{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7EMBCGCSXFVZSXCPHTXBHHTCLD","short_pith_number":"pith:7EMBCGCS","canonical_record":{"source":{"id":"1009.0319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-02T02:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"64a506bacc8b981ca2b114145d42e30e84da92f70739e31ab33daaecb477b08d","abstract_canon_sha256":"80410d4be18eaf694acccafd7864842637e0eb4edabfbd09c3977f269efc38bd"},"schema_version":"1.0"},"canonical_sha256":"f918111852b96b995c4f3cee139e6258dfe63749c4cde465f1a3f47a1d06b986","source":{"kind":"arxiv","id":"1009.0319","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0319","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0319v2","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0319","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"7EMBCGCSXFVZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EMBCGCSXFVZSXCP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EMBCGCS","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7EMBCGCSXFVZSXCPHTXBHHTCLD","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0319","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-02T02:44:40Z","cross_cats_sorted":[],"title_canon_sha256":"64a506bacc8b981ca2b114145d42e30e84da92f70739e31ab33daaecb477b08d","abstract_canon_sha256":"80410d4be18eaf694acccafd7864842637e0eb4edabfbd09c3977f269efc38bd"},"schema_version":"1.0"},"canonical_sha256":"f918111852b96b995c4f3cee139e6258dfe63749c4cde465f1a3f47a1d06b986","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:35.771338Z","signature_b64":"+yOP49je/yifzrMMxPfj+CBjBBq7bXkWdtyrKLOVnnxDbHVv17tlbthYFMraHyq1EIY1Hse9hCH1xbnb7b5mCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f918111852b96b995c4f3cee139e6258dfe63749c4cde465f1a3f47a1d06b986","last_reissued_at":"2026-05-18T01:28:35.770818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:35.770818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0319","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":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vE+HTOq1XqVscivZuTKTKjtRaWJrm99Jx+TPVd7uVnDwz4UhZx/y7trTyMX3gcFbG0xmuW1e1wpDC5paxNRLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:01:35.522718Z"},"content_sha256":"d75352a8f8fd64cfe96968733b67cee1432705d8adf5d6ef5e10805ac8eccb6b","schema_version":"1.0","event_id":"sha256:d75352a8f8fd64cfe96968733b67cee1432705d8adf5d6ef5e10805ac8eccb6b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7EMBCGCSXFVZSXCPHTXBHHTCLD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stefano Nardulli","submitted_at":"2010-09-02T02:44:40Z","abstract_excerpt":"In the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0319","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":"2026-05-18T01:28:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1xgXxSAPoPZOblvd4sWBDwVqLA8a1tesAX/TFNxGvw2g/Ocemr9xo8OvF4fGJuVLd0Jj254HaR4X8LJWjcQAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:01:35.523545Z"},"content_sha256":"dfbefcdb7310372f1ce95d9db9079bc5d5df3aa3b0ebb43055a792ec79bce4cc","schema_version":"1.0","event_id":"sha256:dfbefcdb7310372f1ce95d9db9079bc5d5df3aa3b0ebb43055a792ec79bce4cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/bundle.json","state_url":"https://pith.science/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/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":"2026-06-11T22:01:35Z","links":{"resolver":"https://pith.science/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD","bundle":"https://pith.science/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/bundle.json","state":"https://pith.science/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EMBCGCSXFVZSXCPHTXBHHTCLD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7EMBCGCSXFVZSXCPHTXBHHTCLD","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":"80410d4be18eaf694acccafd7864842637e0eb4edabfbd09c3977f269efc38bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-02T02:44:40Z","title_canon_sha256":"64a506bacc8b981ca2b114145d42e30e84da92f70739e31ab33daaecb477b08d"},"schema_version":"1.0","source":{"id":"1009.0319","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0319","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0319v2","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0319","created_at":"2026-05-18T01:28:35Z"},{"alias_kind":"pith_short_12","alias_value":"7EMBCGCSXFVZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EMBCGCSXFVZSXCP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EMBCGCS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:dfbefcdb7310372f1ce95d9db9079bc5d5df3aa3b0ebb43055a792ec79bce4cc","target":"graph","created_at":"2026-05-18T01:28:35Z","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 the main theorem of this paper we treat the problem of existence of minimizers of the isoperimetric problem under the assumption of small volumes. Applications of the main theorem to asymptotic expansions of the isoperimetric problem are given.","authors_text":"Stefano Nardulli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-02T02:44:40Z","title":"The Isoperimetric Profile of a Noncompact Riemannian Manifold for Small Volumes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0319","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:d75352a8f8fd64cfe96968733b67cee1432705d8adf5d6ef5e10805ac8eccb6b","target":"record","created_at":"2026-05-18T01:28:35Z","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":"80410d4be18eaf694acccafd7864842637e0eb4edabfbd09c3977f269efc38bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-02T02:44:40Z","title_canon_sha256":"64a506bacc8b981ca2b114145d42e30e84da92f70739e31ab33daaecb477b08d"},"schema_version":"1.0","source":{"id":"1009.0319","kind":"arxiv","version":2}},"canonical_sha256":"f918111852b96b995c4f3cee139e6258dfe63749c4cde465f1a3f47a1d06b986","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f918111852b96b995c4f3cee139e6258dfe63749c4cde465f1a3f47a1d06b986","first_computed_at":"2026-05-18T01:28:35.770818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:35.770818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+yOP49je/yifzrMMxPfj+CBjBBq7bXkWdtyrKLOVnnxDbHVv17tlbthYFMraHyq1EIY1Hse9hCH1xbnb7b5mCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:35.771338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d75352a8f8fd64cfe96968733b67cee1432705d8adf5d6ef5e10805ac8eccb6b","sha256:dfbefcdb7310372f1ce95d9db9079bc5d5df3aa3b0ebb43055a792ec79bce4cc"],"state_sha256":"543aa05482dd1ea3910ab97d3d87893a209875936fd2bd9349df3413b2818b15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"leBlBomufNnOgpKLCuh6WihXEm+kkATKyeOXmNCWr2Lxj01MMeO18NyIoGeZVD7IxqzOeV4sh+BbkCHFoZ9sCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:01:35.527963Z","bundle_sha256":"5b795d07cb3fa661a7c7f50ce97bc00a6ed659dfc7a76ec189253fac400f535a"}}