{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EN7KIHUVXWSSVSZOH3UXVTF3VW","short_pith_number":"pith:EN7KIHUV","canonical_record":{"source":{"id":"1306.1195","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-05T18:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"65ecbe05e541e39e198ff752714e81352ef793cbc3c9292d81e8f74df2e5e9f4","abstract_canon_sha256":"894b10904d47e386342afb2c6c36dd9a5931425d342d91c543a9acc7bb65d807"},"schema_version":"1.0"},"canonical_sha256":"237ea41e95bda52acb2e3ee97accbbad9b86344f91af99d243c98a023a5be735","source":{"kind":"arxiv","id":"1306.1195","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1195","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1195v4","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1195","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"EN7KIHUVXWSS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EN7KIHUVXWSSVSZO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EN7KIHUV","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EN7KIHUVXWSSVSZOH3UXVTF3VW","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1195","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-05T18:03:37Z","cross_cats_sorted":[],"title_canon_sha256":"65ecbe05e541e39e198ff752714e81352ef793cbc3c9292d81e8f74df2e5e9f4","abstract_canon_sha256":"894b10904d47e386342afb2c6c36dd9a5931425d342d91c543a9acc7bb65d807"},"schema_version":"1.0"},"canonical_sha256":"237ea41e95bda52acb2e3ee97accbbad9b86344f91af99d243c98a023a5be735","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:16.540497Z","signature_b64":"T7u345GyLC2DjLj7Gx9MQOFWHJj6DkNpOM6Hw/5/t2NJB2+RZShXZSHLdsa9Al66aTeP34q12zv0wo4mFN5DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"237ea41e95bda52acb2e3ee97accbbad9b86344f91af99d243c98a023a5be735","last_reissued_at":"2026-05-18T02:43:16.539972Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:16.539972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1195","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n/429ARJnxCvvRar5z9wKuRjrx5/r/Y/xXjtUUhRtcpnp4Rwl7qrIol6V8627Nti7SE26DVv+NGqhpSL0cUyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:13:26.424824Z"},"content_sha256":"50b43a1c0686e7c315ee2ce94521c7fab3baa353a957d9772d33e30e84965ca1","schema_version":"1.0","event_id":"sha256:50b43a1c0686e7c315ee2ce94521c7fab3baa353a957d9772d33e30e84965ca1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EN7KIHUVXWSSVSZOH3UXVTF3VW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regularity of area minimizing currents I: gradient L^p estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Camillo De Lellis, Emanuele Spadaro","submitted_at":"2013-06-05T18:03:37Z","abstract_excerpt":"In a series of papers, including the present one, we give a new, shorter proof of Almgren's partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs. Our new a priori estimate is an higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1195","kind":"arxiv","version":4},"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":"2026-05-18T02:43:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5qpXiKOQkG5lrZ0nb3mNK1AYFv5ymP8zgHCBWRy5oKC+YJj26215G/v/+m+Z0WHxJESv8yKnYGj2BiMtrrtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:13:26.425156Z"},"content_sha256":"77c78441f99f1cae3f5da29b48a75efdab1e1713125db9f75e5ae90688483424","schema_version":"1.0","event_id":"sha256:77c78441f99f1cae3f5da29b48a75efdab1e1713125db9f75e5ae90688483424"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/bundle.json","state_url":"https://pith.science/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/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":"2026-06-02T03:13:26Z","links":{"resolver":"https://pith.science/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW","bundle":"https://pith.science/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/bundle.json","state":"https://pith.science/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EN7KIHUVXWSSVSZOH3UXVTF3VW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EN7KIHUVXWSSVSZOH3UXVTF3VW","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":"894b10904d47e386342afb2c6c36dd9a5931425d342d91c543a9acc7bb65d807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-05T18:03:37Z","title_canon_sha256":"65ecbe05e541e39e198ff752714e81352ef793cbc3c9292d81e8f74df2e5e9f4"},"schema_version":"1.0","source":{"id":"1306.1195","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1195","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1195v4","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1195","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"EN7KIHUVXWSS","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EN7KIHUVXWSSVSZO","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EN7KIHUV","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:77c78441f99f1cae3f5da29b48a75efdab1e1713125db9f75e5ae90688483424","target":"graph","created_at":"2026-05-18T02:43:16Z","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 a series of papers, including the present one, we give a new, shorter proof of Almgren's partial regularity theorem for area minimizing currents in a Riemannian manifold, with a slight improvement on the regularity assumption for the latter. This note establishes a new a priori estimate on the excess measure of an area minimizing current, together with several statements concerning approximations with Lipschitz multiple valued graphs. Our new a priori estimate is an higher integrability type result, which has a counterpart in the theory of Dir-minimizing multiple valued functions and plays ","authors_text":"Camillo De Lellis, Emanuele Spadaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-05T18:03:37Z","title":"Regularity of area minimizing currents I: gradient L^p estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1195","kind":"arxiv","version":4},"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":"sha256:50b43a1c0686e7c315ee2ce94521c7fab3baa353a957d9772d33e30e84965ca1","target":"record","created_at":"2026-05-18T02:43:16Z","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":"894b10904d47e386342afb2c6c36dd9a5931425d342d91c543a9acc7bb65d807","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-06-05T18:03:37Z","title_canon_sha256":"65ecbe05e541e39e198ff752714e81352ef793cbc3c9292d81e8f74df2e5e9f4"},"schema_version":"1.0","source":{"id":"1306.1195","kind":"arxiv","version":4}},"canonical_sha256":"237ea41e95bda52acb2e3ee97accbbad9b86344f91af99d243c98a023a5be735","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"237ea41e95bda52acb2e3ee97accbbad9b86344f91af99d243c98a023a5be735","first_computed_at":"2026-05-18T02:43:16.539972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:16.539972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T7u345GyLC2DjLj7Gx9MQOFWHJj6DkNpOM6Hw/5/t2NJB2+RZShXZSHLdsa9Al66aTeP34q12zv0wo4mFN5DAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:16.540497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1195","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50b43a1c0686e7c315ee2ce94521c7fab3baa353a957d9772d33e30e84965ca1","sha256:77c78441f99f1cae3f5da29b48a75efdab1e1713125db9f75e5ae90688483424"],"state_sha256":"6fe3d8e2ceaffcec6d7b63bc7d2dfc5b18f8002b6112f130334fd879fcc46939"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZC5fvVRCznPYBMdjWNZeWVfq5DaBNlzn5QaPX8HA+JZoTIY+roZzp+TdAml3M8XlQ9762bPnBem6doouDoP7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:13:26.426979Z","bundle_sha256":"3893b8e93fd0ba1097231f34a7a7fcdaa4717c513e139341a05053340120f53e"}}