{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DEU4N6HAM6ZPWXPTSC67MGHHQQ","short_pith_number":"pith:DEU4N6HA","canonical_record":{"source":{"id":"1311.0538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-03T22:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"ac1193d446a85bc55e39e0759e090c3411bccb01bbb4f34faad6d4a9c9837be6","abstract_canon_sha256":"41458527d0c4ff3db9500a0eac65e0ee746bd0932e5f7f7dfed4043c5ac76022"},"schema_version":"1.0"},"canonical_sha256":"1929c6f8e067b2fb5df390bdf618e78404b9f01cf69300031e3e198b63b829dd","source":{"kind":"arxiv","id":"1311.0538","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0538","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0538v2","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0538","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"DEU4N6HAM6ZP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DEU4N6HAM6ZPWXPT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DEU4N6HA","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DEU4N6HAM6ZPWXPTSC67MGHHQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-03T22:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"ac1193d446a85bc55e39e0759e090c3411bccb01bbb4f34faad6d4a9c9837be6","abstract_canon_sha256":"41458527d0c4ff3db9500a0eac65e0ee746bd0932e5f7f7dfed4043c5ac76022"},"schema_version":"1.0"},"canonical_sha256":"1929c6f8e067b2fb5df390bdf618e78404b9f01cf69300031e3e198b63b829dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:37.276400Z","signature_b64":"3ryPj71r+MoIsSJf2k4ooRyxxs0IhVlW0nkKKz7qjFQ7++7TvaHlcrOp/UlcgsyRikI1angBlPECkz8XCwfQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1929c6f8e067b2fb5df390bdf618e78404b9f01cf69300031e3e198b63b829dd","last_reissued_at":"2026-05-18T02:42:37.275813Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:37.275813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0538","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kKDDs8TJja7S50c9Zumo0tsicwQP9D8/u/YPhTrGvJo60fXi2jmQepvNbbOr2etF+CIRePwg9lKs/0YkScAPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:11:43.292277Z"},"content_sha256":"5ea251577825123b9871a66daab116aa03fdc9790d3cc70fb73f5c64bc6870e2","schema_version":"1.0","event_id":"sha256:5ea251577825123b9871a66daab116aa03fdc9790d3cc70fb73f5c64bc6870e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DEU4N6HAM6ZPWXPTSC67MGHHQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Normal Subgroup Theorem for Commensurators of Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Darren Creutz, Yehuda Shalom","submitted_at":"2013-11-03T22:38:36Z","abstract_excerpt":"We establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank lattices, relies heavily on analytic tools pertaining to amenability and Kazhdan's property (T). It is a counterpart to the normal subgroup theorem for irreducible lattices of Bader and the second named author, and may also be used to sharpen that result when one of the ambient factors is totally disconnected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0538","kind":"arxiv","version":2},"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":"2026-05-18T02:42:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"roMfw0o4+CKcmkgcBTqTUa4Jxuf6M3SWVY8TXJtIsaIKnOyzR+9v1fUAWCl8WyanqSGyNtBB4YMM+BKhUbSSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:11:43.292861Z"},"content_sha256":"48d2f350d710aee953b1890a478e252b44f77e0e604a88d9cb94c69aac24cc86","schema_version":"1.0","event_id":"sha256:48d2f350d710aee953b1890a478e252b44f77e0e604a88d9cb94c69aac24cc86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/bundle.json","state_url":"https://pith.science/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/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":"2026-06-11T05:11:43Z","links":{"resolver":"https://pith.science/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ","bundle":"https://pith.science/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/bundle.json","state":"https://pith.science/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEU4N6HAM6ZPWXPTSC67MGHHQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DEU4N6HAM6ZPWXPTSC67MGHHQQ","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":"41458527d0c4ff3db9500a0eac65e0ee746bd0932e5f7f7dfed4043c5ac76022","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-03T22:38:36Z","title_canon_sha256":"ac1193d446a85bc55e39e0759e090c3411bccb01bbb4f34faad6d4a9c9837be6"},"schema_version":"1.0","source":{"id":"1311.0538","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0538","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0538v2","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0538","created_at":"2026-05-18T02:42:37Z"},{"alias_kind":"pith_short_12","alias_value":"DEU4N6HAM6ZP","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DEU4N6HAM6ZPWXPT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DEU4N6HA","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:48d2f350d710aee953b1890a478e252b44f77e0e604a88d9cb94c69aac24cc86","target":"graph","created_at":"2026-05-18T02:42:37Z","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 establish a general normal subgroup theorem for commensurators of lattices in locally compact groups. While the statement is completely elementary, its proof, which rests on the original strategy of Margulis in the case of higher rank lattices, relies heavily on analytic tools pertaining to amenability and Kazhdan's property (T). It is a counterpart to the normal subgroup theorem for irreducible lattices of Bader and the second named author, and may also be used to sharpen that result when one of the ambient factors is totally disconnected.","authors_text":"Darren Creutz, Yehuda Shalom","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-03T22:38:36Z","title":"A Normal Subgroup Theorem for Commensurators of Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0538","kind":"arxiv","version":2},"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":"sha256:5ea251577825123b9871a66daab116aa03fdc9790d3cc70fb73f5c64bc6870e2","target":"record","created_at":"2026-05-18T02:42:37Z","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":"41458527d0c4ff3db9500a0eac65e0ee746bd0932e5f7f7dfed4043c5ac76022","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-11-03T22:38:36Z","title_canon_sha256":"ac1193d446a85bc55e39e0759e090c3411bccb01bbb4f34faad6d4a9c9837be6"},"schema_version":"1.0","source":{"id":"1311.0538","kind":"arxiv","version":2}},"canonical_sha256":"1929c6f8e067b2fb5df390bdf618e78404b9f01cf69300031e3e198b63b829dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1929c6f8e067b2fb5df390bdf618e78404b9f01cf69300031e3e198b63b829dd","first_computed_at":"2026-05-18T02:42:37.275813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:37.275813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ryPj71r+MoIsSJf2k4ooRyxxs0IhVlW0nkKKz7qjFQ7++7TvaHlcrOp/UlcgsyRikI1angBlPECkz8XCwfQBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:37.276400Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0538","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ea251577825123b9871a66daab116aa03fdc9790d3cc70fb73f5c64bc6870e2","sha256:48d2f350d710aee953b1890a478e252b44f77e0e604a88d9cb94c69aac24cc86"],"state_sha256":"00d2766d2153943e4c2b90f22f63eabc9049375d9646cb84e73b95dbf5971a50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ykMXKWjSNDCzSHz98dPE/ZD1DWdTtNsiJKgpWdYCnzonDEc5/ObCh4x+eRsuDhRNOn2EDGnUbdP/tsI416+BDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:11:43.295906Z","bundle_sha256":"b9981e972cf472032c5925ffc94ebac2e1e6c55eefe9e4fe905039ed338a754b"}}