{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DSKTWSEMFETIND74YR65WJL2IN","short_pith_number":"pith:DSKTWSEM","canonical_record":{"source":{"id":"1809.03021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"9a13aa8db25a97a7adc681fef12d81c1f5692c405fda1c6dc7327f092cd33d96","abstract_canon_sha256":"fdd99fc560b7587260fab9d8fb7efda9d4419498135b734457be6ff82384b1b3"},"schema_version":"1.0"},"canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","source":{"kind":"arxiv","id":"1809.03021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03021","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03021v1","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03021","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"DSKTWSEMFETI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSKTWSEMFETIND74","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSKTWSEM","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DSKTWSEMFETIND74YR65WJL2IN","target":"record","payload":{"canonical_record":{"source":{"id":"1809.03021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"9a13aa8db25a97a7adc681fef12d81c1f5692c405fda1c6dc7327f092cd33d96","abstract_canon_sha256":"fdd99fc560b7587260fab9d8fb7efda9d4419498135b734457be6ff82384b1b3"},"schema_version":"1.0"},"canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:13.585565Z","signature_b64":"g2R8YLEoQYKU0jpb8RvAuq2Dp97CGpGF321Oh6tCgczIBBkyA9uYSyvs9bc2I288c5mkTpzC8VWzaLiuu2NeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","last_reissued_at":"2026-05-18T00:05:13.584656Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:13.584656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.03021","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":"2026-05-18T00:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XFrObKvR7CMIAFtWFKqBQ6y6YCbDhz961/kzW7keE1aWsOoKb8ACet/BQW6BlxjhIsmHj3Dfp0gPp40oy3R3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:03.760378Z"},"content_sha256":"331150fc806e6bffb9c5e740dabc0ea0c565c99c0f9f6f993ef08b3cd15432f6","schema_version":"1.0","event_id":"sha256:331150fc806e6bffb9c5e740dabc0ea0c565c99c0f9f6f993ef08b3cd15432f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DSKTWSEMFETIND74YR65WJL2IN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomological equation and cocycle rigidity of discrete parabolic actions in some higher rank Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"James Tanis, Zhenqi Jenny Wang","submitted_at":"2018-09-09T18:41:31Z","abstract_excerpt":"Let $\\mathbb{G}$ denote a higher rank $\\mathbb R$-split simple Lie group of the following type: $SL(n,\\mathbb R)$, $SO_o(m,m)$, $E_{6(6)}$, $E_{7(7)}$ and $E_{8(8)}$, where $m\\geq 4$ and $n \\geq 3$. We study the cohomological equation for discrete parabolic actions on $\\mathbb G$ via representation theory. Specifically, we characterize the obstructions to solving the cohomological equation and construct smooth solutions with Sobolev estimates. We prove that global estimates of the solution are generally not tame, and our non-tame estimates in the case $\\mathbb G=SL(n,\\mathbb R)$ are sharp up t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03021","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":"2026-05-18T00:05:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWIK+nSBfZnkqsZMBQ/p+ppr8bLHMjNudf8nmHC+sEsmtg2YEMIxKhconvZ1PWoD8DcgFANqufOUMdbcSB6cBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:37:03.760736Z"},"content_sha256":"f5e698851db418fdacbde83665838853d4a982791767531af674cf66c0b93161","schema_version":"1.0","event_id":"sha256:f5e698851db418fdacbde83665838853d4a982791767531af674cf66c0b93161"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DSKTWSEMFETIND74YR65WJL2IN/bundle.json","state_url":"https://pith.science/pith/DSKTWSEMFETIND74YR65WJL2IN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DSKTWSEMFETIND74YR65WJL2IN/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":"2026-06-03T18:37:03Z","links":{"resolver":"https://pith.science/pith/DSKTWSEMFETIND74YR65WJL2IN","bundle":"https://pith.science/pith/DSKTWSEMFETIND74YR65WJL2IN/bundle.json","state":"https://pith.science/pith/DSKTWSEMFETIND74YR65WJL2IN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DSKTWSEMFETIND74YR65WJL2IN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DSKTWSEMFETIND74YR65WJL2IN","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":"fdd99fc560b7587260fab9d8fb7efda9d4419498135b734457be6ff82384b1b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","title_canon_sha256":"9a13aa8db25a97a7adc681fef12d81c1f5692c405fda1c6dc7327f092cd33d96"},"schema_version":"1.0","source":{"id":"1809.03021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03021","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03021v1","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03021","created_at":"2026-05-18T00:05:13Z"},{"alias_kind":"pith_short_12","alias_value":"DSKTWSEMFETI","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DSKTWSEMFETIND74","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DSKTWSEM","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:f5e698851db418fdacbde83665838853d4a982791767531af674cf66c0b93161","target":"graph","created_at":"2026-05-18T00:05:13Z","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":"Let $\\mathbb{G}$ denote a higher rank $\\mathbb R$-split simple Lie group of the following type: $SL(n,\\mathbb R)$, $SO_o(m,m)$, $E_{6(6)}$, $E_{7(7)}$ and $E_{8(8)}$, where $m\\geq 4$ and $n \\geq 3$. We study the cohomological equation for discrete parabolic actions on $\\mathbb G$ via representation theory. Specifically, we characterize the obstructions to solving the cohomological equation and construct smooth solutions with Sobolev estimates. We prove that global estimates of the solution are generally not tame, and our non-tame estimates in the case $\\mathbb G=SL(n,\\mathbb R)$ are sharp up t","authors_text":"James Tanis, Zhenqi Jenny Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","title":"Cohomological equation and cocycle rigidity of discrete parabolic actions in some higher rank Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03021","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":"sha256:331150fc806e6bffb9c5e740dabc0ea0c565c99c0f9f6f993ef08b3cd15432f6","target":"record","created_at":"2026-05-18T00:05:13Z","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":"fdd99fc560b7587260fab9d8fb7efda9d4419498135b734457be6ff82384b1b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-09T18:41:31Z","title_canon_sha256":"9a13aa8db25a97a7adc681fef12d81c1f5692c405fda1c6dc7327f092cd33d96"},"schema_version":"1.0","source":{"id":"1809.03021","kind":"arxiv","version":1}},"canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c953b488c2926868ffcc47ddb257a437e23f0b8e2223b9a49b0665abe563479","first_computed_at":"2026-05-18T00:05:13.584656Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:13.584656Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g2R8YLEoQYKU0jpb8RvAuq2Dp97CGpGF321Oh6tCgczIBBkyA9uYSyvs9bc2I288c5mkTpzC8VWzaLiuu2NeCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:13.585565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:331150fc806e6bffb9c5e740dabc0ea0c565c99c0f9f6f993ef08b3cd15432f6","sha256:f5e698851db418fdacbde83665838853d4a982791767531af674cf66c0b93161"],"state_sha256":"92916731460c5920ab2d2bb3c3b0122891ee238072d99790512a870040565227"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0mCBJ8uPqFu/X5PjCOyxLhFCIhnXqG3UgCNuvSZVaRgYP38e+WsE79cz7G5TzEBgyohDJfKRwmaW4SbCg12wAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:37:03.762768Z","bundle_sha256":"1dbcd064f004ccbc5572610b3f520154b0aad23856a290243ff05c131a0b8cc8"}}