{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J7E2OSPIYR4MJKGE2DJEVT4YJP","short_pith_number":"pith:J7E2OSPI","canonical_record":{"source":{"id":"1403.5019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T01:47:35Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"1a72ddecae3944e1ee7c020c6797e7594a795a6ed8c1ff38b4b6d326d1ead872","abstract_canon_sha256":"8b4372cb7b82e9153867a688f79f826c1bd9611227af6ba4f025544cc526aa1b"},"schema_version":"1.0"},"canonical_sha256":"4fc9a749e8c478c4a8c4d0d24acf984bc1d9e275c3cb29febcde3d4436074732","source":{"kind":"arxiv","id":"1403.5019","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5019","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5019v1","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5019","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"J7E2OSPIYR4M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J7E2OSPIYR4MJKGE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J7E2OSPI","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J7E2OSPIYR4MJKGE2DJEVT4YJP","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T01:47:35Z","cross_cats_sorted":["math.GT","math.MG"],"title_canon_sha256":"1a72ddecae3944e1ee7c020c6797e7594a795a6ed8c1ff38b4b6d326d1ead872","abstract_canon_sha256":"8b4372cb7b82e9153867a688f79f826c1bd9611227af6ba4f025544cc526aa1b"},"schema_version":"1.0"},"canonical_sha256":"4fc9a749e8c478c4a8c4d0d24acf984bc1d9e275c3cb29febcde3d4436074732","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:40.811019Z","signature_b64":"02/G5Wk2NN5SDBQoK7OsOrwkeYCGCYRfr47PZwCtLmBonduoxJ5IUvU+bvlaCopSI9H5qwzUfXwCHhfVGkR0Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fc9a749e8c478c4a8c4d0d24acf984bc1d9e275c3cb29febcde3d4436074732","last_reissued_at":"2026-05-18T00:53:40.810395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:40.810395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5019","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":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WtmUZdBva9fWXiXkmRCInGl1XLaCxUgIJdk5Rfd1NtBVW9CK9WTbIxXKKxTrpliUGW6Nf7jbU7ZLmTYqnGw5Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:25:27.917257Z"},"content_sha256":"73b072ed85187e63e065436b112cccb9e0f5131b47887272b7822d7a9fade0b9","schema_version":"1.0","event_id":"sha256:73b072ed85187e63e065436b112cccb9e0f5131b47887272b7822d7a9fade0b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J7E2OSPIYR4MJKGE2DJEVT4YJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reflection groups in non-negative curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Fuquan Fang, Karsten Grove","submitted_at":"2014-03-20T01:47:35Z","abstract_excerpt":"We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that the building blocks consist of the classical constant curvature models and generalized open books with non negatively curved bundle pages, and derive a corresponding splitting theorem for the universal cover."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5019","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":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YFsjiorFZCfHxjJdfC2JKkjTEJW1dji337Q3pUhNRTAZyVO60xQj9IktbgoaZR/0B/Fg1v6LCedaDZSQtv5qCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:25:27.917619Z"},"content_sha256":"6d436247fe1a58b4e9227130fcdcb4da8993ac2beb79552dca59e80386df831c","schema_version":"1.0","event_id":"sha256:6d436247fe1a58b4e9227130fcdcb4da8993ac2beb79552dca59e80386df831c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/bundle.json","state_url":"https://pith.science/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/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":"2026-06-20T22:25:27Z","links":{"resolver":"https://pith.science/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP","bundle":"https://pith.science/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/bundle.json","state":"https://pith.science/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J7E2OSPIYR4MJKGE2DJEVT4YJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J7E2OSPIYR4MJKGE2DJEVT4YJP","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":"8b4372cb7b82e9153867a688f79f826c1bd9611227af6ba4f025544cc526aa1b","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T01:47:35Z","title_canon_sha256":"1a72ddecae3944e1ee7c020c6797e7594a795a6ed8c1ff38b4b6d326d1ead872"},"schema_version":"1.0","source":{"id":"1403.5019","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5019","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5019v1","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5019","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"J7E2OSPIYR4M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J7E2OSPIYR4MJKGE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J7E2OSPI","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6d436247fe1a58b4e9227130fcdcb4da8993ac2beb79552dca59e80386df831c","target":"graph","created_at":"2026-05-18T00:53:40Z","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 provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that the building blocks consist of the classical constant curvature models and generalized open books with non negatively curved bundle pages, and derive a corresponding splitting theorem for the universal cover.","authors_text":"Fuquan Fang, Karsten Grove","cross_cats":["math.GT","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T01:47:35Z","title":"Reflection groups in non-negative curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5019","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":"sha256:73b072ed85187e63e065436b112cccb9e0f5131b47887272b7822d7a9fade0b9","target":"record","created_at":"2026-05-18T00:53:40Z","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":"8b4372cb7b82e9153867a688f79f826c1bd9611227af6ba4f025544cc526aa1b","cross_cats_sorted":["math.GT","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-03-20T01:47:35Z","title_canon_sha256":"1a72ddecae3944e1ee7c020c6797e7594a795a6ed8c1ff38b4b6d326d1ead872"},"schema_version":"1.0","source":{"id":"1403.5019","kind":"arxiv","version":1}},"canonical_sha256":"4fc9a749e8c478c4a8c4d0d24acf984bc1d9e275c3cb29febcde3d4436074732","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fc9a749e8c478c4a8c4d0d24acf984bc1d9e275c3cb29febcde3d4436074732","first_computed_at":"2026-05-18T00:53:40.810395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.810395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"02/G5Wk2NN5SDBQoK7OsOrwkeYCGCYRfr47PZwCtLmBonduoxJ5IUvU+bvlaCopSI9H5qwzUfXwCHhfVGkR0Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.811019Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5019","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73b072ed85187e63e065436b112cccb9e0f5131b47887272b7822d7a9fade0b9","sha256:6d436247fe1a58b4e9227130fcdcb4da8993ac2beb79552dca59e80386df831c"],"state_sha256":"851f3420e309977c0c39ca11a9850fa6a24cf5b3989236e5d753f536cce568dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mGB39rbJzOBW+N7ivssrEAzGUtGQWRD5VLBmIS9rJrOcoHKz0Rz/DLZytngz4sjoh6r0J62oaw4BE1cm9C9ACQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:25:27.919503Z","bundle_sha256":"393bc102507eda5f8e46e075eb94f456249a5aeb4bbbdb899c80d6a241f8e31e"}}