{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WPEZLQVTGLNHGXN4VBHH545XSO","short_pith_number":"pith:WPEZLQVT","canonical_record":{"source":{"id":"1103.4460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-23T06:25:42Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"faabcec2c4b639534c668fbb853044f8fc6a76e9dae03590d324a8f14c8c2d3f","abstract_canon_sha256":"2c9d966548fc435f61a890ea3b797b7b397eaac6bb7a5874c2b377f046ab88a1"},"schema_version":"1.0"},"canonical_sha256":"b3c995c2b332da735dbca84e7ef3b79387003c061d21552cfc8793a51c71401c","source":{"kind":"arxiv","id":"1103.4460","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4460","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4460v1","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4460","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"WPEZLQVTGLNH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WPEZLQVTGLNHGXN4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WPEZLQVT","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WPEZLQVTGLNHGXN4VBHH545XSO","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4460","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-23T06:25:42Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"faabcec2c4b639534c668fbb853044f8fc6a76e9dae03590d324a8f14c8c2d3f","abstract_canon_sha256":"2c9d966548fc435f61a890ea3b797b7b397eaac6bb7a5874c2b377f046ab88a1"},"schema_version":"1.0"},"canonical_sha256":"b3c995c2b332da735dbca84e7ef3b79387003c061d21552cfc8793a51c71401c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:02.000970Z","signature_b64":"PfpVmP7y8yeuq+ahODuDzKyVDnYYO3qxPnzu1B9AriVh4aTFVWcAy08QWvU+cMYzCjwt/ed9q1kKgDPiyaMYAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3c995c2b332da735dbca84e7ef3b79387003c061d21552cfc8793a51c71401c","last_reissued_at":"2026-05-18T04:26:02.000572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:02.000572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4460","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":"2026-05-18T04:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1MJ443DovVyqsUvL2N8EoYg8ZVk1iAWC6yu8nCXnbkUgqGjJw1sfihn4HG63oLZkCP5QpYZRn/8+sujHOTteAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:41:39.367701Z"},"content_sha256":"c344269e199681a286726bd9587646c8449c1b7901600ca374c7d4a3167fd9e3","schema_version":"1.0","event_id":"sha256:c344269e199681a286726bd9587646c8449c1b7901600ca374c7d4a3167fd9e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WPEZLQVTGLNHGXN4VBHH545XSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pincement du plan hyperbolique complexe","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Pierre Pansu (LM-Orsay)","submitted_at":"2011-03-23T06:25:42Z","abstract_excerpt":"$L^p$-cohomology of rank one symmetric spaces of noncompact type is shown to be Hausdorff for values of $p$ where this does not follow from curvature pinching. Using the multiplicative structure on $L^p$-cohomology, it is shown that no simply connected Riemannian manifold with strictly -1/4-pinched sectional curvature can be quasiisometric to complex hyperbolic plane. Unfortunately, the method does not extend to other rank one symmetric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4460","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":"2026-05-18T04:26:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+qcZxG5CDxO0C8GrSqA4rv8pF4pCqWjlJVIMJRfvZ7XNNkaKpdecmAZ9xIxetDKpAddgqw6fQrBOFjwFfnu8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:41:39.368041Z"},"content_sha256":"4c9b3e40253a5f5805d2b58e9702baecbf6a9a2773005b27ca5ca8d7cc3515c7","schema_version":"1.0","event_id":"sha256:4c9b3e40253a5f5805d2b58e9702baecbf6a9a2773005b27ca5ca8d7cc3515c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WPEZLQVTGLNHGXN4VBHH545XSO/bundle.json","state_url":"https://pith.science/pith/WPEZLQVTGLNHGXN4VBHH545XSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WPEZLQVTGLNHGXN4VBHH545XSO/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":"2026-06-26T10:41:39Z","links":{"resolver":"https://pith.science/pith/WPEZLQVTGLNHGXN4VBHH545XSO","bundle":"https://pith.science/pith/WPEZLQVTGLNHGXN4VBHH545XSO/bundle.json","state":"https://pith.science/pith/WPEZLQVTGLNHGXN4VBHH545XSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WPEZLQVTGLNHGXN4VBHH545XSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WPEZLQVTGLNHGXN4VBHH545XSO","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":"2c9d966548fc435f61a890ea3b797b7b397eaac6bb7a5874c2b377f046ab88a1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-23T06:25:42Z","title_canon_sha256":"faabcec2c4b639534c668fbb853044f8fc6a76e9dae03590d324a8f14c8c2d3f"},"schema_version":"1.0","source":{"id":"1103.4460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4460","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4460v1","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4460","created_at":"2026-05-18T04:26:02Z"},{"alias_kind":"pith_short_12","alias_value":"WPEZLQVTGLNH","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WPEZLQVTGLNHGXN4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WPEZLQVT","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:4c9b3e40253a5f5805d2b58e9702baecbf6a9a2773005b27ca5ca8d7cc3515c7","target":"graph","created_at":"2026-05-18T04:26:02Z","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":"$L^p$-cohomology of rank one symmetric spaces of noncompact type is shown to be Hausdorff for values of $p$ where this does not follow from curvature pinching. Using the multiplicative structure on $L^p$-cohomology, it is shown that no simply connected Riemannian manifold with strictly -1/4-pinched sectional curvature can be quasiisometric to complex hyperbolic plane. Unfortunately, the method does not extend to other rank one symmetric spaces.","authors_text":"Pierre Pansu (LM-Orsay)","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-23T06:25:42Z","title":"Pincement du plan hyperbolique complexe"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4460","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:c344269e199681a286726bd9587646c8449c1b7901600ca374c7d4a3167fd9e3","target":"record","created_at":"2026-05-18T04:26:02Z","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":"2c9d966548fc435f61a890ea3b797b7b397eaac6bb7a5874c2b377f046ab88a1","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-23T06:25:42Z","title_canon_sha256":"faabcec2c4b639534c668fbb853044f8fc6a76e9dae03590d324a8f14c8c2d3f"},"schema_version":"1.0","source":{"id":"1103.4460","kind":"arxiv","version":1}},"canonical_sha256":"b3c995c2b332da735dbca84e7ef3b79387003c061d21552cfc8793a51c71401c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3c995c2b332da735dbca84e7ef3b79387003c061d21552cfc8793a51c71401c","first_computed_at":"2026-05-18T04:26:02.000572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:02.000572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfpVmP7y8yeuq+ahODuDzKyVDnYYO3qxPnzu1B9AriVh4aTFVWcAy08QWvU+cMYzCjwt/ed9q1kKgDPiyaMYAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:02.000970Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c344269e199681a286726bd9587646c8449c1b7901600ca374c7d4a3167fd9e3","sha256:4c9b3e40253a5f5805d2b58e9702baecbf6a9a2773005b27ca5ca8d7cc3515c7"],"state_sha256":"9b4ac6175936cb5f01aa2137f5aa1c6ede5cc4f86394aac739cb454f63d8514d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SFyLObvPG4JERdd1yzAnTPnloIHHXq9gN1DeKs4xXhKY3AUIjmt9JFxkv5l3pB1eU6p2cT1qFWIRHGDWY6C9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:41:39.369905Z","bundle_sha256":"a5bce9b3dd1d46b5ef1af7bd88b698b167ea3fa80abbb5bbf5e0bf432cad3641"}}