{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S4ONTLXKPSOZJH56RRX55WWE4B","short_pith_number":"pith:S4ONTLXK","canonical_record":{"source":{"id":"1309.2352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-10T00:47:33Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"deecdfc4225f3fb48616af7265a49c3c91e2731d36636b14a3c2035170acde2b","abstract_canon_sha256":"21403fdca4d10473f746e2ad09ce467e788ba536757fa403e1da4579e4261a8d"},"schema_version":"1.0"},"canonical_sha256":"971cd9aeea7c9d949fbe8c6fdedac4e06107ffacf9031560ff6c2fd493d7e453","source":{"kind":"arxiv","id":"1309.2352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2352","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2352v1","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2352","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"S4ONTLXKPSOZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S4ONTLXKPSOZJH56","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S4ONTLXK","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S4ONTLXKPSOZJH56RRX55WWE4B","target":"record","payload":{"canonical_record":{"source":{"id":"1309.2352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-10T00:47:33Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"deecdfc4225f3fb48616af7265a49c3c91e2731d36636b14a3c2035170acde2b","abstract_canon_sha256":"21403fdca4d10473f746e2ad09ce467e788ba536757fa403e1da4579e4261a8d"},"schema_version":"1.0"},"canonical_sha256":"971cd9aeea7c9d949fbe8c6fdedac4e06107ffacf9031560ff6c2fd493d7e453","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:44.998832Z","signature_b64":"Fwn6YBnssiZQgCwwhL0BKG16B380kMRedra9GTuu/AJTpWeqw+Cl4i/5BLSKX/50/yc41YXZIbk4il4/3NgKDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"971cd9aeea7c9d949fbe8c6fdedac4e06107ffacf9031560ff6c2fd493d7e453","last_reissued_at":"2026-05-18T03:13:44.998039Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:44.998039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.2352","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":"2026-05-18T03:13:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jGU+D0sTXNqV6oNnM77I3qB99mHy7zkQJE3MG0TxhyG0n4Gn+f0qLDpTxiIg/lnVfGuOBUt06S+oWtIrafulDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:22:27.034584Z"},"content_sha256":"10bb04f475fdab16149ca3c315d0a5cbf55f88b48b2f70c128a3063e8b3f499e","schema_version":"1.0","event_id":"sha256:10bb04f475fdab16149ca3c315d0a5cbf55f88b48b2f70c128a3063e8b3f499e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S4ONTLXKPSOZJH56RRX55WWE4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Translate of horospheres and counting problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.DS","authors_text":"Alireza Salehi Golsefidy, Amir Mohammadi","submitted_at":"2013-09-10T00:47:33Z","abstract_excerpt":"Let G be a semisimple Lie group without compact factors, \\Gamma be an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability \"horospherical measures\" is convergent. And the limiting measure is also determined when it is convergent (see Theorems 1 and 2 for the precise statements). In the second part, two applications are presented. The first one is of geometric nature and the second one gives an alternative way to count the number of rational points on a flag variety."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2352","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":"2026-05-18T03:13:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lxru9elPo/WRP//30ibMnPgFmtiHk/6QuvHH7p7SQKXCxvgR/HiPoeP+LoIvIworp4ntbQXZmFetOVh8iaJhBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:22:27.034939Z"},"content_sha256":"aa8fd5f22cb1c650c154f25156ada36ff578ce3baf5dfbedfd8fba2411af5c9a","schema_version":"1.0","event_id":"sha256:aa8fd5f22cb1c650c154f25156ada36ff578ce3baf5dfbedfd8fba2411af5c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4ONTLXKPSOZJH56RRX55WWE4B/bundle.json","state_url":"https://pith.science/pith/S4ONTLXKPSOZJH56RRX55WWE4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4ONTLXKPSOZJH56RRX55WWE4B/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":"2026-05-28T02:22:27Z","links":{"resolver":"https://pith.science/pith/S4ONTLXKPSOZJH56RRX55WWE4B","bundle":"https://pith.science/pith/S4ONTLXKPSOZJH56RRX55WWE4B/bundle.json","state":"https://pith.science/pith/S4ONTLXKPSOZJH56RRX55WWE4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4ONTLXKPSOZJH56RRX55WWE4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S4ONTLXKPSOZJH56RRX55WWE4B","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":"21403fdca4d10473f746e2ad09ce467e788ba536757fa403e1da4579e4261a8d","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-10T00:47:33Z","title_canon_sha256":"deecdfc4225f3fb48616af7265a49c3c91e2731d36636b14a3c2035170acde2b"},"schema_version":"1.0","source":{"id":"1309.2352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2352","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2352v1","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2352","created_at":"2026-05-18T03:13:44Z"},{"alias_kind":"pith_short_12","alias_value":"S4ONTLXKPSOZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S4ONTLXKPSOZJH56","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S4ONTLXK","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:aa8fd5f22cb1c650c154f25156ada36ff578ce3baf5dfbedfd8fba2411af5c9a","target":"graph","created_at":"2026-05-18T03:13:44Z","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 G be a semisimple Lie group without compact factors, \\Gamma be an irreducible lattice in G. In the first part of the article we give the necessary and sufficient condition under which a sequence of translates of probability \"horospherical measures\" is convergent. And the limiting measure is also determined when it is convergent (see Theorems 1 and 2 for the precise statements). In the second part, two applications are presented. The first one is of geometric nature and the second one gives an alternative way to count the number of rational points on a flag variety.","authors_text":"Alireza Salehi Golsefidy, Amir Mohammadi","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-10T00:47:33Z","title":"Translate of horospheres and counting problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2352","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":"sha256:10bb04f475fdab16149ca3c315d0a5cbf55f88b48b2f70c128a3063e8b3f499e","target":"record","created_at":"2026-05-18T03:13:44Z","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":"21403fdca4d10473f746e2ad09ce467e788ba536757fa403e1da4579e4261a8d","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-10T00:47:33Z","title_canon_sha256":"deecdfc4225f3fb48616af7265a49c3c91e2731d36636b14a3c2035170acde2b"},"schema_version":"1.0","source":{"id":"1309.2352","kind":"arxiv","version":1}},"canonical_sha256":"971cd9aeea7c9d949fbe8c6fdedac4e06107ffacf9031560ff6c2fd493d7e453","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"971cd9aeea7c9d949fbe8c6fdedac4e06107ffacf9031560ff6c2fd493d7e453","first_computed_at":"2026-05-18T03:13:44.998039Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:44.998039Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fwn6YBnssiZQgCwwhL0BKG16B380kMRedra9GTuu/AJTpWeqw+Cl4i/5BLSKX/50/yc41YXZIbk4il4/3NgKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:44.998832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10bb04f475fdab16149ca3c315d0a5cbf55f88b48b2f70c128a3063e8b3f499e","sha256:aa8fd5f22cb1c650c154f25156ada36ff578ce3baf5dfbedfd8fba2411af5c9a"],"state_sha256":"28840d4530979f0816aa31362b1a173577b229bb52ca987ede7b6f2af9d6127e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lbcyCnpXtOz2cliv1FWKDkpNHpUTtqu0/LJ+UCcOizAxbPBbfJbJG3RlgzSsQWyfcpeEhz9NbI32i4UeS0LqCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:22:27.037034Z","bundle_sha256":"db3aba65cafec95cc48279f53b6c055de18d0e5455a36df14074fbeb51afba20"}}