{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4FTAFXAXW46IPN7UETYOHIC6R3","short_pith_number":"pith:4FTAFXAX","canonical_record":{"source":{"id":"1206.6307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-27T15:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"e09b2746de92de6676ae5e2cfbe28e561c04e4361c06cff2bcf17fd4610308db","abstract_canon_sha256":"6f8fbcf46ced540ed348f80586058c0a502eb98c6ba1eabf6229e4cfb1b49202"},"schema_version":"1.0"},"canonical_sha256":"e16602dc17b73c87b7f424f0e3a05e8ee5eb4df04e370fc37363b2008080f6be","source":{"kind":"arxiv","id":"1206.6307","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6307","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6307v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6307","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"4FTAFXAXW46I","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FTAFXAXW46IPN7U","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FTAFXAX","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4FTAFXAXW46IPN7UETYOHIC6R3","target":"record","payload":{"canonical_record":{"source":{"id":"1206.6307","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-27T15:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"e09b2746de92de6676ae5e2cfbe28e561c04e4361c06cff2bcf17fd4610308db","abstract_canon_sha256":"6f8fbcf46ced540ed348f80586058c0a502eb98c6ba1eabf6229e4cfb1b49202"},"schema_version":"1.0"},"canonical_sha256":"e16602dc17b73c87b7f424f0e3a05e8ee5eb4df04e370fc37363b2008080f6be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:27.052108Z","signature_b64":"4uk0taTV4tWwPTzgPMElM2fCiKSYlJY/2m6OGx9j6I3hWN14vyvO7Kv82JizU8ag31SXrH26Ph5DDFt5FAYRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e16602dc17b73c87b7f424f0e3a05e8ee5eb4df04e370fc37363b2008080f6be","last_reissued_at":"2026-05-18T03:52:27.051380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:27.051380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.6307","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AzYzPzbfAWRtf27JFdmjZ08yhlbmgHyNpRotqITYs8lMYbh23GWRkw38CV7/QMVUO7sdzMuCjsrckoa5lb/sCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:24:48.886157Z"},"content_sha256":"1c5e431ef1de1c94db99d0c28bfc10fb8b47b232d881128d3a0ac4fef0b6af39","schema_version":"1.0","event_id":"sha256:1c5e431ef1de1c94db99d0c28bfc10fb8b47b232d881128d3a0ac4fef0b6af39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4FTAFXAXW46IPN7UETYOHIC6R3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alessio Figalli, Eris Runa, Luigi Ambrosio","submitted_at":"2012-06-27T15:25:36Z","abstract_excerpt":"We study sets of finite perimeter in Wiener space, and prove that at almost every point (with respect to the perimeter measure) a set of finite perimeter blows-up to a halfspace."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6307","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dVZb3mcnyiP4qOtZbTtQeIKUZ+6YU3NYVaIuci1EdN+8W7lFtdICEd/WKKDEKS2duMocKY5B/V5XitSYjKKMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:24:48.886529Z"},"content_sha256":"92d11f8abddd568ea393fc5c940fa8ddda74035912ba272bf085ad6cd6ecb4bd","schema_version":"1.0","event_id":"sha256:92d11f8abddd568ea393fc5c940fa8ddda74035912ba272bf085ad6cd6ecb4bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4FTAFXAXW46IPN7UETYOHIC6R3/bundle.json","state_url":"https://pith.science/pith/4FTAFXAXW46IPN7UETYOHIC6R3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4FTAFXAXW46IPN7UETYOHIC6R3/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":"2026-06-05T09:24:48Z","links":{"resolver":"https://pith.science/pith/4FTAFXAXW46IPN7UETYOHIC6R3","bundle":"https://pith.science/pith/4FTAFXAXW46IPN7UETYOHIC6R3/bundle.json","state":"https://pith.science/pith/4FTAFXAXW46IPN7UETYOHIC6R3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4FTAFXAXW46IPN7UETYOHIC6R3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4FTAFXAXW46IPN7UETYOHIC6R3","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":"6f8fbcf46ced540ed348f80586058c0a502eb98c6ba1eabf6229e4cfb1b49202","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-27T15:25:36Z","title_canon_sha256":"e09b2746de92de6676ae5e2cfbe28e561c04e4361c06cff2bcf17fd4610308db"},"schema_version":"1.0","source":{"id":"1206.6307","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6307","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6307v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6307","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"4FTAFXAXW46I","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4FTAFXAXW46IPN7U","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4FTAFXAX","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:92d11f8abddd568ea393fc5c940fa8ddda74035912ba272bf085ad6cd6ecb4bd","target":"graph","created_at":"2026-05-18T03:52:27Z","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":"We study sets of finite perimeter in Wiener space, and prove that at almost every point (with respect to the perimeter measure) a set of finite perimeter blows-up to a halfspace.","authors_text":"Alessio Figalli, Eris Runa, Luigi Ambrosio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-27T15:25:36Z","title":"On sets of finite perimeter in Wiener spaces: reduced boundary and convergence to halfspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6307","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":"sha256:1c5e431ef1de1c94db99d0c28bfc10fb8b47b232d881128d3a0ac4fef0b6af39","target":"record","created_at":"2026-05-18T03:52:27Z","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":"6f8fbcf46ced540ed348f80586058c0a502eb98c6ba1eabf6229e4cfb1b49202","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-06-27T15:25:36Z","title_canon_sha256":"e09b2746de92de6676ae5e2cfbe28e561c04e4361c06cff2bcf17fd4610308db"},"schema_version":"1.0","source":{"id":"1206.6307","kind":"arxiv","version":1}},"canonical_sha256":"e16602dc17b73c87b7f424f0e3a05e8ee5eb4df04e370fc37363b2008080f6be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e16602dc17b73c87b7f424f0e3a05e8ee5eb4df04e370fc37363b2008080f6be","first_computed_at":"2026-05-18T03:52:27.051380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:27.051380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4uk0taTV4tWwPTzgPMElM2fCiKSYlJY/2m6OGx9j6I3hWN14vyvO7Kv82JizU8ag31SXrH26Ph5DDFt5FAYRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:27.052108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6307","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c5e431ef1de1c94db99d0c28bfc10fb8b47b232d881128d3a0ac4fef0b6af39","sha256:92d11f8abddd568ea393fc5c940fa8ddda74035912ba272bf085ad6cd6ecb4bd"],"state_sha256":"397a3ee69a8362570f33a1da84662ae017dc873b5bd0055a6162f4e4cd682ad0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWJZ+165jP5uqzHwcKUAxcFYbKDBt+QBVhyPFjyJ6hXg0M4zx0XHgKK++66tl2TZRFnegkzJ8NeOch1Y3m3pDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:24:48.888511Z","bundle_sha256":"a2a907fc525071fd2ac2e49741cf437d0e77da553060bbe9430db5a1878e45c7"}}