{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Y66C26GL2G63JA3MHFN3JS56PV","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":"2223c7dc3090670d819a1fd2d2891640c1e7fdc085d94f6fc6c6a88c915e918f","cross_cats_sorted":["cs.DM","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-15T02:04:55Z","title_canon_sha256":"535eda7bcc4afe07de55631861c9eaefe4cbb91143438285584cc97eaac815f5"},"schema_version":"1.0","source":{"id":"1801.04639","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04639","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04639v1","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04639","created_at":"2026-05-18T00:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"Y66C26GL2G63","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Y66C26GL2G63JA3M","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Y66C26GL","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:7e51c8ad10afe52ab618adac2c8d427f6785a36804c3c27c9c8136cf2db8d51d","target":"graph","created_at":"2026-05-18T00:26:03Z","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":"The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence of the spectral formula chi(G)=sum_x (-1)^dim(x) = p(G)-n(G), where p(G) is the number of positive eigenvalues and n(G) is the number of negative eigenvalues of L, both the Euler characteristic chi(G)=zeta(0)-2 i zeta'(0)/pi as well as determinant det(L)=e^zeta'(0)/pi can be written in terms of zeta. (II) As a consequence of the generalized Cau","authors_text":"Oliver Knill","cross_cats":["cs.DM","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-15T02:04:55Z","title":"An Elementary Dyadic Riemann Hypothesis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04639","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:aeac014fb3d712db638e781908b1315b11d716099833cf46aa25a995e63ad10a","target":"record","created_at":"2026-05-18T00:26:03Z","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":"2223c7dc3090670d819a1fd2d2891640c1e7fdc085d94f6fc6c6a88c915e918f","cross_cats_sorted":["cs.DM","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-01-15T02:04:55Z","title_canon_sha256":"535eda7bcc4afe07de55631861c9eaefe4cbb91143438285584cc97eaac815f5"},"schema_version":"1.0","source":{"id":"1801.04639","kind":"arxiv","version":1}},"canonical_sha256":"c7bc2d78cbd1bdb4836c395bb4cbbe7d7b680559c4f038558a40fae41e4a633a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7bc2d78cbd1bdb4836c395bb4cbbe7d7b680559c4f038558a40fae41e4a633a","first_computed_at":"2026-05-18T00:26:03.770156Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:03.770156Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iJont5Ll0ka0gl8h0I8/xUb7SsB9TaCBJPGbGiFZ6vE83v3VEpsrh9//OD2gIGcmrErHsmR8G1niJMN+q/RfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:03.770973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04639","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aeac014fb3d712db638e781908b1315b11d716099833cf46aa25a995e63ad10a","sha256:7e51c8ad10afe52ab618adac2c8d427f6785a36804c3c27c9c8136cf2db8d51d"],"state_sha256":"aefb1ecc677de523d3c2b88d214cfbe0537f48158ecd4cce315c83cad5270092"}