{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2WMZCY4J5OF6H4FAQ4XSJCNFZ4","short_pith_number":"pith:2WMZCY4J","canonical_record":{"source":{"id":"1509.01749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-06T00:23:18Z","cross_cats_sorted":[],"title_canon_sha256":"aa8b8d7b09ce04ed4a553129319b6137ecec260e9e8f77d48cb6e248a1b19d79","abstract_canon_sha256":"005f404d155dd790b4e2135187ed0ed4dd93ab30d0f9f59a84cd0171b6c70175"},"schema_version":"1.0"},"canonical_sha256":"d599916389eb8be3f0a0872f2489a5cf19691729a59e6822e8cec0fed6ffca75","source":{"kind":"arxiv","id":"1509.01749","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01749","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01749v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01749","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"2WMZCY4J5OF6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2WMZCY4J5OF6H4FA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2WMZCY4J","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2WMZCY4J5OF6H4FAQ4XSJCNFZ4","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-06T00:23:18Z","cross_cats_sorted":[],"title_canon_sha256":"aa8b8d7b09ce04ed4a553129319b6137ecec260e9e8f77d48cb6e248a1b19d79","abstract_canon_sha256":"005f404d155dd790b4e2135187ed0ed4dd93ab30d0f9f59a84cd0171b6c70175"},"schema_version":"1.0"},"canonical_sha256":"d599916389eb8be3f0a0872f2489a5cf19691729a59e6822e8cec0fed6ffca75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.695204Z","signature_b64":"z73R9D6om7xTE1PRlyoTWE0WkGn3iddwD8ibbPP0jPewLir2mtSqJn/jxSkEUHf7ekSDZHW5K4j+TCdZuM+bDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d599916389eb8be3f0a0872f2489a5cf19691729a59e6822e8cec0fed6ffca75","last_reissued_at":"2026-05-18T01:33:50.694737Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.694737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01749","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BuPv4BI7srsm9WyyHrrHVcQXtIQNv9fKq2VBf0fSUbptj9dIADzKEUK5pj1Z6wx3F68F6aM1QirLXDDNibK5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:00:55.573165Z"},"content_sha256":"dcb773121869801d577f404b9e2f78136a5c0cdc280e70145c955fe67e8d2382","schema_version":"1.0","event_id":"sha256:dcb773121869801d577f404b9e2f78136a5c0cdc280e70145c955fe67e8d2382"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2WMZCY4J5OF6H4FAQ4XSJCNFZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abelianized fundamental group of the affine space over a finite field and big Witt vectors in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Henrik Russell","submitted_at":"2015-09-06T00:23:18Z","abstract_excerpt":"Let $X$ be a normal proper variety over a perfect field $k$. We describe abelian coverings of X in terms of the functor $\\underline{\\rm HDiv}_X$ of principal relative Cartier divisors on $X$. If the base field $k$ is finite, the geometric Galois group of the maximal abelian extension of the function field of $X$ is given by the $k$-valued points of the Cartier dual of the completion of $\\underline{\\rm HDiv}_X$. As another application, we present the geometric abelianized fundamental group of the affine $n$-space over a finite field by the group of big Witt vectors in $n$ variables, a generaliz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01749","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":"2026-05-18T01:33:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2UNQQJY7AIz5UjEMLVN+EwhfpoEG3SEU9NUHi+0OHoEOL2ud3e2buCrXjOZC5f//QL+NcAqZYThLmM+Jt3VCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T17:00:55.573724Z"},"content_sha256":"bd23953d168b490ff015986b019b9200ea4ef8d750bfb2b518ca983e8409166c","schema_version":"1.0","event_id":"sha256:bd23953d168b490ff015986b019b9200ea4ef8d750bfb2b518ca983e8409166c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/bundle.json","state_url":"https://pith.science/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/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":"2026-06-30T17:00:55Z","links":{"resolver":"https://pith.science/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4","bundle":"https://pith.science/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/bundle.json","state":"https://pith.science/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2WMZCY4J5OF6H4FAQ4XSJCNFZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2WMZCY4J5OF6H4FAQ4XSJCNFZ4","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":"005f404d155dd790b4e2135187ed0ed4dd93ab30d0f9f59a84cd0171b6c70175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-06T00:23:18Z","title_canon_sha256":"aa8b8d7b09ce04ed4a553129319b6137ecec260e9e8f77d48cb6e248a1b19d79"},"schema_version":"1.0","source":{"id":"1509.01749","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01749","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01749v1","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01749","created_at":"2026-05-18T01:33:50Z"},{"alias_kind":"pith_short_12","alias_value":"2WMZCY4J5OF6","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2WMZCY4J5OF6H4FA","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2WMZCY4J","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:bd23953d168b490ff015986b019b9200ea4ef8d750bfb2b518ca983e8409166c","target":"graph","created_at":"2026-05-18T01:33:50Z","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 $X$ be a normal proper variety over a perfect field $k$. We describe abelian coverings of X in terms of the functor $\\underline{\\rm HDiv}_X$ of principal relative Cartier divisors on $X$. If the base field $k$ is finite, the geometric Galois group of the maximal abelian extension of the function field of $X$ is given by the $k$-valued points of the Cartier dual of the completion of $\\underline{\\rm HDiv}_X$. As another application, we present the geometric abelianized fundamental group of the affine $n$-space over a finite field by the group of big Witt vectors in $n$ variables, a generaliz","authors_text":"Henrik Russell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-06T00:23:18Z","title":"Abelianized fundamental group of the affine space over a finite field and big Witt vectors in several variables"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01749","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:dcb773121869801d577f404b9e2f78136a5c0cdc280e70145c955fe67e8d2382","target":"record","created_at":"2026-05-18T01:33:50Z","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":"005f404d155dd790b4e2135187ed0ed4dd93ab30d0f9f59a84cd0171b6c70175","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-09-06T00:23:18Z","title_canon_sha256":"aa8b8d7b09ce04ed4a553129319b6137ecec260e9e8f77d48cb6e248a1b19d79"},"schema_version":"1.0","source":{"id":"1509.01749","kind":"arxiv","version":1}},"canonical_sha256":"d599916389eb8be3f0a0872f2489a5cf19691729a59e6822e8cec0fed6ffca75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d599916389eb8be3f0a0872f2489a5cf19691729a59e6822e8cec0fed6ffca75","first_computed_at":"2026-05-18T01:33:50.694737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:50.694737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z73R9D6om7xTE1PRlyoTWE0WkGn3iddwD8ibbPP0jPewLir2mtSqJn/jxSkEUHf7ekSDZHW5K4j+TCdZuM+bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:50.695204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01749","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcb773121869801d577f404b9e2f78136a5c0cdc280e70145c955fe67e8d2382","sha256:bd23953d168b490ff015986b019b9200ea4ef8d750bfb2b518ca983e8409166c"],"state_sha256":"9c4af522cf36bc662197b86fbcfb554a3fc9a0b0bb31188127ecd8e19c9233b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnnSVlqIcNnv9TeypvZnOCcE4x/kYajuCEsSV6VB6PnCbLYkyT81QE6V0kKqnroOBi6XJR6mOHB5OLFhue2EAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T17:00:55.576193Z","bundle_sha256":"cb7dbdd102ce9be56b5787e8133bd447c09ed73957a2638e1a87742338a52fb3"}}