{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KFPFCPAATCJBXLJZ5COH4CZJNI","short_pith_number":"pith:KFPFCPAA","canonical_record":{"source":{"id":"1112.0185","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-01T14:15:18Z","cross_cats_sorted":["math.AG","math.CO","math.GN","math.RA"],"title_canon_sha256":"549b666fe79a0aedfc7f89d8ee1880d4d476ee4c675aae9889f85e29ee6049e4","abstract_canon_sha256":"18808ad6069b8884dd4220d9cbcef44b67302c78aaa41dca80ac4155c6740e6c"},"schema_version":"1.0"},"canonical_sha256":"515e513c0098921bad39e89c7e0b296a2e8f09895567d3bf025579230bfcd209","source":{"kind":"arxiv","id":"1112.0185","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0185","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0185v3","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0185","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"KFPFCPAATCJB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KFPFCPAATCJBXLJZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KFPFCPAA","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KFPFCPAATCJBXLJZ5COH4CZJNI","target":"record","payload":{"canonical_record":{"source":{"id":"1112.0185","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-01T14:15:18Z","cross_cats_sorted":["math.AG","math.CO","math.GN","math.RA"],"title_canon_sha256":"549b666fe79a0aedfc7f89d8ee1880d4d476ee4c675aae9889f85e29ee6049e4","abstract_canon_sha256":"18808ad6069b8884dd4220d9cbcef44b67302c78aaa41dca80ac4155c6740e6c"},"schema_version":"1.0"},"canonical_sha256":"515e513c0098921bad39e89c7e0b296a2e8f09895567d3bf025579230bfcd209","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.865412Z","signature_b64":"OE7XV8Kfl3VTGcCUxuXiPQhoVIo9WpoVr8/pa9hvw4Du8hqZdS9JxJTUlWxj2NEONlh924w+/+Zw37HCoLitBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"515e513c0098921bad39e89c7e0b296a2e8f09895567d3bf025579230bfcd209","last_reissued_at":"2026-05-18T01:34:13.864675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.864675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.0185","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMh7lK+7rZaBqg6IJAu3RDjDwaMlITIMl3CbBJ1PPUPq4h8agLnc7A3EtUBktyAed6zxBnEFuyuzW865ENTwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:32:16.209416Z"},"content_sha256":"c5f175426fd53878dfd5dba5a1df6831d1bce4e9660d8831f513138fbe520371","schema_version":"1.0","event_id":"sha256:c5f175426fd53878dfd5dba5a1df6831d1bce4e9660d8831f513138fbe520371"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KFPFCPAATCJBXLJZ5COH4CZJNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-divisor graphs of nilpotent-free semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO","math.GN","math.RA"],"primary_cat":"math.AC","authors_text":"Neil Epstein, Peyman Nasehpour","submitted_at":"2011-12-01T14:15:18Z","abstract_excerpt":"We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \\emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0185","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zdr3i9qad/xH8LucuCMZQDW17gwbKoKkWPse+obINAoYF+ynBL6+VEU1+ZoqjBXrRv82bJ95+lk8HD1v45IyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:32:16.210216Z"},"content_sha256":"2083fd22be42ebd6dd6a43fd4c187e140061c15d3fd5e99072f0db3f3f318070","schema_version":"1.0","event_id":"sha256:2083fd22be42ebd6dd6a43fd4c187e140061c15d3fd5e99072f0db3f3f318070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/bundle.json","state_url":"https://pith.science/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T11:32:16Z","links":{"resolver":"https://pith.science/pith/KFPFCPAATCJBXLJZ5COH4CZJNI","bundle":"https://pith.science/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/bundle.json","state":"https://pith.science/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFPFCPAATCJBXLJZ5COH4CZJNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KFPFCPAATCJBXLJZ5COH4CZJNI","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":"18808ad6069b8884dd4220d9cbcef44b67302c78aaa41dca80ac4155c6740e6c","cross_cats_sorted":["math.AG","math.CO","math.GN","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-01T14:15:18Z","title_canon_sha256":"549b666fe79a0aedfc7f89d8ee1880d4d476ee4c675aae9889f85e29ee6049e4"},"schema_version":"1.0","source":{"id":"1112.0185","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0185","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0185v3","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0185","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"KFPFCPAATCJB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KFPFCPAATCJBXLJZ","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KFPFCPAA","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:2083fd22be42ebd6dd6a43fd4c187e140061c15d3fd5e99072f0db3f3f318070","target":"graph","created_at":"2026-05-18T01:34:13Z","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":"We find strong relationships between the zero-divisor graphs of apparently disparate kinds of nilpotent-free semigroups by introducing the notion of an \\emph{Armendariz map} between such semigroups, which preserves many graph-theoretic invariants. We use it to give relationships between the zero-divisor graph of a ring, a polynomial ring, and the annihilating-ideal graph. Then we give relationships between the zero-divisor graphs of certain topological spaces (so-called pearled spaces), prime spectra, maximal spectra, tensor-product semigroups, and the semigroup of ideals under addition, obtai","authors_text":"Neil Epstein, Peyman Nasehpour","cross_cats":["math.AG","math.CO","math.GN","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-01T14:15:18Z","title":"Zero-divisor graphs of nilpotent-free semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0185","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:c5f175426fd53878dfd5dba5a1df6831d1bce4e9660d8831f513138fbe520371","target":"record","created_at":"2026-05-18T01:34:13Z","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":"18808ad6069b8884dd4220d9cbcef44b67302c78aaa41dca80ac4155c6740e6c","cross_cats_sorted":["math.AG","math.CO","math.GN","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-12-01T14:15:18Z","title_canon_sha256":"549b666fe79a0aedfc7f89d8ee1880d4d476ee4c675aae9889f85e29ee6049e4"},"schema_version":"1.0","source":{"id":"1112.0185","kind":"arxiv","version":3}},"canonical_sha256":"515e513c0098921bad39e89c7e0b296a2e8f09895567d3bf025579230bfcd209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515e513c0098921bad39e89c7e0b296a2e8f09895567d3bf025579230bfcd209","first_computed_at":"2026-05-18T01:34:13.864675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:13.864675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OE7XV8Kfl3VTGcCUxuXiPQhoVIo9WpoVr8/pa9hvw4Du8hqZdS9JxJTUlWxj2NEONlh924w+/+Zw37HCoLitBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:13.865412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0185","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5f175426fd53878dfd5dba5a1df6831d1bce4e9660d8831f513138fbe520371","sha256:2083fd22be42ebd6dd6a43fd4c187e140061c15d3fd5e99072f0db3f3f318070"],"state_sha256":"8007f8caa53c4221d8ac7261450a04f9c79029b9de45a1c569469447fd2b7db0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CHrii42/DkhRdethKQ3S/FG2yXH8tsU+Q9YWWFCQu+9CfP8rFSdpSPdSx9Q8Ub1bI8+FiJ2fFxM8GgTNB/PvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:32:16.217684Z","bundle_sha256":"5d6947c7d293c01a826812ef4fa438899e4ac38409cdbeff8dd19345acd7db10"}}