{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6LNY4HMQN7CXIMNVYCYGH6O7EN","short_pith_number":"pith:6LNY4HMQ","canonical_record":{"source":{"id":"1107.4689","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T13:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"e4593faffe9ed3df7be5fc57ec52f3e512d78dfedfca5186524a74120f45dead","abstract_canon_sha256":"5370f4c9f6934a5d8aacccbad15bc86855bc66e87e32434c672228892b699137"},"schema_version":"1.0"},"canonical_sha256":"f2db8e1d906fc57431b5c0b063f9df23507eb2c9d94afbf69fe4a30196e19def","source":{"kind":"arxiv","id":"1107.4689","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4689","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4689v3","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4689","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"6LNY4HMQN7CX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LNY4HMQN7CXIMNV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LNY4HMQ","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6LNY4HMQN7CXIMNVYCYGH6O7EN","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4689","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T13:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"e4593faffe9ed3df7be5fc57ec52f3e512d78dfedfca5186524a74120f45dead","abstract_canon_sha256":"5370f4c9f6934a5d8aacccbad15bc86855bc66e87e32434c672228892b699137"},"schema_version":"1.0"},"canonical_sha256":"f2db8e1d906fc57431b5c0b063f9df23507eb2c9d94afbf69fe4a30196e19def","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:38.819626Z","signature_b64":"4q6lIFbS00bba4krxB7bNuns2ofKsnzMwOKrfIq6ieIiIeu813TGc9nuxokx+SGd06RIakvQ9+Jc8UNbixoDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2db8e1d906fc57431b5c0b063f9df23507eb2c9d94afbf69fe4a30196e19def","last_reissued_at":"2026-05-18T03:04:38.818970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:38.818970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4689","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4OKrD7VafmSxcHhGLcV6bv7cJLDMWHKN5GRwXd2w0043UCBRiX5vyp081136yZLlhrcjsgBKoyLvj6DFXjnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:38:48.317868Z"},"content_sha256":"935f2714186da6ab418fae2cfa421376d06edc40d645100e36d323d7b8e63bbe","schema_version":"1.0","event_id":"sha256:935f2714186da6ab418fae2cfa421376d06edc40d645100e36d323d7b8e63bbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6LNY4HMQN7CXIMNVYCYGH6O7EN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher cohomology for Anosov 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":"2011-07-23T13:34:10Z","abstract_excerpt":"We study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \\times \\cdot \\cdot \\cdot \\times SL(2, R)]/{\\Gamma} by the subgroup of diagonal matrices, where {\\Gamma} is an irreducible lattice. In the top degree, we show that the obstructions to solving the coboundary equation come from distributions that are invariant under the action. In intermediate degrees, we show that the cohomology trivializes. It has been conjectured by A. and S. Katok that, for a standard partially hyperbolic R^d- or Z^d-action, the obstructions to solving the top-degree coboundary equatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4689","kind":"arxiv","version":3},"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":"2026-05-18T03:04:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0i/i8HEqAaP5U10oEM1GVT1PYTpdW0pvgxGGz1BFiS8xyaIaG5BYZ5FpoCFCy/XZAQYJAmsijaTCZkSpJ99EAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:38:48.318214Z"},"content_sha256":"2b2f203359b8da67d3dd2dfd24ba9fce69e43e0cd0e0388fa75d3c6d945db2cd","schema_version":"1.0","event_id":"sha256:2b2f203359b8da67d3dd2dfd24ba9fce69e43e0cd0e0388fa75d3c6d945db2cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/bundle.json","state_url":"https://pith.science/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/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":"2026-06-26T15:38:48Z","links":{"resolver":"https://pith.science/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN","bundle":"https://pith.science/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/bundle.json","state":"https://pith.science/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LNY4HMQN7CXIMNVYCYGH6O7EN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6LNY4HMQN7CXIMNVYCYGH6O7EN","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":"5370f4c9f6934a5d8aacccbad15bc86855bc66e87e32434c672228892b699137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T13:34:10Z","title_canon_sha256":"e4593faffe9ed3df7be5fc57ec52f3e512d78dfedfca5186524a74120f45dead"},"schema_version":"1.0","source":{"id":"1107.4689","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4689","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4689v3","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4689","created_at":"2026-05-18T03:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"6LNY4HMQN7CX","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6LNY4HMQN7CXIMNV","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6LNY4HMQ","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:2b2f203359b8da67d3dd2dfd24ba9fce69e43e0cd0e0388fa75d3c6d945db2cd","target":"graph","created_at":"2026-05-18T03:04:38Z","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 study the smooth untwisted cohomology with real coefficients for the action on [SL(2, R) \\times \\cdot \\cdot \\cdot \\times SL(2, R)]/{\\Gamma} by the subgroup of diagonal matrices, where {\\Gamma} is an irreducible lattice. In the top degree, we show that the obstructions to solving the coboundary equation come from distributions that are invariant under the action. In intermediate degrees, we show that the cohomology trivializes. It has been conjectured by A. and S. Katok that, for a standard partially hyperbolic R^d- or Z^d-action, the obstructions to solving the top-degree coboundary equatio","authors_text":"Felipe A. Ramirez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T13:34:10Z","title":"Higher cohomology for Anosov actions on certain homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4689","kind":"arxiv","version":3},"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":"sha256:935f2714186da6ab418fae2cfa421376d06edc40d645100e36d323d7b8e63bbe","target":"record","created_at":"2026-05-18T03:04:38Z","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":"5370f4c9f6934a5d8aacccbad15bc86855bc66e87e32434c672228892b699137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-23T13:34:10Z","title_canon_sha256":"e4593faffe9ed3df7be5fc57ec52f3e512d78dfedfca5186524a74120f45dead"},"schema_version":"1.0","source":{"id":"1107.4689","kind":"arxiv","version":3}},"canonical_sha256":"f2db8e1d906fc57431b5c0b063f9df23507eb2c9d94afbf69fe4a30196e19def","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2db8e1d906fc57431b5c0b063f9df23507eb2c9d94afbf69fe4a30196e19def","first_computed_at":"2026-05-18T03:04:38.818970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:38.818970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4q6lIFbS00bba4krxB7bNuns2ofKsnzMwOKrfIq6ieIiIeu813TGc9nuxokx+SGd06RIakvQ9+Jc8UNbixoDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:38.819626Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4689","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:935f2714186da6ab418fae2cfa421376d06edc40d645100e36d323d7b8e63bbe","sha256:2b2f203359b8da67d3dd2dfd24ba9fce69e43e0cd0e0388fa75d3c6d945db2cd"],"state_sha256":"b3e45848469f6e782dc08cad4212f02a7bd74115c09a284331af49b666cce5c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVN5Pho4qNgfAfAjC/Q/NOMK63vmZpQSfK01BRYsY92FUQZejj4XMeLzQ/QU+SVnHlqC0Zy+OMhgo84UT54vDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:38:48.320232Z","bundle_sha256":"2bb74fadb90a55197f306a2ecedefffe399c2d618d7181ab50b666db5e8296c6"}}