{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TVQFQNPKVVGRXOGEK3N4ZKPYCL","short_pith_number":"pith:TVQFQNPK","canonical_record":{"source":{"id":"1711.11080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"bb829ac76e23389dec5abca84ee88d0821689b22d1da9d5aa42f4767a6c40355","abstract_canon_sha256":"2b94ca83a8803240106170e196e9f5486f4b1a4327630ff9f0af6e7534e5efa9"},"schema_version":"1.0"},"canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","source":{"kind":"arxiv","id":"1711.11080","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11080","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11080v4","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11080","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"TVQFQNPKVVGR","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"TVQFQNPKVVGRXOGE","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"TVQFQNPK","created_at":"2026-07-05T00:48:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TVQFQNPKVVGRXOGEK3N4ZKPYCL","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11080","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","cross_cats_sorted":["math.GR","math.RT"],"title_canon_sha256":"bb829ac76e23389dec5abca84ee88d0821689b22d1da9d5aa42f4767a6c40355","abstract_canon_sha256":"2b94ca83a8803240106170e196e9f5486f4b1a4327630ff9f0af6e7534e5efa9"},"schema_version":"1.0"},"canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:35.929205Z","signature_b64":"DizUCdogOxAwkfLRoYztT9AEjAaup3/d+UhSiaSzC/91uB7b/Gd8knLi1nAB5LWyX5qYB2/FV6he16gGH+YnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","last_reissued_at":"2026-07-05T00:48:35.928826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:35.928826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11080","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5w0FwDFWv/VW9Pa/cNikWfpXqxmhvrKMb5NuMUdHV/MTctsfykpqyj7e81Z4lwwfoF4wGstiRbjduBJzjpPGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:42:19.514247Z"},"content_sha256":"8ee90d871547908d974e28ca60f5a044561307b375d0e18b20322f78ce354166","schema_version":"1.0","event_id":"sha256:8ee90d871547908d974e28ca60f5a044561307b375d0e18b20322f78ce354166"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TVQFQNPKVVGRXOGEK3N4ZKPYCL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability in the homology of unipotent groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.AT","authors_text":"Andrew Putman, Andrew Snowden, Steven V Sam","submitted_at":"2017-11-29T19:55:59Z","abstract_excerpt":"Let $R$ be a (not necessarily commutative) ring whose additive group is finitely generated and let $U_n(R) \\subset GL_n(R)$ be the group of upper-triangular unipotent matrices over $R$. We study how the homology groups of $U_n(R)$ vary with $n$ from the point of view of representation stability. Our main theorem asserts that if for each $n$ we have representations $M_n$ of $U_n(R)$ over a ring $\\mathbf{k}$ that are appropriately compatible and satisfy suitable finiteness hypotheses, then the rule $[n] \\mapsto \\widetilde{H}_i(U_n(R),M_n)$ defines a finitely generated OI-module. As a consequence"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11080","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1711.11080/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjy4zYnTlvLZaJCjF9qIdiiZ10S81tuA1vr9f7nw6D+ezIJi8WiI1ONpP5aNGLkMknJOyGpgQfz6ZVdjsrlzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:42:19.514632Z"},"content_sha256":"9b17eb4689ff98795ac42de95776ecaf81246c29a3822ed6020a0697339e454b","schema_version":"1.0","event_id":"sha256:9b17eb4689ff98795ac42de95776ecaf81246c29a3822ed6020a0697339e454b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/bundle.json","state_url":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/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":"2026-07-05T08:42:19Z","links":{"resolver":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL","bundle":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/bundle.json","state":"https://pith.science/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TVQFQNPKVVGRXOGEK3N4ZKPYCL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TVQFQNPKVVGRXOGEK3N4ZKPYCL","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":"2b94ca83a8803240106170e196e9f5486f4b1a4327630ff9f0af6e7534e5efa9","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","title_canon_sha256":"bb829ac76e23389dec5abca84ee88d0821689b22d1da9d5aa42f4767a6c40355"},"schema_version":"1.0","source":{"id":"1711.11080","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11080","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11080v4","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11080","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"TVQFQNPKVVGR","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_16","alias_value":"TVQFQNPKVVGRXOGE","created_at":"2026-07-05T00:48:35Z"},{"alias_kind":"pith_short_8","alias_value":"TVQFQNPK","created_at":"2026-07-05T00:48:35Z"}],"graph_snapshots":[{"event_id":"sha256:9b17eb4689ff98795ac42de95776ecaf81246c29a3822ed6020a0697339e454b","target":"graph","created_at":"2026-07-05T00:48:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1711.11080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be a (not necessarily commutative) ring whose additive group is finitely generated and let $U_n(R) \\subset GL_n(R)$ be the group of upper-triangular unipotent matrices over $R$. We study how the homology groups of $U_n(R)$ vary with $n$ from the point of view of representation stability. Our main theorem asserts that if for each $n$ we have representations $M_n$ of $U_n(R)$ over a ring $\\mathbf{k}$ that are appropriately compatible and satisfy suitable finiteness hypotheses, then the rule $[n] \\mapsto \\widetilde{H}_i(U_n(R),M_n)$ defines a finitely generated OI-module. As a consequence","authors_text":"Andrew Putman, Andrew Snowden, Steven V Sam","cross_cats":["math.GR","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","title":"Stability in the homology of unipotent groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11080","kind":"arxiv","version":4},"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":"sha256:8ee90d871547908d974e28ca60f5a044561307b375d0e18b20322f78ce354166","target":"record","created_at":"2026-07-05T00:48:35Z","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":"2b94ca83a8803240106170e196e9f5486f4b1a4327630ff9f0af6e7534e5efa9","cross_cats_sorted":["math.GR","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-11-29T19:55:59Z","title_canon_sha256":"bb829ac76e23389dec5abca84ee88d0821689b22d1da9d5aa42f4767a6c40355"},"schema_version":"1.0","source":{"id":"1711.11080","kind":"arxiv","version":4}},"canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d605835eaad4d1bb8c456dbcca9f812ca9bf44e87262c81b185c3dcb94374bb","first_computed_at":"2026-07-05T00:48:35.928826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:35.928826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DizUCdogOxAwkfLRoYztT9AEjAaup3/d+UhSiaSzC/91uB7b/Gd8knLi1nAB5LWyX5qYB2/FV6he16gGH+YnAA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:35.929205Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11080","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ee90d871547908d974e28ca60f5a044561307b375d0e18b20322f78ce354166","sha256:9b17eb4689ff98795ac42de95776ecaf81246c29a3822ed6020a0697339e454b"],"state_sha256":"d4207bfdbf2fa89e6f88a18c668776047c04c3d3f777c4950708f4710813aa53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5GVEJoFPsRM/3+d1tLvw9U7ef9ejfPoRKUEaqCnv934HXqYn34OZgw/tss3aGkDcE+ZHJaUttosoKMKIWPb5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:42:19.516625Z","bundle_sha256":"21e2f6de08d1bd05a76a7770bb68c363307e7e4f542a965b84a5606d9a5a9fca"}}