{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VA34H77AGZ4XC5ZARV4WR6266I","short_pith_number":"pith:VA34H77A","canonical_record":{"source":{"id":"1505.00183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-01T14:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"b4ba7c14ac18210849488e0e6c8784021a4cd5c640a5b5a59f517555067fa56c","abstract_canon_sha256":"7e8b86b6e96fbd8bc98428bf5e016d2cbebff8591c8ba4870d83c2bf2fb0f30c"},"schema_version":"1.0"},"canonical_sha256":"a837c3ffe036797177208d7968fb5ef20af8d40c47bd7fdd23b705cd4783bf90","source":{"kind":"arxiv","id":"1505.00183","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00183","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00183v2","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00183","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"VA34H77AGZ4X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VA34H77AGZ4XC5ZA","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VA34H77A","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VA34H77AGZ4XC5ZARV4WR6266I","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00183","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-01T14:18:18Z","cross_cats_sorted":[],"title_canon_sha256":"b4ba7c14ac18210849488e0e6c8784021a4cd5c640a5b5a59f517555067fa56c","abstract_canon_sha256":"7e8b86b6e96fbd8bc98428bf5e016d2cbebff8591c8ba4870d83c2bf2fb0f30c"},"schema_version":"1.0"},"canonical_sha256":"a837c3ffe036797177208d7968fb5ef20af8d40c47bd7fdd23b705cd4783bf90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.361310Z","signature_b64":"f8K0OI1KOPOEik+3I0EkAuNDe69C1Q/5yvMXDrZkKLnZo6Lq9DTMM10RczGUqBNLcVL9k8XLCPGfbYm/U+XUDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a837c3ffe036797177208d7968fb5ef20af8d40c47bd7fdd23b705cd4783bf90","last_reissued_at":"2026-05-18T01:05:46.360780Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.360780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00183","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j97c+FCd07D/tyTbuKyyLprAsX8v71KtmKSRomg7W4YgyuWJUF74AHPZ0cbN5IGNoqseBuInSCx4hdST4FFrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:25:28.230914Z"},"content_sha256":"f97e27fd93e3368df1cd8d48b645dc4988904b23e21ffe0ada573cd3cf3dc575","schema_version":"1.0","event_id":"sha256:f97e27fd93e3368df1cd8d48b645dc4988904b23e21ffe0ada573cd3cf3dc575"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VA34H77AGZ4XC5ZARV4WR6266I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solitons for the inverse mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Glen Wheeler, Gregory Drugan, Hojoo Lee","submitted_at":"2015-05-01T14:18:18Z","abstract_excerpt":"We investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. In the case of one dimensional planar solitons, we explicitly classify all homothetic solitons and translators. Generalizing Andrews' theorem that circles are the only compact homothetic planar solitons, we apply the Hsiung-Minkowski integral formula to prove the rigidity of the hypersphere in the class of compact expanders of codimension one. We also establish that the moduli space of compact expanding surfaces of codimension two is big. Finally, we update the list of Huisken-Ilmanen's rotational expa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00183","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HaaeDpZJaw8w5dVyi3B1f+uX8G/cUt2NKIlQwpuFB9SsTc5HfKqNmxqL6SlJPuRrJ+K2tMXE2aqXvWRHD8SAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:25:28.231612Z"},"content_sha256":"7df95fe35f99043505e061c3302a212ec716b1ad8320c77fad1f97d93fc21248","schema_version":"1.0","event_id":"sha256:7df95fe35f99043505e061c3302a212ec716b1ad8320c77fad1f97d93fc21248"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VA34H77AGZ4XC5ZARV4WR6266I/bundle.json","state_url":"https://pith.science/pith/VA34H77AGZ4XC5ZARV4WR6266I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VA34H77AGZ4XC5ZARV4WR6266I/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":"2026-05-28T21:25:28Z","links":{"resolver":"https://pith.science/pith/VA34H77AGZ4XC5ZARV4WR6266I","bundle":"https://pith.science/pith/VA34H77AGZ4XC5ZARV4WR6266I/bundle.json","state":"https://pith.science/pith/VA34H77AGZ4XC5ZARV4WR6266I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VA34H77AGZ4XC5ZARV4WR6266I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VA34H77AGZ4XC5ZARV4WR6266I","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":"7e8b86b6e96fbd8bc98428bf5e016d2cbebff8591c8ba4870d83c2bf2fb0f30c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-01T14:18:18Z","title_canon_sha256":"b4ba7c14ac18210849488e0e6c8784021a4cd5c640a5b5a59f517555067fa56c"},"schema_version":"1.0","source":{"id":"1505.00183","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00183","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00183v2","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00183","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"VA34H77AGZ4X","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VA34H77AGZ4XC5ZA","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VA34H77A","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:7df95fe35f99043505e061c3302a212ec716b1ad8320c77fad1f97d93fc21248","target":"graph","created_at":"2026-05-18T01:05:46Z","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 investigate self-similar solutions to the inverse mean curvature flow in Euclidean space. In the case of one dimensional planar solitons, we explicitly classify all homothetic solitons and translators. Generalizing Andrews' theorem that circles are the only compact homothetic planar solitons, we apply the Hsiung-Minkowski integral formula to prove the rigidity of the hypersphere in the class of compact expanders of codimension one. We also establish that the moduli space of compact expanding surfaces of codimension two is big. Finally, we update the list of Huisken-Ilmanen's rotational expa","authors_text":"Glen Wheeler, Gregory Drugan, Hojoo Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-01T14:18:18Z","title":"Solitons for the inverse mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00183","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:f97e27fd93e3368df1cd8d48b645dc4988904b23e21ffe0ada573cd3cf3dc575","target":"record","created_at":"2026-05-18T01:05:46Z","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":"7e8b86b6e96fbd8bc98428bf5e016d2cbebff8591c8ba4870d83c2bf2fb0f30c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-01T14:18:18Z","title_canon_sha256":"b4ba7c14ac18210849488e0e6c8784021a4cd5c640a5b5a59f517555067fa56c"},"schema_version":"1.0","source":{"id":"1505.00183","kind":"arxiv","version":2}},"canonical_sha256":"a837c3ffe036797177208d7968fb5ef20af8d40c47bd7fdd23b705cd4783bf90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a837c3ffe036797177208d7968fb5ef20af8d40c47bd7fdd23b705cd4783bf90","first_computed_at":"2026-05-18T01:05:46.360780Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.360780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f8K0OI1KOPOEik+3I0EkAuNDe69C1Q/5yvMXDrZkKLnZo6Lq9DTMM10RczGUqBNLcVL9k8XLCPGfbYm/U+XUDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.361310Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00183","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f97e27fd93e3368df1cd8d48b645dc4988904b23e21ffe0ada573cd3cf3dc575","sha256:7df95fe35f99043505e061c3302a212ec716b1ad8320c77fad1f97d93fc21248"],"state_sha256":"e8bbad547f81485e7a91a7b2ee75ed6cdacf39f293efe1bbb1cf2ce2644e644b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrKl4oNyROE0iUQI/4pKhuIwMabOM26uTfj3GKLiP6/Q6yOZcs9N3Jyf4XwjLwlDHiId5zDslOkdr47YmlMSCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:25:28.235246Z","bundle_sha256":"ab1d91b133cfb03bdb948aa95ae4cc5c83fdeb6fed49cfa609518527347006b3"}}