{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UL3DFHSN4XGEBAZCFHWOJLEUUW","short_pith_number":"pith:UL3DFHSN","canonical_record":{"source":{"id":"1107.4643","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-22T23:11:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8645526345d2ad0dfb0f96ecccec146446d30e366c493d6746c78ed9374e2e40","abstract_canon_sha256":"dde3d19d8c7359ac6d11f3c458562f7ae30ec2a023a478a403b3a4546033e03f"},"schema_version":"1.0"},"canonical_sha256":"a2f6329e4de5cc40832229ece4ac94a5aa52638eb36bce99ffed52fa8f9a2502","source":{"kind":"arxiv","id":"1107.4643","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4643","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4643v3","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4643","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"UL3DFHSN4XGE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UL3DFHSN4XGEBAZC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UL3DFHSN","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UL3DFHSN4XGEBAZCFHWOJLEUUW","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4643","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-22T23:11:14Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8645526345d2ad0dfb0f96ecccec146446d30e366c493d6746c78ed9374e2e40","abstract_canon_sha256":"dde3d19d8c7359ac6d11f3c458562f7ae30ec2a023a478a403b3a4546033e03f"},"schema_version":"1.0"},"canonical_sha256":"a2f6329e4de5cc40832229ece4ac94a5aa52638eb36bce99ffed52fa8f9a2502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:17.692738Z","signature_b64":"RJW5VgG4DDgT/aTQqSn0ckCw8dWjzH2bMO+KZ5pnpbEjydFaT56bxiOPLVUKewGCSaZe/Wi1gR6zUJgPUgtMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2f6329e4de5cc40832229ece4ac94a5aa52638eb36bce99ffed52fa8f9a2502","last_reissued_at":"2026-05-18T04:11:17.692161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:17.692161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4643","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"keCyhAAm/MkEkS02p3aIbAels+XMzddrl5TlQpA91U5DJuX6bN1kkNx8IN5FKQJJ1QH134dDaZES6vj6IH0YDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:36:39.202835Z"},"content_sha256":"188165485d10330fe7b77c66db4921756424b670fe068bdeffc2de123defae78","schema_version":"1.0","event_id":"sha256:188165485d10330fe7b77c66db4921756424b670fe068bdeffc2de123defae78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UL3DFHSN4XGEBAZCFHWOJLEUUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of compact tangent flows in Mean Curvature Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Felix Schulze","submitted_at":"2011-07-22T23:11:14Z","abstract_excerpt":"We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That is the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings. Furthermore, given such a closed, multiplicity-one, smoothly embedded self-similarly shrinker $\\Sigma$, we show that any solution of the rescaled flow, which is sufficiently close to $\\Sigma$, with Gaussian density ratios greater or equal to that of $\\Si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4643","kind":"arxiv","version":3},"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":"2026-05-18T04:11:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gf3gXssgMmOjKvGktfwySUIK4I4Ur0ElOUY/qAtz5yKcDy+pUMcZI4pHsoP/db/pfB+yZ9esEy0W6XHRULSOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:36:39.203566Z"},"content_sha256":"1e465205135e5e112294ed42eb5f5b0990f334571fa8c4878490c9c9ec6b9d21","schema_version":"1.0","event_id":"sha256:1e465205135e5e112294ed42eb5f5b0990f334571fa8c4878490c9c9ec6b9d21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/bundle.json","state_url":"https://pith.science/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/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":"2026-05-26T01:36:39Z","links":{"resolver":"https://pith.science/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW","bundle":"https://pith.science/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/bundle.json","state":"https://pith.science/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UL3DFHSN4XGEBAZCFHWOJLEUUW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UL3DFHSN4XGEBAZCFHWOJLEUUW","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":"dde3d19d8c7359ac6d11f3c458562f7ae30ec2a023a478a403b3a4546033e03f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-22T23:11:14Z","title_canon_sha256":"8645526345d2ad0dfb0f96ecccec146446d30e366c493d6746c78ed9374e2e40"},"schema_version":"1.0","source":{"id":"1107.4643","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4643","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4643v3","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4643","created_at":"2026-05-18T04:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"UL3DFHSN4XGE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UL3DFHSN4XGEBAZC","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UL3DFHSN","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:1e465205135e5e112294ed42eb5f5b0990f334571fa8c4878490c9c9ec6b9d21","target":"graph","created_at":"2026-05-18T04:11:17Z","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 show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That is the limit of the parabolic rescalings does not depend on the chosen sequence of rescalings. Furthermore, given such a closed, multiplicity-one, smoothly embedded self-similarly shrinker $\\Sigma$, we show that any solution of the rescaled flow, which is sufficiently close to $\\Sigma$, with Gaussian density ratios greater or equal to that of $\\Si","authors_text":"Felix Schulze","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-22T23:11:14Z","title":"Uniqueness of compact tangent flows in Mean Curvature Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4643","kind":"arxiv","version":3},"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":"sha256:188165485d10330fe7b77c66db4921756424b670fe068bdeffc2de123defae78","target":"record","created_at":"2026-05-18T04:11:17Z","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":"dde3d19d8c7359ac6d11f3c458562f7ae30ec2a023a478a403b3a4546033e03f","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-07-22T23:11:14Z","title_canon_sha256":"8645526345d2ad0dfb0f96ecccec146446d30e366c493d6746c78ed9374e2e40"},"schema_version":"1.0","source":{"id":"1107.4643","kind":"arxiv","version":3}},"canonical_sha256":"a2f6329e4de5cc40832229ece4ac94a5aa52638eb36bce99ffed52fa8f9a2502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2f6329e4de5cc40832229ece4ac94a5aa52638eb36bce99ffed52fa8f9a2502","first_computed_at":"2026-05-18T04:11:17.692161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:17.692161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RJW5VgG4DDgT/aTQqSn0ckCw8dWjzH2bMO+KZ5pnpbEjydFaT56bxiOPLVUKewGCSaZe/Wi1gR6zUJgPUgtMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:17.692738Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4643","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:188165485d10330fe7b77c66db4921756424b670fe068bdeffc2de123defae78","sha256:1e465205135e5e112294ed42eb5f5b0990f334571fa8c4878490c9c9ec6b9d21"],"state_sha256":"c9eef1036a37a0af06965f546a0549aec2f7cd9ce4fa4627de8f16763cff8947"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUCGKGcImhXIQGQmXtpHZE2bhCkShf3bciYc1SZ8CUjSk2B/MUicPD4ed00Ucz/nHPs7cf1JfGy8RX8NirN4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:36:39.207224Z","bundle_sha256":"4bd96ee5eb38826635ae39eefc2cea67b59196db3e7aa9e6f91655c0c9157cd2"}}