{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6CPDCL5XQABSXRIHQKVLPWFRP3","short_pith_number":"pith:6CPDCL5X","canonical_record":{"source":{"id":"1204.0750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-03T18:01:50Z","cross_cats_sorted":[],"title_canon_sha256":"e32b609790b5411b32ea44770c3a3987aaab54325bdacb7343915cebeb853723","abstract_canon_sha256":"8340ff169f415b07f722ff340c58aa6550e660a44ac131ee27827feb5f29fe4a"},"schema_version":"1.0"},"canonical_sha256":"f09e312fb780032bc50782aab7d8b17ec3bd1c63a70351f5fbc2d1755a1f7f34","source":{"kind":"arxiv","id":"1204.0750","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0750","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0750v2","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0750","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"6CPDCL5XQABS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6CPDCL5XQABSXRIH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6CPDCL5X","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6CPDCL5XQABSXRIHQKVLPWFRP3","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-03T18:01:50Z","cross_cats_sorted":[],"title_canon_sha256":"e32b609790b5411b32ea44770c3a3987aaab54325bdacb7343915cebeb853723","abstract_canon_sha256":"8340ff169f415b07f722ff340c58aa6550e660a44ac131ee27827feb5f29fe4a"},"schema_version":"1.0"},"canonical_sha256":"f09e312fb780032bc50782aab7d8b17ec3bd1c63a70351f5fbc2d1755a1f7f34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:44.416440Z","signature_b64":"gNfWHgBdp36r9SiICncYvh4dvyO6h0MSNL+RvtrepXkQp85fsd+++au1nUL9B5R5gDwmP1x7FtgjMuz8NbATAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f09e312fb780032bc50782aab7d8b17ec3bd1c63a70351f5fbc2d1755a1f7f34","last_reissued_at":"2026-05-18T03:42:44.415878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:44.415878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0750","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":"2026-05-18T03:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NuiasVJ+Z0rKkixJuAur7B/KagKkbxekWYs+4Lf6k7zgIEsE8fbuTzW2osPPlhh5N/nIkW8Oy2Zr3Nfb2nUOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:48:59.729932Z"},"content_sha256":"dfda842781ab88e2e1fc0f9d91dfc44ef9774212a99687579bc9189998e406a5","schema_version":"1.0","event_id":"sha256:dfda842781ab88e2e1fc0f9d91dfc44ef9774212a99687579bc9189998e406a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6CPDCL5XQABSXRIHQKVLPWFRP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of the $s$-perimeter as $s\\searrow 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessio Figalli, Enrico Valdinoci, Giampiero Palatucci, Serena Dipierro","submitted_at":"2012-04-03T18:01:50Z","abstract_excerpt":"We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\\Omega$ as $s\\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\\Omega$. Moreover, we construct examples of sets for which the limit does not exist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0750","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":"2026-05-18T03:42:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EFLhXuYcFhuybYS1o7hDwnD/OLMXuhaUsRpDXOQD887HNsI5pw2z0R2znVx73oIHkOe42BWkG7j3rjPibU/PAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T04:48:59.730505Z"},"content_sha256":"fdef8a4b49f19ae75883e1e90bdf525b86e63eba05b958fec3362eac38837f1c","schema_version":"1.0","event_id":"sha256:fdef8a4b49f19ae75883e1e90bdf525b86e63eba05b958fec3362eac38837f1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/bundle.json","state_url":"https://pith.science/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/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":"2026-06-05T04:48:59Z","links":{"resolver":"https://pith.science/pith/6CPDCL5XQABSXRIHQKVLPWFRP3","bundle":"https://pith.science/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/bundle.json","state":"https://pith.science/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CPDCL5XQABSXRIHQKVLPWFRP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6CPDCL5XQABSXRIHQKVLPWFRP3","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":"8340ff169f415b07f722ff340c58aa6550e660a44ac131ee27827feb5f29fe4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-03T18:01:50Z","title_canon_sha256":"e32b609790b5411b32ea44770c3a3987aaab54325bdacb7343915cebeb853723"},"schema_version":"1.0","source":{"id":"1204.0750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0750","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0750v2","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0750","created_at":"2026-05-18T03:42:44Z"},{"alias_kind":"pith_short_12","alias_value":"6CPDCL5XQABS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6CPDCL5XQABSXRIH","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6CPDCL5X","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:fdef8a4b49f19ae75883e1e90bdf525b86e63eba05b958fec3362eac38837f1c","target":"graph","created_at":"2026-05-18T03:42:44Z","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 deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\\Omega$ as $s\\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\\Omega$. Moreover, we construct examples of sets for which the limit does not exist.","authors_text":"Alessio Figalli, Enrico Valdinoci, Giampiero Palatucci, Serena Dipierro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-03T18:01:50Z","title":"Asymptotics of the $s$-perimeter as $s\\searrow 0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0750","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:dfda842781ab88e2e1fc0f9d91dfc44ef9774212a99687579bc9189998e406a5","target":"record","created_at":"2026-05-18T03:42:44Z","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":"8340ff169f415b07f722ff340c58aa6550e660a44ac131ee27827feb5f29fe4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-03T18:01:50Z","title_canon_sha256":"e32b609790b5411b32ea44770c3a3987aaab54325bdacb7343915cebeb853723"},"schema_version":"1.0","source":{"id":"1204.0750","kind":"arxiv","version":2}},"canonical_sha256":"f09e312fb780032bc50782aab7d8b17ec3bd1c63a70351f5fbc2d1755a1f7f34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f09e312fb780032bc50782aab7d8b17ec3bd1c63a70351f5fbc2d1755a1f7f34","first_computed_at":"2026-05-18T03:42:44.415878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:44.415878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gNfWHgBdp36r9SiICncYvh4dvyO6h0MSNL+RvtrepXkQp85fsd+++au1nUL9B5R5gDwmP1x7FtgjMuz8NbATAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:44.416440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfda842781ab88e2e1fc0f9d91dfc44ef9774212a99687579bc9189998e406a5","sha256:fdef8a4b49f19ae75883e1e90bdf525b86e63eba05b958fec3362eac38837f1c"],"state_sha256":"2f6a17ee556da323c526d8cfaa12203d0e081feb74fe5e831dc1419ababc1b8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"784vXsHhKOPoF1OOBLjnqd7GpGN4HANOlXtHCCpCPwtQiDH3JAUH6HThgC55ZoVrfs/ESmwHD1+89LOG9CaHCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T04:48:59.733343Z","bundle_sha256":"4bba7b875298861acf15cce3cab5efbf9003eb58b1d5494d8c5eecbbc8cdf741"}}