{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QYMTVVV7EX4MEIJKKDJBYF5VI6","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":"76c5f65f625a46e69d2aec222199c5e6ff3af36677a63b8b7d96ad66f7e7aadd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T07:19:06Z","title_canon_sha256":"d79e62d115b1ce2b39002c4ae4f52ee68bac1983cb3d5f58f0d42c66b1c8fcb4"},"schema_version":"1.0","source":{"id":"1806.10801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.10801","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1806.10801v2","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.10801","created_at":"2026-05-18T00:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"QYMTVVV7EX4M","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QYMTVVV7EX4MEIJK","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QYMTVVV7","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:1a2595f156105a30eef320a6ec6f24f4d569a03da6cb84f8f0160a901b5a4782","target":"graph","created_at":"2026-05-18T00:07:17Z","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":"After the first heuristic ideas about `the field of one element' F_1 and `geometry in characteristics 1' (J.~Tits, C.~Deninger, M.~Kapranov, A.~Smirnov et al.), there were developed several general approaches to the construction of `geometries below Spec Z'. Homotopy theory and the `the brave new algebra' were taking more and more important places in these developments, systematically explored by B.~To\\\"en and M.~Vaqui\\'e, among others.\n  This article contains a brief survey and some new results on counting problems in this context, including various approaches to zeta--functions and generalis","authors_text":"Matilde Marcolli, Yuri I. Manin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T07:19:06Z","title":"Homotopy types and geometries below Spec Z"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.10801","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":"sha256:3154b28de4dd87239f34441c741e929fae1c2a40d39c9844220952332c3849e6","target":"record","created_at":"2026-05-18T00:07:17Z","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":"76c5f65f625a46e69d2aec222199c5e6ff3af36677a63b8b7d96ad66f7e7aadd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-06-28T07:19:06Z","title_canon_sha256":"d79e62d115b1ce2b39002c4ae4f52ee68bac1983cb3d5f58f0d42c66b1c8fcb4"},"schema_version":"1.0","source":{"id":"1806.10801","kind":"arxiv","version":2}},"canonical_sha256":"86193ad6bf25f8c2212a50d21c17b547aafe82b4c372348f47c634c9b306088a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86193ad6bf25f8c2212a50d21c17b547aafe82b4c372348f47c634c9b306088a","first_computed_at":"2026-05-18T00:07:17.265198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:17.265198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IoNmlKxn3mQ00usSmggBxrg4lSRX9HTxOFLX6PSQwcSaGgDOtG+7xl0mr42jcCoA2oDtE0tUWFg4qMB01VGlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:17.265770Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.10801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3154b28de4dd87239f34441c741e929fae1c2a40d39c9844220952332c3849e6","sha256:1a2595f156105a30eef320a6ec6f24f4d569a03da6cb84f8f0160a901b5a4782"],"state_sha256":"13f5f446dc62c4c29e154795bc4669ba713e4e66fb8ca66d974496e83fccd75e"}