{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BDXJLVSHSITRF7CUKVLLPP7BXP","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":"d75957584d5e20c2c4eaf64f20a0bce0e434ed8426c359d65f430defa272bb82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-17T07:14:08Z","title_canon_sha256":"aebfd99fdb2daf196614fc7393f71a5fb630a8fe11811c1e1fdb183f3118cf95"},"schema_version":"1.0","source":{"id":"1310.4594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4594","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4594v1","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4594","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"BDXJLVSHSITR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BDXJLVSHSITRF7CU","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BDXJLVSH","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:e40959c351f95d5fc969d36c23015abb819cb1c2c68373de41cfe84ce2365a2c","target":"graph","created_at":"2026-05-18T03:10:13Z","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 introduce the zero divisor graph of a multiplicative lattice. We provide a counter example to Beck's conjecture for multiplicative lattices. Further, we prove that Beck's conjecture is true for reduced multiplicative lattice which extends the result of Behboodi and Rakeei[7], and Aalipour et. al.[1].","authors_text":"Sachin Sarode, Vinayak Joshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-17T07:14:08Z","title":"Beck's Conjecture For Multiplicative Lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4594","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":"sha256:0a7815f237bbd841f7f9fbdf2b0f9f9cf1fecd7c5a268a62b146ea8b50bd7c74","target":"record","created_at":"2026-05-18T03:10:13Z","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":"d75957584d5e20c2c4eaf64f20a0bce0e434ed8426c359d65f430defa272bb82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-17T07:14:08Z","title_canon_sha256":"aebfd99fdb2daf196614fc7393f71a5fb630a8fe11811c1e1fdb183f3118cf95"},"schema_version":"1.0","source":{"id":"1310.4594","kind":"arxiv","version":1}},"canonical_sha256":"08ee95d647922712fc545556b7bfe1bbd4c95277b6fc8f8fd701b1c744e75bf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"08ee95d647922712fc545556b7bfe1bbd4c95277b6fc8f8fd701b1c744e75bf2","first_computed_at":"2026-05-18T03:10:13.620523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:13.620523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yY5blcFmvRvtSafLIT6czuKYaxC2fhjdHJ5/9oSYXg5RnyCPSdj1naqjXL7ZzzS6yfWwtGOzRlmYHijNrDSsAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:13.621138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a7815f237bbd841f7f9fbdf2b0f9f9cf1fecd7c5a268a62b146ea8b50bd7c74","sha256:e40959c351f95d5fc969d36c23015abb819cb1c2c68373de41cfe84ce2365a2c"],"state_sha256":"f046455d2baa07003fef2e7b4ffbb7e60644a293fc047044a0ef3b1ca5914e37"}