{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:B536TIR4J5BFMZPNRRNMI2NYGW","short_pith_number":"pith:B536TIR4","canonical_record":{"source":{"id":"1504.05104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-04-20T16:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"93f2e8c30217cb0c84365ec7b6a24916d3711dc2b08b50506aa25df69593af3a","abstract_canon_sha256":"c488b3ba9cef10ac42cad4226e4b025f02348743262f36a1f2ff66883e8447f7"},"schema_version":"1.0"},"canonical_sha256":"0f77e9a23c4f425665ed8c5ac469b83594ea212871046f51a54196b47bff749b","source":{"kind":"arxiv","id":"1504.05104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05104","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05104v1","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05104","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"B536TIR4J5BF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B536TIR4J5BFMZPN","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B536TIR4","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:B536TIR4J5BFMZPNRRNMI2NYGW","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-04-20T16:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"93f2e8c30217cb0c84365ec7b6a24916d3711dc2b08b50506aa25df69593af3a","abstract_canon_sha256":"c488b3ba9cef10ac42cad4226e4b025f02348743262f36a1f2ff66883e8447f7"},"schema_version":"1.0"},"canonical_sha256":"0f77e9a23c4f425665ed8c5ac469b83594ea212871046f51a54196b47bff749b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:22.615756Z","signature_b64":"eVEDwWffLaLNkg+V0uQ5o/fmXzxy6M0WJR08zqj3a8AC1LhX1cx/xjsGUbtJDTTTW1M8aoAG8tT5UAmwRVzlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f77e9a23c4f425665ed8c5ac469b83594ea212871046f51a54196b47bff749b","last_reissued_at":"2026-05-18T02:18:22.615106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:22.615106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05104","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":"2026-05-18T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYV7cmq+2CAK3aEdXexLJHO98z8qbJk+yzBh8/usduYh9NoUh9K8DKGDUMWnT9g5kvPrNXpUwJm2RWUPNK7yDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:35:57.181506Z"},"content_sha256":"7c94990db20f3b9f623ec9ff4be782642217da6d14849171ab13ccedaa162453","schema_version":"1.0","event_id":"sha256:7c94990db20f3b9f623ec9ff4be782642217da6d14849171ab13ccedaa162453"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:B536TIR4J5BFMZPNRRNMI2NYGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized compactness for finite perimeter sets and applications to the isoperimetric problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Abraham Enrique Mu\\~noz Flores, Stefano Nardulli","submitted_at":"2015-04-20T16:17:33Z","abstract_excerpt":"For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extends previous results contained in [Nar14a], in such a way that the generalized existence theorem, Theorem 1 of [Nar14a] is actually a generalized compactness theorem. The suitable modifications to the arguments and statements of the results in [Nar14a] are non-trivial. As a consequence we give a multipointed version of Theorem 1.1 of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05104","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":"2026-05-18T02:18:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DtQJvIWYGOmdXT5EGXeu5bBr/6XO4U6oa7Nv32bozaZyx7HoZmsF6QnvRzgc4LHy0lHoBZYMXJ1/b95zWo2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:35:57.182183Z"},"content_sha256":"2d2eeca7a005ba5b3cab99489b376f0cc1d4f58f760812af18d7a1fd13169fd6","schema_version":"1.0","event_id":"sha256:2d2eeca7a005ba5b3cab99489b376f0cc1d4f58f760812af18d7a1fd13169fd6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B536TIR4J5BFMZPNRRNMI2NYGW/bundle.json","state_url":"https://pith.science/pith/B536TIR4J5BFMZPNRRNMI2NYGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B536TIR4J5BFMZPNRRNMI2NYGW/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":"2026-06-11T21:35:57Z","links":{"resolver":"https://pith.science/pith/B536TIR4J5BFMZPNRRNMI2NYGW","bundle":"https://pith.science/pith/B536TIR4J5BFMZPNRRNMI2NYGW/bundle.json","state":"https://pith.science/pith/B536TIR4J5BFMZPNRRNMI2NYGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B536TIR4J5BFMZPNRRNMI2NYGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B536TIR4J5BFMZPNRRNMI2NYGW","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":"c488b3ba9cef10ac42cad4226e4b025f02348743262f36a1f2ff66883e8447f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-04-20T16:17:33Z","title_canon_sha256":"93f2e8c30217cb0c84365ec7b6a24916d3711dc2b08b50506aa25df69593af3a"},"schema_version":"1.0","source":{"id":"1504.05104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05104","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05104v1","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05104","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"B536TIR4J5BF","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B536TIR4J5BFMZPN","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B536TIR4","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:2d2eeca7a005ba5b3cab99489b376f0cc1d4f58f760812af18d7a1fd13169fd6","target":"graph","created_at":"2026-05-18T02:18:22Z","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":"For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit manifolds at infinity. We extends previous results contained in [Nar14a], in such a way that the generalized existence theorem, Theorem 1 of [Nar14a] is actually a generalized compactness theorem. The suitable modifications to the arguments and statements of the results in [Nar14a] are non-trivial. As a consequence we give a multipointed version of Theorem 1.1 of","authors_text":"Abraham Enrique Mu\\~noz Flores, Stefano Nardulli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-04-20T16:17:33Z","title":"Generalized compactness for finite perimeter sets and applications to the isoperimetric problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05104","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":"sha256:7c94990db20f3b9f623ec9ff4be782642217da6d14849171ab13ccedaa162453","target":"record","created_at":"2026-05-18T02:18:22Z","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":"c488b3ba9cef10ac42cad4226e4b025f02348743262f36a1f2ff66883e8447f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-04-20T16:17:33Z","title_canon_sha256":"93f2e8c30217cb0c84365ec7b6a24916d3711dc2b08b50506aa25df69593af3a"},"schema_version":"1.0","source":{"id":"1504.05104","kind":"arxiv","version":1}},"canonical_sha256":"0f77e9a23c4f425665ed8c5ac469b83594ea212871046f51a54196b47bff749b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f77e9a23c4f425665ed8c5ac469b83594ea212871046f51a54196b47bff749b","first_computed_at":"2026-05-18T02:18:22.615106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:22.615106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eVEDwWffLaLNkg+V0uQ5o/fmXzxy6M0WJR08zqj3a8AC1LhX1cx/xjsGUbtJDTTTW1M8aoAG8tT5UAmwRVzlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:22.615756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c94990db20f3b9f623ec9ff4be782642217da6d14849171ab13ccedaa162453","sha256:2d2eeca7a005ba5b3cab99489b376f0cc1d4f58f760812af18d7a1fd13169fd6"],"state_sha256":"56c9f6b69063a153934de3a02038aeaaf9a7c36e9e5a0f79ede49d4afb58940f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhUrxmZNT3/pEPhvaGpKrhTfVqVXu4muLI+vxgX4dl3loL1TvetG4yMHnSLPPhn+puiWIs/RHk8XQJd0iuf3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:35:57.185836Z","bundle_sha256":"f35455983602ad24dc7da511d02a0421f102dafbb1fe68e6f7654395edf270cb"}}