lRBKYHqUQImhp4VJppIs2rP/PLdCWJVixQrdX6FyVWpk1UUft/NHcn6xMekYbuFQFAkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:39:25.898883Z"},"content_sha256":"288bd29bd17262b9bccea8c829d2df7e39810e81afa88bbaf319bc5fc728ffea","schema_version":"1.0","event_id":"sha256:288bd29bd17262b9bccea8c829d2df7e39810e81afa88bbaf319bc5fc728ffea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KJ4BYNZSGBUAA2RK7FEH6JYY3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-sided non-collapsing curvature flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Ben Andrews, Mat Langford","submitted_at":"2013-10-02T14:33:40Z","abstract_excerpt":"It was recently proved that embedded solutions of Euclidean hypersurface flows with speeds given by concave (convex), degree one homogeneous functions of the Weingarten map are interior (exterior) non-collapsing. These results were subsequently extended to hypersurface flows in the sphere and hyperbolic space.\n  In the first part of the paper, we show that locally convex solutions are exterior non-collapsing for a larger class of speed functions than previously considered; more precisely, we show that the previous results hold when convexity of the speed function is relaxed to inverse-concavit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0717","kind":"arxiv","version":2},"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":"2026-05-18T03:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djAPL3DsHhazB0ZadGRHOoA0apwIUmDgBDstnser8f536IiML7OE7YaFgM0aSFYfEuo7B1ji20C9CNRQ3BIACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T18:39:25.899486Z"},"content_sha256":"702c24357687e9719a50c379696952ffc1e357e4bfea77b51f7ce916554d3cf5","schema_version":"1.0","event_id":"sha256:702c24357687e9719a50c379696952ffc1e357e4bfea77b51f7ce916554d3cf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/bundle.json","state_url":"https://pith.science/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/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":"2026-06-07T18:39:25Z","links":{"resolver":"https://pith.science/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W","bundle":"https://pith.science/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/bundle.json","state":"https://pith.science/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJ4BYNZSGBUAA2RK7FEH6JYY3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KJ4BYNZSGBUAA2RK7FEH6JYY3W","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":"8f950ca2e74c5a4f037eaa9207475dd82fe90350287da25a5c0472c67b9e2046","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-02T14:33:40Z","title_canon_sha256":"dc1a3aa99d8cf2739b993adf59f0d9775972e537ffdfeb0fdb8e8f907b799915"},"schema_version":"1.0","source":{"id":"1310.0717","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0717","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0717v2","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0717","created_at":"2026-05-18T03:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"KJ4BYNZSGBUA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KJ4BYNZSGBUAA2RK","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KJ4BYNZS","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:702c24357687e9719a50c379696952ffc1e357e4bfea77b51f7ce916554d3cf5","target":"graph","created_at":"2026-05-18T03:03:31Z","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":"It was recently proved that embedded solutions of Euclidean hypersurface flows with speeds given by concave (convex), degree one homogeneous functions of the Weingarten map are interior (exterior) non-collapsing. These results were subsequently extended to hypersurface flows in the sphere and hyperbolic space.\n  In the first part of the paper, we show that locally convex solutions are exterior non-collapsing for a larger class of speed functions than previously considered; more precisely, we show that the previous results hold when convexity of the speed function is relaxed to inverse-concavit","authors_text":"Ben Andrews, Mat Langford","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-02T14:33:40Z","title":"Two-sided non-collapsing curvature flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0717","kind":"arxiv","version":2},"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":"sha256:288bd29bd17262b9bccea8c829d2df7e39810e81afa88bbaf319bc5fc728ffea","target":"record","created_at":"2026-05-18T03:03:31Z","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":"8f950ca2e74c5a4f037eaa9207475dd82fe90350287da25a5c0472c67b9e2046","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-10-02T14:33:40Z","title_canon_sha256":"dc1a3aa99d8cf2739b993adf59f0d9775972e537ffdfeb0fdb8e8f907b799915"},"schema_version":"1.0","source":{"id":"1310.0717","kind":"arxiv","version":2}},"canonical_sha256":"52781c37323068006a2af9487f2718dd9a3b5eb1b09f0bd7afdb9850c5fe0510","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52781c37323068006a2af9487f2718dd9a3b5eb1b09f0bd7afdb9850c5fe0510","first_computed_at":"2026-05-18T03:03:31.760783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:31.760783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qX0L/ZOMrz61w8gQUI9UNXOvLEDfDvpeW2yA3f56Q6UsOoHE9+QAcSWJmZUSSGUghriUpRoZXu6IvmKwDldsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:31.761427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0717","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:288bd29bd17262b9bccea8c829d2df7e39810e81afa88bbaf319bc5fc728ffea","sha256:702c24357687e9719a50c379696952ffc1e357e4bfea77b51f7ce916554d3cf5"],"state_sha256":"a17aec623975321cd7bc61a596a0a0e382885e399de33e317ce65bf13f5b4909"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1KhKplSjXTtjORLeqno/GBREGP+ti68muYtGv/XONbJrPbLfOvc8JUo46Nx8qSlUMm+wvlnF6z+uocQDh5WmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T18:39:25.902896Z","bundle_sha256":"eefbf69c423e567b54e031850d3233e8486221c1b00029d072f32f1a9ed5641f"}}