{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EYWIWKXXGAIO2EGSRFVL7AR4AY","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":"40f3fe4829c8539e65d2f64da6558adf1582f8e7222d72ad91d7bb9000206c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T06:32:55Z","title_canon_sha256":"c99851b24ec78617b6e6654584dd0b4fb8e7b432c93a763407286ba840765692"},"schema_version":"1.0","source":{"id":"1008.2053","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2053","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2053v3","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2053","created_at":"2026-05-18T02:45:41Z"},{"alias_kind":"pith_short_12","alias_value":"EYWIWKXXGAIO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EYWIWKXXGAIO2EGS","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EYWIWKXX","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:eaf7ffb0c41907b27b38bd3b0fac67b848cdf6588f0194e34e4b6ee4774fbb34","target":"graph","created_at":"2026-05-18T02:45:41Z","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":"In this article we investigate the number of subrings of $\\Z^d$ using subring zeta functions and $p$-adic integration.","authors_text":"Jake Marcinek, Nathan Kaplan, Ramin Takloo-Bighash","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T06:32:55Z","title":"Counting Subrings of ${\\mathbb Z}^n$ of finite index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2053","kind":"arxiv","version":3},"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":"sha256:54c86c8e4fd6891045883aac3e61f8b35f56488221652436e7e0fcfe6f11f8c5","target":"record","created_at":"2026-05-18T02:45:41Z","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":"40f3fe4829c8539e65d2f64da6558adf1582f8e7222d72ad91d7bb9000206c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T06:32:55Z","title_canon_sha256":"c99851b24ec78617b6e6654584dd0b4fb8e7b432c93a763407286ba840765692"},"schema_version":"1.0","source":{"id":"1008.2053","kind":"arxiv","version":3}},"canonical_sha256":"262c8b2af73010ed10d2896abf823c063a33a6e1987db01df4df345ba4e04fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"262c8b2af73010ed10d2896abf823c063a33a6e1987db01df4df345ba4e04fcc","first_computed_at":"2026-05-18T02:45:41.366683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:41.366683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FCKTG4qVJTDx2+s9LBwohaQZnUsHARHlYHW78anyXPpV9r+cdCMZNXAVaUluEw6pRCGonV58jN49SslnPG5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:41.367119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2053","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54c86c8e4fd6891045883aac3e61f8b35f56488221652436e7e0fcfe6f11f8c5","sha256:eaf7ffb0c41907b27b38bd3b0fac67b848cdf6588f0194e34e4b6ee4774fbb34"],"state_sha256":"822f3d215d5275e33c4018d0c61df4535dd9a3b4bb70461120b8d9581c4f0c95"}