{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KN3XKB4HIQA2OQLVWE7I4AOQH7","short_pith_number":"pith:KN3XKB4H","canonical_record":{"source":{"id":"1903.09849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-03-23T17:33:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"aa73a3ee52eec70a0b750c76cef5426640873c02f62e99a7af1c6acac33ab215","abstract_canon_sha256":"c771949d4dcfa1aa53c43d2d38d578ba83cb671453bad485a32c0bbdf53f27cd"},"schema_version":"1.0"},"canonical_sha256":"53777507874401a74175b13e8e01d03ff259478887841773873d95652c5bdbad","source":{"kind":"arxiv","id":"1903.09849","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09849","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09849v1","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09849","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"KN3XKB4HIQA2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KN3XKB4HIQA2OQLV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KN3XKB4H","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KN3XKB4HIQA2OQLVWE7I4AOQH7","target":"record","payload":{"canonical_record":{"source":{"id":"1903.09849","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-03-23T17:33:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"aa73a3ee52eec70a0b750c76cef5426640873c02f62e99a7af1c6acac33ab215","abstract_canon_sha256":"c771949d4dcfa1aa53c43d2d38d578ba83cb671453bad485a32c0bbdf53f27cd"},"schema_version":"1.0"},"canonical_sha256":"53777507874401a74175b13e8e01d03ff259478887841773873d95652c5bdbad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:35.330955Z","signature_b64":"q9BW6XaZAuhJNcOXCA9LgaooqC+5zPK9pC5yDfOz86YbhCS8z0kk0T5AqTlQPTYw5FWdqh3Vi66FxaPGPRfmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53777507874401a74175b13e8e01d03ff259478887841773873d95652c5bdbad","last_reissued_at":"2026-05-17T23:50:35.330341Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:35.330341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.09849","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":"2026-05-17T23:50:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xTn5udKoqVg4icmCBMzxvUpCDwFCVmMcwuzIN8uhHqg9fSvwcZGXj7jMjv4YgSwQfYDjSqs8gik25FSBHwcAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:51:48.699812Z"},"content_sha256":"1f6c0c18e544894f5b6aef1ea1ee4dd44214efe4e329faf69680daa6da70cee8","schema_version":"1.0","event_id":"sha256:1f6c0c18e544894f5b6aef1ea1ee4dd44214efe4e329faf69680daa6da70cee8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KN3XKB4HIQA2OQLVWE7I4AOQH7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volumes of quasifuchsian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Jean-Marc Schlenker","submitted_at":"2019-03-23T17:33:49Z","abstract_excerpt":"Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the volume, or more precisely the ``dual volume'', of the convex core. On one hand, there are striking similarities between them, for instance in their variational formulas. On the other, object related to them tend to be within bounded distance. Those analogies and proximities lead to several questions. Both the renormalized volume and the dual volume can be used "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09849","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":"2026-05-17T23:50:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQ4by692O/VyI4OA/jgnyUG/rykHKKHNaTDX7qKwzbwIQmjQkTa6y7p21LuRI1Kaj7iokdKWXSOK6LAucTDCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T09:51:48.700434Z"},"content_sha256":"4cde8d8c5681a6af2bf4f047d05b1fb9b7880bf85fc0fdd16f834c1244958e77","schema_version":"1.0","event_id":"sha256:4cde8d8c5681a6af2bf4f047d05b1fb9b7880bf85fc0fdd16f834c1244958e77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/bundle.json","state_url":"https://pith.science/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/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":"2026-06-07T09:51:48Z","links":{"resolver":"https://pith.science/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7","bundle":"https://pith.science/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/bundle.json","state":"https://pith.science/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KN3XKB4HIQA2OQLVWE7I4AOQH7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KN3XKB4HIQA2OQLVWE7I4AOQH7","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":"c771949d4dcfa1aa53c43d2d38d578ba83cb671453bad485a32c0bbdf53f27cd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-03-23T17:33:49Z","title_canon_sha256":"aa73a3ee52eec70a0b750c76cef5426640873c02f62e99a7af1c6acac33ab215"},"schema_version":"1.0","source":{"id":"1903.09849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09849","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09849v1","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09849","created_at":"2026-05-17T23:50:35Z"},{"alias_kind":"pith_short_12","alias_value":"KN3XKB4HIQA2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KN3XKB4HIQA2OQLV","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KN3XKB4H","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:4cde8d8c5681a6af2bf4f047d05b1fb9b7880bf85fc0fdd16f834c1244958e77","target":"graph","created_at":"2026-05-17T23:50:35Z","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":"Quasifuchsian hyperbolic manifolds, or more generally convex co-compact hyperbolic manifolds, have infinite volume, but they have a well-defined ``renormalized'' volume. We outline some relations between this renormalized volume and the volume, or more precisely the ``dual volume'', of the convex core. On one hand, there are striking similarities between them, for instance in their variational formulas. On the other, object related to them tend to be within bounded distance. Those analogies and proximities lead to several questions. Both the renormalized volume and the dual volume can be used ","authors_text":"Jean-Marc Schlenker","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-03-23T17:33:49Z","title":"Volumes of quasifuchsian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09849","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":"sha256:1f6c0c18e544894f5b6aef1ea1ee4dd44214efe4e329faf69680daa6da70cee8","target":"record","created_at":"2026-05-17T23:50:35Z","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":"c771949d4dcfa1aa53c43d2d38d578ba83cb671453bad485a32c0bbdf53f27cd","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-03-23T17:33:49Z","title_canon_sha256":"aa73a3ee52eec70a0b750c76cef5426640873c02f62e99a7af1c6acac33ab215"},"schema_version":"1.0","source":{"id":"1903.09849","kind":"arxiv","version":1}},"canonical_sha256":"53777507874401a74175b13e8e01d03ff259478887841773873d95652c5bdbad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53777507874401a74175b13e8e01d03ff259478887841773873d95652c5bdbad","first_computed_at":"2026-05-17T23:50:35.330341Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:35.330341Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q9BW6XaZAuhJNcOXCA9LgaooqC+5zPK9pC5yDfOz86YbhCS8z0kk0T5AqTlQPTYw5FWdqh3Vi66FxaPGPRfmCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:35.330955Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f6c0c18e544894f5b6aef1ea1ee4dd44214efe4e329faf69680daa6da70cee8","sha256:4cde8d8c5681a6af2bf4f047d05b1fb9b7880bf85fc0fdd16f834c1244958e77"],"state_sha256":"7cbeb6e0ffcdd13a15f295462c925735a712732a8968482e775411d6c78eca19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2Hn8ZTohqwOT55Gss4cDCD45pQzgkIU0xQBK3jsI0Szc4DYpCpYKlK3airoCpBqVx4vJAjob6zV7htN9cfoDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T09:51:48.704109Z","bundle_sha256":"5bcf447d476aa6f5546cf6a95d26b4a81ee51eaa74bddd9255c85700f0a0457b"}}