{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ERNVST44MRS5GCVN2SIIFLUWUY","short_pith_number":"pith:ERNVST44","canonical_record":{"source":{"id":"1202.6398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-28T22:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"781bdf5456fcf6918044dceb18206677903546cdec64db2c0f54e052497d0ff2","abstract_canon_sha256":"4a754b6651c4d77b79fc70e648b0385fe92e8e6e0842f096f6fe6a266e16a81d"},"schema_version":"1.0"},"canonical_sha256":"245b594f9c6465d30aadd49082ae96a63f7cd68d4d127c13e451168c3664d31f","source":{"kind":"arxiv","id":"1202.6398","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6398","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6398v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6398","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"ERNVST44MRS5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ERNVST44MRS5GCVN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ERNVST44","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ERNVST44MRS5GCVN2SIIFLUWUY","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6398","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-28T22:08:59Z","cross_cats_sorted":[],"title_canon_sha256":"781bdf5456fcf6918044dceb18206677903546cdec64db2c0f54e052497d0ff2","abstract_canon_sha256":"4a754b6651c4d77b79fc70e648b0385fe92e8e6e0842f096f6fe6a266e16a81d"},"schema_version":"1.0"},"canonical_sha256":"245b594f9c6465d30aadd49082ae96a63f7cd68d4d127c13e451168c3664d31f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.294455Z","signature_b64":"jYQ/9GF2egrOiHmom0Va0EvJ/dwZyXYZYK5t5UXsS6dq0X9w4ySQ3Ya72L4/elVrVvs4a7Fg5Vihwlz0mds/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"245b594f9c6465d30aadd49082ae96a63f7cd68d4d127c13e451168c3664d31f","last_reissued_at":"2026-05-17T23:53:36.293687Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.293687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6398","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Ch9bRxtIkjOEgL9gVz5ccxsSUTUjxVEgliiRHlbz2Fd8MEN2veRuI7VInZRDk+eJHHEBv1RrSJHH8i6pskTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:01:42.634291Z"},"content_sha256":"467b188c57bec5abd21f03af5139be5a5bf44c384f728c7e333152c1a00e9e1a","schema_version":"1.0","event_id":"sha256:467b188c57bec5abd21f03af5139be5a5bf44c384f728c7e333152c1a00e9e1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ERNVST44MRS5GCVN2SIIFLUWUY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skinning measures in negative curvature and equidistribution of equidistant submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","submitted_at":"2012-02-28T22:08:59Z","abstract_excerpt":"Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back the Patterson-Sullivan measures at infinity, and give a finiteness result of skinning measures, generalising the work of Oh and Shah, with different methods. We prove that the skinning measures, when finite, of the equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on the unit tangent bundle of M, assuming only that the Bowen-Margulis measure is finite and mixing for the geodesic flow. Under additional a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6398","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+dwzTvMtCXi0zIQm9Loq8HakYZ5AZuZR67syfpW1CIpWe9fvyhz3c/zIqbyRY3sYZ9lS+wHPZAoBik9/01gQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:01:42.635027Z"},"content_sha256":"758d4b45f8e73064c04e7a05fa32808da8273035ff8ecb65646e88e5a7d1aea7","schema_version":"1.0","event_id":"sha256:758d4b45f8e73064c04e7a05fa32808da8273035ff8ecb65646e88e5a7d1aea7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ERNVST44MRS5GCVN2SIIFLUWUY/bundle.json","state_url":"https://pith.science/pith/ERNVST44MRS5GCVN2SIIFLUWUY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ERNVST44MRS5GCVN2SIIFLUWUY/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":"2026-06-08T17:01:42Z","links":{"resolver":"https://pith.science/pith/ERNVST44MRS5GCVN2SIIFLUWUY","bundle":"https://pith.science/pith/ERNVST44MRS5GCVN2SIIFLUWUY/bundle.json","state":"https://pith.science/pith/ERNVST44MRS5GCVN2SIIFLUWUY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ERNVST44MRS5GCVN2SIIFLUWUY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ERNVST44MRS5GCVN2SIIFLUWUY","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":"4a754b6651c4d77b79fc70e648b0385fe92e8e6e0842f096f6fe6a266e16a81d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-28T22:08:59Z","title_canon_sha256":"781bdf5456fcf6918044dceb18206677903546cdec64db2c0f54e052497d0ff2"},"schema_version":"1.0","source":{"id":"1202.6398","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6398","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6398v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6398","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"ERNVST44MRS5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ERNVST44MRS5GCVN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ERNVST44","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:758d4b45f8e73064c04e7a05fa32808da8273035ff8ecb65646e88e5a7d1aea7","target":"graph","created_at":"2026-05-17T23:53:36Z","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":"Let C be a locally convex subset of a negatively curved Riemannian manifold M. We define the skinning measure on the outer unit normal bundle to C in M by pulling back the Patterson-Sullivan measures at infinity, and give a finiteness result of skinning measures, generalising the work of Oh and Shah, with different methods. We prove that the skinning measures, when finite, of the equidistant hypersurfaces to C equidistribute to the Bowen-Margulis measure on the unit tangent bundle of M, assuming only that the Bowen-Margulis measure is finite and mixing for the geodesic flow. Under additional a","authors_text":"Fr\\'ed\\'eric Paulin, Jouni Parkkonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-28T22:08:59Z","title":"Skinning measures in negative curvature and equidistribution of equidistant submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6398","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":"sha256:467b188c57bec5abd21f03af5139be5a5bf44c384f728c7e333152c1a00e9e1a","target":"record","created_at":"2026-05-17T23:53:36Z","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":"4a754b6651c4d77b79fc70e648b0385fe92e8e6e0842f096f6fe6a266e16a81d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-02-28T22:08:59Z","title_canon_sha256":"781bdf5456fcf6918044dceb18206677903546cdec64db2c0f54e052497d0ff2"},"schema_version":"1.0","source":{"id":"1202.6398","kind":"arxiv","version":2}},"canonical_sha256":"245b594f9c6465d30aadd49082ae96a63f7cd68d4d127c13e451168c3664d31f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"245b594f9c6465d30aadd49082ae96a63f7cd68d4d127c13e451168c3664d31f","first_computed_at":"2026-05-17T23:53:36.293687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.293687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jYQ/9GF2egrOiHmom0Va0EvJ/dwZyXYZYK5t5UXsS6dq0X9w4ySQ3Ya72L4/elVrVvs4a7Fg5Vihwlz0mds/CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.294455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6398","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:467b188c57bec5abd21f03af5139be5a5bf44c384f728c7e333152c1a00e9e1a","sha256:758d4b45f8e73064c04e7a05fa32808da8273035ff8ecb65646e88e5a7d1aea7"],"state_sha256":"7615a7f20cd5ccfe2360ebbca85283e4bed91383139c720c5be8ee8581342f69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Xx2VCB2mWavpwWHUHZ30zDrLjkmuCbo4bZ8jA5BTGMoOTwaBxH6DbEaII4YdL/8tnvjXfEfbuXPnlhUTnoJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:01:42.639288Z","bundle_sha256":"18c5811f774f58252b5df92feddbfa0e3872c10c53cb623998f147322870072a"}}