{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K4XBNDA7C3RGMHDUVH5VU4HL4X","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":"ebd29d6cda80b1e4ad4bb795d6b9073bf81b4595c930f16b888cf341bc6f9bd7","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-22T13:09:34Z","title_canon_sha256":"c8f6ab3a09b4b4efd42a835309fccddfbfcc62dcb4542bdd88f795caf6d4a618"},"schema_version":"1.0","source":{"id":"1505.06059","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.06059","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"1505.06059v3","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06059","created_at":"2026-05-18T01:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"K4XBNDA7C3RG","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K4XBNDA7C3RGMHDU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K4XBNDA7","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:01e23eae23e3ee4e7c2eb21710694210b3fe00e9ca1dca963a8ebc3aaa152348","target":"graph","created_at":"2026-05-18T01:11:35Z","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":"This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a better understanding of the multiplicative ideal theory of invariant rings, and connections between the Noether number and the Davenport constants of finite groups.","authors_text":"A. Geroldinger, K. Cziszter, M. Domokos","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-22T13:09:34Z","title":"The interplay of Invariant Theory with Multiplicative Ideal Theory and with Arithmetic Combinatorics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06059","kind":"arxiv","version":3},"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:f719db4133edd8b950b525f928efe511941ce1c712f8b844ed54d2a0b9f566dd","target":"record","created_at":"2026-05-18T01:11:35Z","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":"ebd29d6cda80b1e4ad4bb795d6b9073bf81b4595c930f16b888cf341bc6f9bd7","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-22T13:09:34Z","title_canon_sha256":"c8f6ab3a09b4b4efd42a835309fccddfbfcc62dcb4542bdd88f795caf6d4a618"},"schema_version":"1.0","source":{"id":"1505.06059","kind":"arxiv","version":3}},"canonical_sha256":"572e168c1f16e2661c74a9fb5a70ebe5e2194dc6f9051bcca3b1da9e82275c0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"572e168c1f16e2661c74a9fb5a70ebe5e2194dc6f9051bcca3b1da9e82275c0a","first_computed_at":"2026-05-18T01:11:35.313083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:35.313083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a0HiLGHPk/AmxvUBTnwjcaup2jk8TEzMko1ctelcBv2oaqUO53zOHOUkyuDbzeU0Mzo4PP4lVkbkQ0QzG8nVAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:35.313476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.06059","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f719db4133edd8b950b525f928efe511941ce1c712f8b844ed54d2a0b9f566dd","sha256:01e23eae23e3ee4e7c2eb21710694210b3fe00e9ca1dca963a8ebc3aaa152348"],"state_sha256":"e1b3250d09ac6530709b873fb6596d9be4900d43ead75e18c32823863414c722"}