{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CNG5ASWMJGMHSXMHCZYYX2FHT3","short_pith_number":"pith:CNG5ASWM","canonical_record":{"source":{"id":"1405.4230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"a9c6e8af0a378f09a74d444e18e1019d81c9077f39484083cdc9c90f6b0e4275","abstract_canon_sha256":"808d4b6828b58cdade08bfd913bf38f28182dc9f38b754c2accef723f17b7b4a"},"schema_version":"1.0"},"canonical_sha256":"134dd04acc4998795d8716718be8a79ed28eefba270f522a682543935bcfaf17","source":{"kind":"arxiv","id":"1405.4230","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4230","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4230v1","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4230","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"CNG5ASWMJGMH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CNG5ASWMJGMHSXMH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CNG5ASWM","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CNG5ASWMJGMHSXMHCZYYX2FHT3","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:21:41Z","cross_cats_sorted":[],"title_canon_sha256":"a9c6e8af0a378f09a74d444e18e1019d81c9077f39484083cdc9c90f6b0e4275","abstract_canon_sha256":"808d4b6828b58cdade08bfd913bf38f28182dc9f38b754c2accef723f17b7b4a"},"schema_version":"1.0"},"canonical_sha256":"134dd04acc4998795d8716718be8a79ed28eefba270f522a682543935bcfaf17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:59.459490Z","signature_b64":"tAwc8aLuwhPKXdYWDHaaVrFbtOpbPyl4ZSDry8zuzuNz/rXo0A130dkkgFK/9p8iDdVamK9mnWVqOsQgDVZmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"134dd04acc4998795d8716718be8a79ed28eefba270f522a682543935bcfaf17","last_reissued_at":"2026-05-18T00:21:59.458934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:59.458934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4230","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":"2026-05-18T00:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F1w051d6rfLHCO5ph9P5btrtSQFYbUkg+2+9PmYV4DPmZaYMFGhnJnb0GI2Tz4t7GX7bGmlG3S7rvyPRzeDIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:27:54.904728Z"},"content_sha256":"dd26cbf9b6b30644de1ca6c5330cbaa1069fba36b147639b6efd1227bf8f21ae","schema_version":"1.0","event_id":"sha256:dd26cbf9b6b30644de1ca6c5330cbaa1069fba36b147639b6efd1227bf8f21ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CNG5ASWMJGMHSXMHCZYYX2FHT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Shrinkers With Second Fundamental Form of Constant Length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Qiang Guang","submitted_at":"2014-05-16T16:21:41Z","abstract_excerpt":"In this note, we give a new and simple proof of a result in {\\cite{DX1}} which states that any smooth complete self-shrinker in $\\mathbb{R}^3$ with second fundamental form of constant length must be a generalized cylinder $\\mathbb{S}^k \\times \\mathbb{R}^{2-k}$ for some $k\\leq2$. Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4230","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":"2026-05-18T00:21:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G5UqyZN0uc0KO1LCEKEAUhBIG39xGOhD45c87ReBG9aH2SUxOGtRwsrsu6Ww+4Iqig0jfYRmqSFqh+HthHaXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:27:54.905085Z"},"content_sha256":"ce5609536921352767e0ea93523f34b372312570ac1d3287020032a3fe58021b","schema_version":"1.0","event_id":"sha256:ce5609536921352767e0ea93523f34b372312570ac1d3287020032a3fe58021b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/bundle.json","state_url":"https://pith.science/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/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":"2026-06-09T15:27:54Z","links":{"resolver":"https://pith.science/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3","bundle":"https://pith.science/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/bundle.json","state":"https://pith.science/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNG5ASWMJGMHSXMHCZYYX2FHT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CNG5ASWMJGMHSXMHCZYYX2FHT3","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":"808d4b6828b58cdade08bfd913bf38f28182dc9f38b754c2accef723f17b7b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:21:41Z","title_canon_sha256":"a9c6e8af0a378f09a74d444e18e1019d81c9077f39484083cdc9c90f6b0e4275"},"schema_version":"1.0","source":{"id":"1405.4230","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4230","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4230v1","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4230","created_at":"2026-05-18T00:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"CNG5ASWMJGMH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CNG5ASWMJGMHSXMH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CNG5ASWM","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:ce5609536921352767e0ea93523f34b372312570ac1d3287020032a3fe58021b","target":"graph","created_at":"2026-05-18T00:21:59Z","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":"In this note, we give a new and simple proof of a result in {\\cite{DX1}} which states that any smooth complete self-shrinker in $\\mathbb{R}^3$ with second fundamental form of constant length must be a generalized cylinder $\\mathbb{S}^k \\times \\mathbb{R}^{2-k}$ for some $k\\leq2$. Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions.","authors_text":"Qiang Guang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:21:41Z","title":"Self-Shrinkers With Second Fundamental Form of Constant Length"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4230","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:dd26cbf9b6b30644de1ca6c5330cbaa1069fba36b147639b6efd1227bf8f21ae","target":"record","created_at":"2026-05-18T00:21:59Z","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":"808d4b6828b58cdade08bfd913bf38f28182dc9f38b754c2accef723f17b7b4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:21:41Z","title_canon_sha256":"a9c6e8af0a378f09a74d444e18e1019d81c9077f39484083cdc9c90f6b0e4275"},"schema_version":"1.0","source":{"id":"1405.4230","kind":"arxiv","version":1}},"canonical_sha256":"134dd04acc4998795d8716718be8a79ed28eefba270f522a682543935bcfaf17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"134dd04acc4998795d8716718be8a79ed28eefba270f522a682543935bcfaf17","first_computed_at":"2026-05-18T00:21:59.458934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:59.458934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tAwc8aLuwhPKXdYWDHaaVrFbtOpbPyl4ZSDry8zuzuNz/rXo0A130dkkgFK/9p8iDdVamK9mnWVqOsQgDVZmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:59.459490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4230","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd26cbf9b6b30644de1ca6c5330cbaa1069fba36b147639b6efd1227bf8f21ae","sha256:ce5609536921352767e0ea93523f34b372312570ac1d3287020032a3fe58021b"],"state_sha256":"efd74515fee663be271b5c1200c32ba28fa8ae2f24e378d4384688947eaff749"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q62i6T6Gg9x/nPGvJNWz5/0mGk2vtKcqRGAaznBCsiwhIKO2DioACbsZLv0ihnltjdOEnSYMS8lOSzsxl885Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:27:54.907218Z","bundle_sha256":"cb043f9cce8f290955e3329ca678de2dec804613d93b44cde58d12159e016087"}}