{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PGBERAY4BEJMF3UKPH7HTGXYPJ","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":"59a81ecd0a8c51956d3cd0c67e049dd54f0b785455fa5dfb34bdf10d64bdb4da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-25T10:31:45Z","title_canon_sha256":"d3e0a0db583adda8e5face1f8016d2c3f1c3f505b1bdeff8a1b22d2b8f5213ba"},"schema_version":"1.0","source":{"id":"1710.09156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.09156","created_at":"2026-05-18T00:20:38Z"},{"alias_kind":"arxiv_version","alias_value":"1710.09156v2","created_at":"2026-05-18T00:20:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.09156","created_at":"2026-05-18T00:20:38Z"},{"alias_kind":"pith_short_12","alias_value":"PGBERAY4BEJM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PGBERAY4BEJMF3UK","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PGBERAY4","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:16b86f5a1a5095a5651fdf9a8830765a9c1c43dfd9b67b49f7f7178129521844","target":"graph","created_at":"2026-05-18T00:20:38Z","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 paper we consider the integral orthogonal group with respect to the quadratic form of signature $(2,3)$ given by $\\left(\\begin{smallmatrix}\n  0 & 1 \\\\ 1 & 0\n  \\end{smallmatrix}\\right) \\perp \\left(\\begin{smallmatrix}\n  0 & 1 \\\\ 1 & 0\n  \\end{smallmatrix}\\right) \\perp (-2N)$ for squarefree $N\\in \\mathbb{N}$. The associated Hecke algebra is commutative and the tensor product of its primary components, which turn out to be polynomial rings over $\\mathbb{Z}$ in $2$ algebraically independent elements.\n  The integral orthogonal group is isomorphic to the paramodular group of degree $2$ and lev","authors_text":"Aloys Krieg, Jonas Gallenk\\\"amper","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-25T10:31:45Z","title":"The Hecke algebras for the orthogonal group $SO(2,3)$ and the paramodular group of degree $2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09156","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:f8a8e9955790b88b97b798bfacf426f799455313221cea2e1a1acec2f08a1e1d","target":"record","created_at":"2026-05-18T00:20:38Z","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":"59a81ecd0a8c51956d3cd0c67e049dd54f0b785455fa5dfb34bdf10d64bdb4da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-25T10:31:45Z","title_canon_sha256":"d3e0a0db583adda8e5face1f8016d2c3f1c3f505b1bdeff8a1b22d2b8f5213ba"},"schema_version":"1.0","source":{"id":"1710.09156","kind":"arxiv","version":2}},"canonical_sha256":"798248831c0912c2ee8a79fe799af87a7d5647df42f5e9eb478b313876a5fa02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"798248831c0912c2ee8a79fe799af87a7d5647df42f5e9eb478b313876a5fa02","first_computed_at":"2026-05-18T00:20:38.677576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:38.677576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GrKIb7iFoNO7es7xoN9+voFd+I6O1fg9tCrrcAMGNM37k2wG2pZia+LPQNfMJyW7QZR2Jvp8wTNp1ozXWSeWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:38.678240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.09156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a8e9955790b88b97b798bfacf426f799455313221cea2e1a1acec2f08a1e1d","sha256:16b86f5a1a5095a5651fdf9a8830765a9c1c43dfd9b67b49f7f7178129521844"],"state_sha256":"e318c1a615064540e197ae3f8b923087f3a6ea065aed45db317957fe48f78d48"}