{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IXSWWK4LJ5D2ZDAHP6CN7HM5AW","short_pith_number":"pith:IXSWWK4L","canonical_record":{"source":{"id":"1709.02652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T11:20:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6ed24329bae39e68c2c68705855333825cbc8ce37ec9df79487bbb9eadba7416","abstract_canon_sha256":"eaf5edf215557d8946b2dfa529f77c73036ed792dda9a84f758ff5ff4a001a04"},"schema_version":"1.0"},"canonical_sha256":"45e56b2b8b4f47ac8c077f84df9d9d05bbb4014ff685b3a35af68ab575ce29bb","source":{"kind":"arxiv","id":"1709.02652","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02652","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02652v2","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02652","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"IXSWWK4LJ5D2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXSWWK4LJ5D2ZDAH","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXSWWK4L","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IXSWWK4LJ5D2ZDAHP6CN7HM5AW","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02652","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T11:20:17Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6ed24329bae39e68c2c68705855333825cbc8ce37ec9df79487bbb9eadba7416","abstract_canon_sha256":"eaf5edf215557d8946b2dfa529f77c73036ed792dda9a84f758ff5ff4a001a04"},"schema_version":"1.0"},"canonical_sha256":"45e56b2b8b4f47ac8c077f84df9d9d05bbb4014ff685b3a35af68ab575ce29bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:27.167354Z","signature_b64":"EHpYFlw8pmR3kndaxqrL1of5fpzxO149JzDcAXymff7BeJczItv+C1wqVoY97qkywiMkTh1k6USmhi8FBtpRCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45e56b2b8b4f47ac8c077f84df9d9d05bbb4014ff685b3a35af68ab575ce29bb","last_reissued_at":"2026-05-18T00:17:27.166752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:27.166752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02652","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYLzCTj6fqNG4pBGdoe1CMYqKGnYXK9RKqoK58L8xRfX7hslxGgU5YaUJdj4FWHFjRpzRQGlL+ZtJaofzwyrCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:09:30.809922Z"},"content_sha256":"f4e280baa93857f737f161a595c972a18ef835dd8bba662c55feaf78976eb26f","schema_version":"1.0","event_id":"sha256:f4e280baa93857f737f161a595c972a18ef835dd8bba662c55feaf78976eb26f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IXSWWK4LJ5D2ZDAHP6CN7HM5AW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Andrea Marchese, Dominik Inauen","submitted_at":"2017-09-08T11:20:17Z","abstract_excerpt":"In this paper we extend the results of \"A strong minimax property of nondegenerate minimal submanifolds\" by White, where it is proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in a certain geodesic tubular neighbourhood. We prove a similar result, replacing the tubular neighbourhood with one induced by the flat distance and we provide quantitative estimates. Our proof is based on the introduction of a penalized minimization problem, in the spirit of \"A selection principle for the sharp quantita"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02652","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":"2026-05-18T00:17:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1iY6ZUKIetaS/OcIyhEmioKZBuVKlYUOE83qiSszOY7WH21fZCTxJcBW1aF3Ss4qWWdKim+6oBhAxle18PgAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:09:30.810261Z"},"content_sha256":"57d1a821128fa17faf7895284ee547f47df0477ffa0a6dc31dd573ef289e60b7","schema_version":"1.0","event_id":"sha256:57d1a821128fa17faf7895284ee547f47df0477ffa0a6dc31dd573ef289e60b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/bundle.json","state_url":"https://pith.science/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/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":"2026-06-01T20:09:30Z","links":{"resolver":"https://pith.science/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW","bundle":"https://pith.science/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/bundle.json","state":"https://pith.science/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IXSWWK4LJ5D2ZDAHP6CN7HM5AW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IXSWWK4LJ5D2ZDAHP6CN7HM5AW","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":"eaf5edf215557d8946b2dfa529f77c73036ed792dda9a84f758ff5ff4a001a04","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T11:20:17Z","title_canon_sha256":"6ed24329bae39e68c2c68705855333825cbc8ce37ec9df79487bbb9eadba7416"},"schema_version":"1.0","source":{"id":"1709.02652","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02652","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02652v2","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02652","created_at":"2026-05-18T00:17:27Z"},{"alias_kind":"pith_short_12","alias_value":"IXSWWK4LJ5D2","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IXSWWK4LJ5D2ZDAH","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IXSWWK4L","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:57d1a821128fa17faf7895284ee547f47df0477ffa0a6dc31dd573ef289e60b7","target":"graph","created_at":"2026-05-18T00:17:27Z","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 paper we extend the results of \"A strong minimax property of nondegenerate minimal submanifolds\" by White, where it is proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric functional, is the unique minimizer in a certain geodesic tubular neighbourhood. We prove a similar result, replacing the tubular neighbourhood with one induced by the flat distance and we provide quantitative estimates. Our proof is based on the introduction of a penalized minimization problem, in the spirit of \"A selection principle for the sharp quantita","authors_text":"Andrea Marchese, Dominik Inauen","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T11:20:17Z","title":"Quantitative minimality of strictly stable extremal submanifolds in a flat neighbourhood"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02652","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:f4e280baa93857f737f161a595c972a18ef835dd8bba662c55feaf78976eb26f","target":"record","created_at":"2026-05-18T00:17:27Z","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":"eaf5edf215557d8946b2dfa529f77c73036ed792dda9a84f758ff5ff4a001a04","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-08T11:20:17Z","title_canon_sha256":"6ed24329bae39e68c2c68705855333825cbc8ce37ec9df79487bbb9eadba7416"},"schema_version":"1.0","source":{"id":"1709.02652","kind":"arxiv","version":2}},"canonical_sha256":"45e56b2b8b4f47ac8c077f84df9d9d05bbb4014ff685b3a35af68ab575ce29bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45e56b2b8b4f47ac8c077f84df9d9d05bbb4014ff685b3a35af68ab575ce29bb","first_computed_at":"2026-05-18T00:17:27.166752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:27.166752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHpYFlw8pmR3kndaxqrL1of5fpzxO149JzDcAXymff7BeJczItv+C1wqVoY97qkywiMkTh1k6USmhi8FBtpRCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:27.167354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02652","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4e280baa93857f737f161a595c972a18ef835dd8bba662c55feaf78976eb26f","sha256:57d1a821128fa17faf7895284ee547f47df0477ffa0a6dc31dd573ef289e60b7"],"state_sha256":"7d77cc0f97df57291bb1ac82bfacc05ba4b9b404389eed434969a0963b38c787"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+1/fMhaTz9ROYXAEZoFRu1WI8HFbsUHJnK8LJYYWqFEp6heA1cpanv6fPfiyF6r48tw74ij/kv+jwTqKU0OUCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:09:30.812158Z","bundle_sha256":"ad3223d7cf054e7d760547de969e28a8708c509a064aeb4da7f2352ba3c726db"}}