{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LZNBSR7Y2RPGUUZ5CSSNCRFBT7","short_pith_number":"pith:LZNBSR7Y","canonical_record":{"source":{"id":"1710.00433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"a368c03e11bcb5b9c86b923de24ea3650f64e9f11af5282eca818733097ffabf","abstract_canon_sha256":"3bc5bb3a55ff2e0694b16938c54f0895aaa9af0b04c610add91828eae6371dc8"},"schema_version":"1.0"},"canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","source":{"kind":"arxiv","id":"1710.00433","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00433","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00433v2","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00433","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"LZNBSR7Y2RPG","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZNBSR7Y2RPGUUZ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZNBSR7Y","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LZNBSR7Y2RPGUUZ5CSSNCRFBT7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"a368c03e11bcb5b9c86b923de24ea3650f64e9f11af5282eca818733097ffabf","abstract_canon_sha256":"3bc5bb3a55ff2e0694b16938c54f0895aaa9af0b04c610add91828eae6371dc8"},"schema_version":"1.0"},"canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:56.220433Z","signature_b64":"kaa858h7lsh3jymL265va+7GG1AqBQ03V/lPLxK9CxjZERKMZNWFgAFYxXcQJVdwZYU61V8D9Wsen0QwwnD8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","last_reissued_at":"2026-05-17T23:58:56.220011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:56.220011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00433","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":"2026-05-17T23:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o36aDSeHWf4Z2W4nB7l9cZg0BkUcTxHY6PKN3xJOnmOq8zzFXm695B8dyeFfMHRNSaCQVjbQGhZbGgBUhYUTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:52:47.493439Z"},"content_sha256":"1fd5eebf6b2cda1816a827db7f08e63d00adc93884836dfb48e0af863426e305","schema_version":"1.0","event_id":"sha256:1fd5eebf6b2cda1816a827db7f08e63d00adc93884836dfb48e0af863426e305"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LZNBSR7Y2RPGUUZ5CSSNCRFBT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A strong stability condition on minimal submanifolds and its implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chung-Jun Tsai, Mu-Tao Wang","submitted_at":"2017-10-01T23:13:02Z","abstract_excerpt":"We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a C^1 neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem [arXiv:1605.03645] which applies only to calibrated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00433","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":"2026-05-17T23:58:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikc4DSNAAE/nCny0s6hL//Vzke77bks27ZERvc/C5liSycq30iA85DOHrV/NGRMWRDCzWBlUvOtOgbewO8n3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:52:47.493788Z"},"content_sha256":"e4ff0b9e0da0dce95e2e5b40a9ae5cba786d3e281eaf7d3668a72115e8553293","schema_version":"1.0","event_id":"sha256:e4ff0b9e0da0dce95e2e5b40a9ae5cba786d3e281eaf7d3668a72115e8553293"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/bundle.json","state_url":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/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":"2026-07-02T12:52:47Z","links":{"resolver":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7","bundle":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/bundle.json","state":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LZNBSR7Y2RPGUUZ5CSSNCRFBT7","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":"3bc5bb3a55ff2e0694b16938c54f0895aaa9af0b04c610add91828eae6371dc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","title_canon_sha256":"a368c03e11bcb5b9c86b923de24ea3650f64e9f11af5282eca818733097ffabf"},"schema_version":"1.0","source":{"id":"1710.00433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00433","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00433v2","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00433","created_at":"2026-05-17T23:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"LZNBSR7Y2RPG","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZNBSR7Y2RPGUUZ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZNBSR7Y","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:e4ff0b9e0da0dce95e2e5b40a9ae5cba786d3e281eaf7d3668a72115e8553293","target":"graph","created_at":"2026-05-17T23:58:56Z","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 identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a C^1 neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem [arXiv:1605.03645] which applies only to calibrated","authors_text":"Chung-Jun Tsai, Mu-Tao Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","title":"A strong stability condition on minimal submanifolds and its implications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00433","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":"sha256:1fd5eebf6b2cda1816a827db7f08e63d00adc93884836dfb48e0af863426e305","target":"record","created_at":"2026-05-17T23:58:56Z","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":"3bc5bb3a55ff2e0694b16938c54f0895aaa9af0b04c610add91828eae6371dc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","title_canon_sha256":"a368c03e11bcb5b9c86b923de24ea3650f64e9f11af5282eca818733097ffabf"},"schema_version":"1.0","source":{"id":"1710.00433","kind":"arxiv","version":2}},"canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","first_computed_at":"2026-05-17T23:58:56.220011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:56.220011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kaa858h7lsh3jymL265va+7GG1AqBQ03V/lPLxK9CxjZERKMZNWFgAFYxXcQJVdwZYU61V8D9Wsen0QwwnD8AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:56.220433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fd5eebf6b2cda1816a827db7f08e63d00adc93884836dfb48e0af863426e305","sha256:e4ff0b9e0da0dce95e2e5b40a9ae5cba786d3e281eaf7d3668a72115e8553293"],"state_sha256":"c76e9e8b274205c8463993bd246cef15d2cb7316b0698b632e9eb5bd6cb0c94b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxQFOH6JBjBradUIZ/a+jIg1YoLLZ2AUcesBfJmxq7YDFBjlEywDHegrkY96boGljIzRInnPPkbqfbhssywyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:52:47.495729Z","bundle_sha256":"273618b864fce4af9b9230f081296f470ecaaf30f8f5f890a253862a05382c74"}}