{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F5VINO2WR7KVHEN4OPWVNGCKRC","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":"66e4c472ed9f9c24e5acea371510ef545b679aea76d069c28602a215501d4baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T04:10:45Z","title_canon_sha256":"5cfda96d8f7cec9cb6f6546c2059238347ec20bfadc3861e9da649753c2706aa"},"schema_version":"1.0","source":{"id":"1805.00179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00179","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00179v1","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00179","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"F5VINO2WR7KV","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_16","alias_value":"F5VINO2WR7KVHEN4","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_8","alias_value":"F5VINO2W","created_at":"2026-07-05T00:28:21Z"}],"graph_snapshots":[{"event_id":"sha256:f9c2bfa8686ca387a3ed412fca0b8a17937ac14659d30d153707eca0884834b4","target":"graph","created_at":"2026-07-05T00:28:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1805.00179/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"With a main tool is signed graphs, we give a full description of the characteristic quasi-polynomials of ideals of classical root systems ($ABCD$) with respect to the integer and root lattices. As a result, we obtain a full description of the characteristic polynomials of the toric arrangements defined by these ideals. As an application, we provide a combinatorial verification to the fact that the characteristic polynomial of every ideal subarrangement factors over the dual partition of the ideal in the classical cases.","authors_text":"Tan Nhat Tran","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T04:10:45Z","title":"Characteristic quasi-polynomials of ideals and signed graphs of classical root systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00179","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":"sha256:2c84a5b66cf981442155b6c11fd5264ec11d3473668844a2246964f81279ad8e","target":"record","created_at":"2026-07-05T00:28:21Z","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":"66e4c472ed9f9c24e5acea371510ef545b679aea76d069c28602a215501d4baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-01T04:10:45Z","title_canon_sha256":"5cfda96d8f7cec9cb6f6546c2059238347ec20bfadc3861e9da649753c2706aa"},"schema_version":"1.0","source":{"id":"1805.00179","kind":"arxiv","version":1}},"canonical_sha256":"2f6a86bb568fd55391bc73ed56984a88a71f88322d780adaebc5602830c126a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f6a86bb568fd55391bc73ed56984a88a71f88322d780adaebc5602830c126a3","first_computed_at":"2026-07-05T00:28:21.487486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:21.487486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZtAGd0xkMOIAg0bC9C/9bNlN0V+Mq6/46BeTus3MkynCTqQk18EgqWQ2Xn9o79dCMOdTkOcLZBv809AmaFuNDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:21.487993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c84a5b66cf981442155b6c11fd5264ec11d3473668844a2246964f81279ad8e","sha256:f9c2bfa8686ca387a3ed412fca0b8a17937ac14659d30d153707eca0884834b4"],"state_sha256":"931ea1c0ea8ef32813e37def81b3572cdc889c5d1fee07df236d882670774a97"}