{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SUNX547FQTWJ6ZB2MMTXCAHG7J","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":"0f4391ca55c2082c6b8858c30aea47d1dc367688a36295f35428910a980c72bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-27T00:08:10Z","title_canon_sha256":"39b62b71f3bb10553fad1076c304c76fd56cf9d322a900fa1e1fbeedfa0d3f17"},"schema_version":"1.0","source":{"id":"1406.7047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7047","created_at":"2026-05-18T02:48:54Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7047v1","created_at":"2026-05-18T02:48:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7047","created_at":"2026-05-18T02:48:54Z"},{"alias_kind":"pith_short_12","alias_value":"SUNX547FQTWJ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SUNX547FQTWJ6ZB2","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SUNX547F","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:b07cc4f9f3747a6ede2d00f9fe375e1ce15a0344450499f68d7780536c6cc74e","target":"graph","created_at":"2026-05-18T02:48:54Z","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 homology and the Borel-Moore homology with coefficients in $\\mathbb{Q}$ of a quotient (called arithmetic quotient) of the Bruhat-Tits building of $\\mathrm{PGL}$ of a nonarchimedean local field of positive characteristic by an arithmetic subgroup (a special case of the general definition in Harder's article (Invent.\\ Math.\\ 42, 135-175 (1977)).\n  We define an analogue of modular symbols in this context and show that the image of the canonical map from homology to Borel-Moore homology is contained in the sub $\\mathbb{Q}$-vector space generated by the modular symbols.\n  By definition","authors_text":"Satoshi Kondo, Seidai Yasuda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-27T00:08:10Z","title":"The Borel-Moore homology of an arithmetic quotient of the Bruhat-Tits building of PGL of a non-archimedean local field in positive characteristic and modular symbols"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7047","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:ceabd0a8de259043b9cf1b75b604a1138f1c3769e6ae218faa5fa944df11c336","target":"record","created_at":"2026-05-18T02:48:54Z","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":"0f4391ca55c2082c6b8858c30aea47d1dc367688a36295f35428910a980c72bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-27T00:08:10Z","title_canon_sha256":"39b62b71f3bb10553fad1076c304c76fd56cf9d322a900fa1e1fbeedfa0d3f17"},"schema_version":"1.0","source":{"id":"1406.7047","kind":"arxiv","version":1}},"canonical_sha256":"951b7ef3e584ec9f643a63277100e6fa736f2f197ce93bae313a33cc30b62cd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"951b7ef3e584ec9f643a63277100e6fa736f2f197ce93bae313a33cc30b62cd7","first_computed_at":"2026-05-18T02:48:54.264005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:54.264005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fC+lQMkb3jzBQlhlvHsxijyNPIiCRgBd+7vq3HOM6TUCPsMeGSck9UEOhUNuuwGRdpreuiWp1kI4cDhUeFNqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:54.264480Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ceabd0a8de259043b9cf1b75b604a1138f1c3769e6ae218faa5fa944df11c336","sha256:b07cc4f9f3747a6ede2d00f9fe375e1ce15a0344450499f68d7780536c6cc74e"],"state_sha256":"dc1cea138bfe9082534325d0be11d6c303714fc864818b21cb92477f0506c66e"}