{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SN3A7CYUOPZ6IIDZ2NSOXKSWH3","short_pith_number":"pith:SN3A7CYU","canonical_record":{"source":{"id":"1404.5365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-04-22T01:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"087b72d6a5315d26378f6eeae8b5cefcc3b850e3fb87467a9e4c49a9a84f03c2","abstract_canon_sha256":"f1f4aeeb4430be24a892be7444eae7c664a07179645bc2bfb2fedf7bf92c7d42"},"schema_version":"1.0"},"canonical_sha256":"93760f8b1473f3e42079d364ebaa563ef3ed505e2c0e1953fbaebea900e2c8fd","source":{"kind":"arxiv","id":"1404.5365","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5365","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5365v2","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5365","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"SN3A7CYUOPZ6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SN3A7CYUOPZ6IIDZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SN3A7CYU","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SN3A7CYUOPZ6IIDZ2NSOXKSWH3","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5365","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-04-22T01:31:24Z","cross_cats_sorted":[],"title_canon_sha256":"087b72d6a5315d26378f6eeae8b5cefcc3b850e3fb87467a9e4c49a9a84f03c2","abstract_canon_sha256":"f1f4aeeb4430be24a892be7444eae7c664a07179645bc2bfb2fedf7bf92c7d42"},"schema_version":"1.0"},"canonical_sha256":"93760f8b1473f3e42079d364ebaa563ef3ed505e2c0e1953fbaebea900e2c8fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:06.898976Z","signature_b64":"E+cFSFPEXq7CjKS7RYepgWsgyUavtuJ/jTOUTdIVq3KHes2Q8XzD7USQfv66vg4IGygNFcTxz7nafBwuSD6hDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93760f8b1473f3e42079d364ebaa563ef3ed505e2c0e1953fbaebea900e2c8fd","last_reissued_at":"2026-05-18T02:53:06.898476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:06.898476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5365","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":"2026-05-18T02:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOElWMJ0TYFKj7JqyamAD2Fzs6BOACnnvG6ym7tdszfGX30QAA/ICYrmNl48hpAaAmtq61NbLB/0r1P5xjt2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:12:49.555150Z"},"content_sha256":"4c2638fddbf66dd702bca7b65217c31a9c4ebd7a271e7adc0e6fdfaf85e1934b","schema_version":"1.0","event_id":"sha256:4c2638fddbf66dd702bca7b65217c31a9c4ebd7a271e7adc0e6fdfaf85e1934b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SN3A7CYUOPZ6IIDZ2NSOXKSWH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Volume and rigidity of hyperbolic polyhedral $3$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Feng Luo, Tian Yang","submitted_at":"2014-04-22T01:31:24Z","abstract_excerpt":"We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. The main tool used in the proof is the Fenchel dual of the volume function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5365","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":"2026-05-18T02:53:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+GAkjRi1DTU6K5M/9cV4IJAm7QZ4N7Zkiz2ipnHy9/qh4FZhlKkkBihBRHDYtcfhov3qpVJ5VwxwbSTN3niBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:12:49.555508Z"},"content_sha256":"6165538e8945c0077196e49d26e68f0eebe1887c072b78556b8fdb2056aa881f","schema_version":"1.0","event_id":"sha256:6165538e8945c0077196e49d26e68f0eebe1887c072b78556b8fdb2056aa881f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/bundle.json","state_url":"https://pith.science/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/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":"2026-07-04T23:12:49Z","links":{"resolver":"https://pith.science/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3","bundle":"https://pith.science/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/bundle.json","state":"https://pith.science/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SN3A7CYUOPZ6IIDZ2NSOXKSWH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SN3A7CYUOPZ6IIDZ2NSOXKSWH3","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":"f1f4aeeb4430be24a892be7444eae7c664a07179645bc2bfb2fedf7bf92c7d42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-04-22T01:31:24Z","title_canon_sha256":"087b72d6a5315d26378f6eeae8b5cefcc3b850e3fb87467a9e4c49a9a84f03c2"},"schema_version":"1.0","source":{"id":"1404.5365","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5365","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5365v2","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5365","created_at":"2026-05-18T02:53:06Z"},{"alias_kind":"pith_short_12","alias_value":"SN3A7CYUOPZ6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SN3A7CYUOPZ6IIDZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SN3A7CYU","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:6165538e8945c0077196e49d26e68f0eebe1887c072b78556b8fdb2056aa881f","target":"graph","created_at":"2026-05-18T02:53:06Z","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":"We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to isometry by its curvature and a decorated ideal hyperbolic polyhedral metric is determined up to isometry and change of decorations by its curvature. The main tool used in the proof is the Fenchel dual of the volume function.","authors_text":"Feng Luo, Tian Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-04-22T01:31:24Z","title":"Volume and rigidity of hyperbolic polyhedral $3$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5365","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":"sha256:4c2638fddbf66dd702bca7b65217c31a9c4ebd7a271e7adc0e6fdfaf85e1934b","target":"record","created_at":"2026-05-18T02:53:06Z","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":"f1f4aeeb4430be24a892be7444eae7c664a07179645bc2bfb2fedf7bf92c7d42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-04-22T01:31:24Z","title_canon_sha256":"087b72d6a5315d26378f6eeae8b5cefcc3b850e3fb87467a9e4c49a9a84f03c2"},"schema_version":"1.0","source":{"id":"1404.5365","kind":"arxiv","version":2}},"canonical_sha256":"93760f8b1473f3e42079d364ebaa563ef3ed505e2c0e1953fbaebea900e2c8fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93760f8b1473f3e42079d364ebaa563ef3ed505e2c0e1953fbaebea900e2c8fd","first_computed_at":"2026-05-18T02:53:06.898476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:06.898476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E+cFSFPEXq7CjKS7RYepgWsgyUavtuJ/jTOUTdIVq3KHes2Q8XzD7USQfv66vg4IGygNFcTxz7nafBwuSD6hDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:06.898976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5365","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c2638fddbf66dd702bca7b65217c31a9c4ebd7a271e7adc0e6fdfaf85e1934b","sha256:6165538e8945c0077196e49d26e68f0eebe1887c072b78556b8fdb2056aa881f"],"state_sha256":"6f81391462de70a7f42f109bb40cc84c46d30936fbd99c37e5b1e68b5e2c5bd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlPNaHiQb/zMyHyJvuBsM1HtQBpqf4c87ajokPft+4lFTm7S9SUJIRO534e9nAJEExhecLXletIcVbwhJA0+Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:12:49.557416Z","bundle_sha256":"f6717c5d7e00200c75b115b78d942f3abdf2d08f0a071483328697ce45613c07"}}