{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QBTS5ABSF2RRZUB3NPELPBIFMK","short_pith_number":"pith:QBTS5ABS","canonical_record":{"source":{"id":"1312.4054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-14T15:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"a100c8b6d4addddb7e36815acfb5b4ebf86321a550d36980036bc11080de1af9","abstract_canon_sha256":"e80b1b4d91f81882155f5fe9c214776eecbb57f9bc3e7ecd78d612fbbeabc235"},"schema_version":"1.0"},"canonical_sha256":"80672e80322ea31cd03b6bc8b785056280bf48d5c94b0006487843abed41bf3b","source":{"kind":"arxiv","id":"1312.4054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4054","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4054v1","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4054","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"pith_short_12","alias_value":"QBTS5ABSF2RR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBTS5ABSF2RRZUB3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBTS5ABS","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QBTS5ABSF2RRZUB3NPELPBIFMK","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-14T15:31:43Z","cross_cats_sorted":[],"title_canon_sha256":"a100c8b6d4addddb7e36815acfb5b4ebf86321a550d36980036bc11080de1af9","abstract_canon_sha256":"e80b1b4d91f81882155f5fe9c214776eecbb57f9bc3e7ecd78d612fbbeabc235"},"schema_version":"1.0"},"canonical_sha256":"80672e80322ea31cd03b6bc8b785056280bf48d5c94b0006487843abed41bf3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:06.669881Z","signature_b64":"anMzaB4ja9bJUuqy1AQijKLo5jjmaL1epKqS2lFcETObiJLNA4iBZUC0hDcxwUlz4KP/qpnOQ1GslmoOwPoKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80672e80322ea31cd03b6bc8b785056280bf48d5c94b0006487843abed41bf3b","last_reissued_at":"2026-05-18T00:38:06.669303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:06.669303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4054","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":"2026-05-18T00:38:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nsn7AeL23DkeUFNDRICT/xdVq7TaHCkL6RGEMqxG9G+YVgCdTJ6DwIv9vas+KB4NOcZDvi+e+eaiPXFJArSDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:24:55.754079Z"},"content_sha256":"ed73bc39c44b7f5363b57187de98fe256a18df7f358655aa9618b17d45179eee","schema_version":"1.0","event_id":"sha256:ed73bc39c44b7f5363b57187de98fe256a18df7f358655aa9618b17d45179eee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QBTS5ABSF2RRZUB3NPELPBIFMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher cohomology of parabolic actions on certain homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Felipe A. Ramirez","submitted_at":"2013-12-14T15:31:43Z","abstract_excerpt":"We show that for a parabolic R^d-action on a compact quotient of PSL(2,R)^d, the cohomologies in degrees 1 through d-1 trivialize, and we give the obstructions to solving the degree-d coboundary equation, along with bounds on Sobolev norms of primitives. In previous papers we have established these results for certain Anosov systems. The present work extends the methods of those papers to systems that are not Anosov. The main new idea is in Section 4, where we define special elements of representation spaces that allow us to modify the arguments from the previous papers. In Section 7 we discus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4054","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":"2026-05-18T00:38:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1N8urMQpE3ekCCrlYW4BoRJFF2cxW7SletR7dZYIc8J96BPEC+0P39yL3n2rTPBDmKXzci5ka2r+0RxVn7FFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:24:55.754426Z"},"content_sha256":"51e3dfc2d41e5bc3204ca0dd4244db708270c6f4e0f21d38680b49aff0141657","schema_version":"1.0","event_id":"sha256:51e3dfc2d41e5bc3204ca0dd4244db708270c6f4e0f21d38680b49aff0141657"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/bundle.json","state_url":"https://pith.science/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/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":"2026-06-26T21:24:55Z","links":{"resolver":"https://pith.science/pith/QBTS5ABSF2RRZUB3NPELPBIFMK","bundle":"https://pith.science/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/bundle.json","state":"https://pith.science/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QBTS5ABSF2RRZUB3NPELPBIFMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QBTS5ABSF2RRZUB3NPELPBIFMK","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":"e80b1b4d91f81882155f5fe9c214776eecbb57f9bc3e7ecd78d612fbbeabc235","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-14T15:31:43Z","title_canon_sha256":"a100c8b6d4addddb7e36815acfb5b4ebf86321a550d36980036bc11080de1af9"},"schema_version":"1.0","source":{"id":"1312.4054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4054","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4054v1","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4054","created_at":"2026-05-18T00:38:06Z"},{"alias_kind":"pith_short_12","alias_value":"QBTS5ABSF2RR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QBTS5ABSF2RRZUB3","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QBTS5ABS","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:51e3dfc2d41e5bc3204ca0dd4244db708270c6f4e0f21d38680b49aff0141657","target":"graph","created_at":"2026-05-18T00:38:06Z","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 show that for a parabolic R^d-action on a compact quotient of PSL(2,R)^d, the cohomologies in degrees 1 through d-1 trivialize, and we give the obstructions to solving the degree-d coboundary equation, along with bounds on Sobolev norms of primitives. In previous papers we have established these results for certain Anosov systems. The present work extends the methods of those papers to systems that are not Anosov. The main new idea is in Section 4, where we define special elements of representation spaces that allow us to modify the arguments from the previous papers. In Section 7 we discus","authors_text":"Felipe A. Ramirez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-14T15:31:43Z","title":"Higher cohomology of parabolic actions on certain homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4054","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:ed73bc39c44b7f5363b57187de98fe256a18df7f358655aa9618b17d45179eee","target":"record","created_at":"2026-05-18T00:38:06Z","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":"e80b1b4d91f81882155f5fe9c214776eecbb57f9bc3e7ecd78d612fbbeabc235","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-14T15:31:43Z","title_canon_sha256":"a100c8b6d4addddb7e36815acfb5b4ebf86321a550d36980036bc11080de1af9"},"schema_version":"1.0","source":{"id":"1312.4054","kind":"arxiv","version":1}},"canonical_sha256":"80672e80322ea31cd03b6bc8b785056280bf48d5c94b0006487843abed41bf3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80672e80322ea31cd03b6bc8b785056280bf48d5c94b0006487843abed41bf3b","first_computed_at":"2026-05-18T00:38:06.669303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:06.669303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anMzaB4ja9bJUuqy1AQijKLo5jjmaL1epKqS2lFcETObiJLNA4iBZUC0hDcxwUlz4KP/qpnOQ1GslmoOwPoKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:06.669881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed73bc39c44b7f5363b57187de98fe256a18df7f358655aa9618b17d45179eee","sha256:51e3dfc2d41e5bc3204ca0dd4244db708270c6f4e0f21d38680b49aff0141657"],"state_sha256":"a5352febe81ccf8f363a18e09abb82634c8c6a9a19d87c6cab17e5447749b0de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6wUZAjb+3qZgdFFY4MDq9sXOzqMofdV4bqIpR5jTjtgL0iEA1w1DNKqSxRo0UoXPfn7CzeINzGMie83eaKXHCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:24:55.756241Z","bundle_sha256":"17d376075b2b6bee7837038ac82368dcd7826f92530a4dd67a9d34d073f2c667"}}