{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WHNWE2QIKUA5TDLWGKR543DPY5","short_pith_number":"pith:WHNWE2QI","canonical_record":{"source":{"id":"1710.05250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-14T23:53:24Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"cff1d2aa68f23e3dd7dcdd6343c9d1aad7175e398d472c915f5d9b8809db5597","abstract_canon_sha256":"728faec79dd9f5d5136d2682d1534fb9f845e1b312d327b8ec8c1e8ee9a8394c"},"schema_version":"1.0"},"canonical_sha256":"b1db626a085501d98d7632a3de6c6fc771fef748e6d86513f44f39b47069d080","source":{"kind":"arxiv","id":"1710.05250","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05250","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05250v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05250","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"WHNWE2QIKUA5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WHNWE2QIKUA5TDLW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WHNWE2QI","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WHNWE2QIKUA5TDLWGKR543DPY5","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05250","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-14T23:53:24Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"cff1d2aa68f23e3dd7dcdd6343c9d1aad7175e398d472c915f5d9b8809db5597","abstract_canon_sha256":"728faec79dd9f5d5136d2682d1534fb9f845e1b312d327b8ec8c1e8ee9a8394c"},"schema_version":"1.0"},"canonical_sha256":"b1db626a085501d98d7632a3de6c6fc771fef748e6d86513f44f39b47069d080","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:53.861891Z","signature_b64":"SybZ8Rif9KqFMJq5yZPPh+2cZCLtq5Ps2CmjrLudT1gFGit3LFrO8DZc4Ck4Htfwk94bszjjVacMIr5atNMwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1db626a085501d98d7632a3de6c6fc771fef748e6d86513f44f39b47069d080","last_reissued_at":"2026-05-18T00:32:53.861218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:53.861218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05250","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOJZqK6rZgTRFTxWcjK7tHtMiegLA1JbGkHgc/VJNC/l5OTgPy3kJAHtJxZjkCZrCy719q5fR6uWKnX1w7ihAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:35:56.365455Z"},"content_sha256":"4d761c8d3192a326637618ebcb4799e86622fee398f25c59ddd98100baae2885","schema_version":"1.0","event_id":"sha256:4d761c8d3192a326637618ebcb4799e86622fee398f25c59ddd98100baae2885"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WHNWE2QIKUA5TDLWGKR543DPY5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commuting Graphs of Boundedly Generated Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CO","authors_text":"Be'eri Greenfeld, Tomer Bauer","submitted_at":"2017-10-14T23:53:24Z","abstract_excerpt":"Ara\\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups.\n  We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest modifications for some of the original problems, generalized to the context of families of semigroups with a bounded number of generators, and pose related problems.\n  We construct monomial semigroups with a bounded number of generators, whose commuting graphs have an arbitrary clique number. In contrast to that, we show that the diameter of the commuting gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05250","kind":"arxiv","version":1},"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":"2026-05-18T00:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q+CfU05lF9Nn9mA8DRDZrCIH2Ct1sXAaK6ML9K89unjUnbkoTzrTAk/vvTQWruEf7n6gMQkvDJ1OsBV738YqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:35:56.365813Z"},"content_sha256":"4f35c68fba952e7fd2ae262ed7437c70190d56e546ab531e052d286177ef9d43","schema_version":"1.0","event_id":"sha256:4f35c68fba952e7fd2ae262ed7437c70190d56e546ab531e052d286177ef9d43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHNWE2QIKUA5TDLWGKR543DPY5/bundle.json","state_url":"https://pith.science/pith/WHNWE2QIKUA5TDLWGKR543DPY5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHNWE2QIKUA5TDLWGKR543DPY5/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":"2026-06-22T18:35:56Z","links":{"resolver":"https://pith.science/pith/WHNWE2QIKUA5TDLWGKR543DPY5","bundle":"https://pith.science/pith/WHNWE2QIKUA5TDLWGKR543DPY5/bundle.json","state":"https://pith.science/pith/WHNWE2QIKUA5TDLWGKR543DPY5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHNWE2QIKUA5TDLWGKR543DPY5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WHNWE2QIKUA5TDLWGKR543DPY5","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":"728faec79dd9f5d5136d2682d1534fb9f845e1b312d327b8ec8c1e8ee9a8394c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-14T23:53:24Z","title_canon_sha256":"cff1d2aa68f23e3dd7dcdd6343c9d1aad7175e398d472c915f5d9b8809db5597"},"schema_version":"1.0","source":{"id":"1710.05250","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05250","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05250v1","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05250","created_at":"2026-05-18T00:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"WHNWE2QIKUA5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WHNWE2QIKUA5TDLW","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WHNWE2QI","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:4f35c68fba952e7fd2ae262ed7437c70190d56e546ab531e052d286177ef9d43","target":"graph","created_at":"2026-05-18T00:32:53Z","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":"Ara\\'ujo, Kinyon and Konieczny (2011) pose several problems concerning the construction of arbitrary commuting graphs of semigroups.\n  We observe that every star-free graph is the commuting graph of some semigroup. Consequently, we suggest modifications for some of the original problems, generalized to the context of families of semigroups with a bounded number of generators, and pose related problems.\n  We construct monomial semigroups with a bounded number of generators, whose commuting graphs have an arbitrary clique number. In contrast to that, we show that the diameter of the commuting gr","authors_text":"Be'eri Greenfeld, Tomer Bauer","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-14T23:53:24Z","title":"Commuting Graphs of Boundedly Generated Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05250","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":"sha256:4d761c8d3192a326637618ebcb4799e86622fee398f25c59ddd98100baae2885","target":"record","created_at":"2026-05-18T00:32:53Z","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":"728faec79dd9f5d5136d2682d1534fb9f845e1b312d327b8ec8c1e8ee9a8394c","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-14T23:53:24Z","title_canon_sha256":"cff1d2aa68f23e3dd7dcdd6343c9d1aad7175e398d472c915f5d9b8809db5597"},"schema_version":"1.0","source":{"id":"1710.05250","kind":"arxiv","version":1}},"canonical_sha256":"b1db626a085501d98d7632a3de6c6fc771fef748e6d86513f44f39b47069d080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1db626a085501d98d7632a3de6c6fc771fef748e6d86513f44f39b47069d080","first_computed_at":"2026-05-18T00:32:53.861218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:53.861218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SybZ8Rif9KqFMJq5yZPPh+2cZCLtq5Ps2CmjrLudT1gFGit3LFrO8DZc4Ck4Htfwk94bszjjVacMIr5atNMwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:53.861891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05250","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d761c8d3192a326637618ebcb4799e86622fee398f25c59ddd98100baae2885","sha256:4f35c68fba952e7fd2ae262ed7437c70190d56e546ab531e052d286177ef9d43"],"state_sha256":"e82821b2e830289dc311f7a81a7f18edd4cdb51e73bab861db80fd0a0d076e44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2aUPcvNX1kSTBLYPvJDDg5SDzloGq9zsd9ag30iYTUOZGworHZIRb+JOnBkVcOP9MJhD+FSw32NzDtNcyN1pCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:35:56.367807Z","bundle_sha256":"0f55f0b9ce928e77335e4a68864afece236856847324c4640a7b74e741e7abee"}}