{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X7FGFVZNKMAS4W7DDU2AGZG4SP","short_pith_number":"pith:X7FGFVZN","canonical_record":{"source":{"id":"1709.06665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T22:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"be901b12d59ebaa589e6bfb46bd24d4daeb86d986905ff7f31285f96515a75b9","abstract_canon_sha256":"525ab0466becaed1c71f197c5e09a8063db79aa04089fd85be9979970b3f48e9"},"schema_version":"1.0"},"canonical_sha256":"bfca62d72d53012e5be31d340364dc93d2f292e41011eadf6ea9badc10b84f13","source":{"kind":"arxiv","id":"1709.06665","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06665","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06665v1","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06665","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"pith_short_12","alias_value":"X7FGFVZNKMAS","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X7FGFVZNKMAS4W7D","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X7FGFVZN","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X7FGFVZNKMAS4W7DDU2AGZG4SP","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T22:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"be901b12d59ebaa589e6bfb46bd24d4daeb86d986905ff7f31285f96515a75b9","abstract_canon_sha256":"525ab0466becaed1c71f197c5e09a8063db79aa04089fd85be9979970b3f48e9"},"schema_version":"1.0"},"canonical_sha256":"bfca62d72d53012e5be31d340364dc93d2f292e41011eadf6ea9badc10b84f13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:40.867218Z","signature_b64":"4QZgfHvQOHqxSCjKcxI+InDRRK8ecCPnhvwVPcUUtZYTEDqBpl9CQJt4vav4VNAIW8yGVKox+UGjfcxvkKQcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfca62d72d53012e5be31d340364dc93d2f292e41011eadf6ea9badc10b84f13","last_reissued_at":"2026-05-18T00:34:40.866500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:40.866500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06665","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":"2026-05-18T00:34:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42KvfiwvAi7kmOYPzrFICjXDzmA1o0jB6akR5K1D/k8lNAmV+TALFifhLwEgU4Frm7pc9BzxnOrzyKojv6L4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:02.862072Z"},"content_sha256":"f4b6db7924adbcd456d86f9cb5b48611a7f8e1a3581c8a4ba4051082c400a734","schema_version":"1.0","event_id":"sha256:f4b6db7924adbcd456d86f9cb5b48611a7f8e1a3581c8a4ba4051082c400a734"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X7FGFVZNKMAS4W7DDU2AGZG4SP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inverse mean curvature evolution of entire graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gerhard Huisken, Panagiota Daskalopoulos","submitted_at":"2017-09-19T22:38:07Z","abstract_excerpt":"We study the evolution of strictly mean-convex entire graphs over $R^n$ by Inverse Mean Curvature flow. First we establish the global existence of starshaped entire graphs with superlinear growth at infinity. The main result in this work concerns the critical case of asymptotically conical entire convex graphs. In this case we show that there exists a time $ T < +\\infty$, which depends on the growth at infinity of the initial data, such that the unique solution of the flow exists for all $t < T$. Moreover, as $t \\to T$ the solution converges to a flat plane. Our techniques exploit the ultra-fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06665","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":""},"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":"2026-05-18T00:34:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MiuN5KlRwTWEI44JwzB+AlDaSiQMLK/XSutbzmonkKIk077t4RrrjVsK8QgXWLBgB/t2E3nEc5l7H+Wbex2/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:48:02.862717Z"},"content_sha256":"08c24cf4dc7f7b62a5f6954c8829553fed96809d658ce790539e84b5bb027c2b","schema_version":"1.0","event_id":"sha256:08c24cf4dc7f7b62a5f6954c8829553fed96809d658ce790539e84b5bb027c2b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/bundle.json","state_url":"https://pith.science/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/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":"2026-06-01T06:48:02Z","links":{"resolver":"https://pith.science/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP","bundle":"https://pith.science/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/bundle.json","state":"https://pith.science/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7FGFVZNKMAS4W7DDU2AGZG4SP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X7FGFVZNKMAS4W7DDU2AGZG4SP","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":"525ab0466becaed1c71f197c5e09a8063db79aa04089fd85be9979970b3f48e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T22:38:07Z","title_canon_sha256":"be901b12d59ebaa589e6bfb46bd24d4daeb86d986905ff7f31285f96515a75b9"},"schema_version":"1.0","source":{"id":"1709.06665","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06665","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06665v1","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06665","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"pith_short_12","alias_value":"X7FGFVZNKMAS","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X7FGFVZNKMAS4W7D","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X7FGFVZN","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:08c24cf4dc7f7b62a5f6954c8829553fed96809d658ce790539e84b5bb027c2b","target":"graph","created_at":"2026-05-18T00:34:40Z","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 study the evolution of strictly mean-convex entire graphs over $R^n$ by Inverse Mean Curvature flow. First we establish the global existence of starshaped entire graphs with superlinear growth at infinity. The main result in this work concerns the critical case of asymptotically conical entire convex graphs. In this case we show that there exists a time $ T < +\\infty$, which depends on the growth at infinity of the initial data, such that the unique solution of the flow exists for all $t < T$. Moreover, as $t \\to T$ the solution converges to a flat plane. Our techniques exploit the ultra-fa","authors_text":"Gerhard Huisken, Panagiota Daskalopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T22:38:07Z","title":"Inverse mean curvature evolution of entire graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06665","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:f4b6db7924adbcd456d86f9cb5b48611a7f8e1a3581c8a4ba4051082c400a734","target":"record","created_at":"2026-05-18T00:34:40Z","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":"525ab0466becaed1c71f197c5e09a8063db79aa04089fd85be9979970b3f48e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T22:38:07Z","title_canon_sha256":"be901b12d59ebaa589e6bfb46bd24d4daeb86d986905ff7f31285f96515a75b9"},"schema_version":"1.0","source":{"id":"1709.06665","kind":"arxiv","version":1}},"canonical_sha256":"bfca62d72d53012e5be31d340364dc93d2f292e41011eadf6ea9badc10b84f13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfca62d72d53012e5be31d340364dc93d2f292e41011eadf6ea9badc10b84f13","first_computed_at":"2026-05-18T00:34:40.866500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:40.866500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4QZgfHvQOHqxSCjKcxI+InDRRK8ecCPnhvwVPcUUtZYTEDqBpl9CQJt4vav4VNAIW8yGVKox+UGjfcxvkKQcBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:40.867218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06665","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4b6db7924adbcd456d86f9cb5b48611a7f8e1a3581c8a4ba4051082c400a734","sha256:08c24cf4dc7f7b62a5f6954c8829553fed96809d658ce790539e84b5bb027c2b"],"state_sha256":"dd72fa63440434d6af889ebb22c2205939d8171332362d57b442f4939695d638"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItsmWMhE6Pk84m+h4mjlZDdNxs6jAw8wMzFmvEOF5ytwOZdXBl66XV9pNrhmtO5tdBqi29O8SoYuGdZ/s2JQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:48:02.865595Z","bundle_sha256":"0ce101a06dbd44518369d7b42f0d61744c59c24087bf36a8163030023df0eb64"}}