{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CM2P22GKJ5MVF57BOSNBK7EI66","short_pith_number":"pith:CM2P22GK","schema_version":"1.0","canonical_sha256":"1334fd68ca4f5952f7e1749a157c88f7a827c0692bcf3cda11ce03e80b58cb96","source":{"kind":"arxiv","id":"1611.07806","version":1},"attestation_state":"computed","paper":{"title":"Graphs, $\\mathbb{F}_1$-schemes and virtual mixed Tate motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Koen Thas, Manuel Merida-Angulo","submitted_at":"2016-11-23T14:19:14Z","abstract_excerpt":"In a number of recent works [6, 7] the authors have introduced and studied a functor $\\mathcal{F}_k$ which associates to each loose graph $\\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a $k$-scheme, such that $\\mathcal{F}_k(\\Gamma)$ is largely controlled by the combinatorics of $\\Gamma$. Here, $k$ is a field, and we allow $k$ to be $\\mathbb{F}_1$, the field with one element. For each finite prime field $\\mathbb{F}_p$, it is noted in [6] that any $\\mathcal{F}_k(\\Gamma)$ is polynomial-count, and the polynomial is independent of the choice of the field"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.07806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-11-23T14:19:14Z","cross_cats_sorted":[],"title_canon_sha256":"bc3845cb2b006e0c8590a804a8ed7073b73f3877ee87a311795160401470bd3b","abstract_canon_sha256":"820a30a7d0e0506cc10f611b49add9f0123bec5a244726411d576d109e2125ad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:59.775683Z","signature_b64":"O3jl1rn838SiERfhHERwSItOnbmQ6RyXIUOSIbtsx9Zt1IJnqs6QnhzQfg1MI/m+USJ5aG5orSnShTYLosa0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1334fd68ca4f5952f7e1749a157c88f7a827c0692bcf3cda11ce03e80b58cb96","last_reissued_at":"2026-05-18T00:56:59.775184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:59.775184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs, $\\mathbb{F}_1$-schemes and virtual mixed Tate motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Koen Thas, Manuel Merida-Angulo","submitted_at":"2016-11-23T14:19:14Z","abstract_excerpt":"In a number of recent works [6, 7] the authors have introduced and studied a functor $\\mathcal{F}_k$ which associates to each loose graph $\\Gamma$ -which is similar to a graph, but where edges with $0$ or $1$ vertex are allowed - a $k$-scheme, such that $\\mathcal{F}_k(\\Gamma)$ is largely controlled by the combinatorics of $\\Gamma$. Here, $k$ is a field, and we allow $k$ to be $\\mathbb{F}_1$, the field with one element. For each finite prime field $\\mathbb{F}_p$, it is noted in [6] that any $\\mathcal{F}_k(\\Gamma)$ is polynomial-count, and the polynomial is independent of the choice of the field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07806","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1611.07806","created_at":"2026-05-18T00:56:59.775263+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.07806v1","created_at":"2026-05-18T00:56:59.775263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07806","created_at":"2026-05-18T00:56:59.775263+00:00"},{"alias_kind":"pith_short_12","alias_value":"CM2P22GKJ5MV","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CM2P22GKJ5MVF57B","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CM2P22GK","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66","json":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66.json","graph_json":"https://pith.science/api/pith-number/CM2P22GKJ5MVF57BOSNBK7EI66/graph.json","events_json":"https://pith.science/api/pith-number/CM2P22GKJ5MVF57BOSNBK7EI66/events.json","paper":"https://pith.science/paper/CM2P22GK"},"agent_actions":{"view_html":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66","download_json":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66.json","view_paper":"https://pith.science/paper/CM2P22GK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.07806&json=true","fetch_graph":"https://pith.science/api/pith-number/CM2P22GKJ5MVF57BOSNBK7EI66/graph.json","fetch_events":"https://pith.science/api/pith-number/CM2P22GKJ5MVF57BOSNBK7EI66/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66/action/storage_attestation","attest_author":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66/action/author_attestation","sign_citation":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66/action/citation_signature","submit_replication":"https://pith.science/pith/CM2P22GKJ5MVF57BOSNBK7EI66/action/replication_record"}},"created_at":"2026-05-18T00:56:59.775263+00:00","updated_at":"2026-05-18T00:56:59.775263+00:00"}