{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Y2NUL2X526C6B3BLQEW2JESJCZ","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":"41e6069d41bb2b58b53cf09deffcffa93e360fbc59d9f732c333e67d851b1ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-17T13:46:17Z","title_canon_sha256":"126b726a436d885569fd3e1634a3cdf814a6230fb22adabdb32c8043462ea909"},"schema_version":"1.0","source":{"id":"1601.04295","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.04295","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"arxiv_version","alias_value":"1601.04295v2","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.04295","created_at":"2026-05-18T01:19:15Z"},{"alias_kind":"pith_short_12","alias_value":"Y2NUL2X526C6","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"Y2NUL2X526C6B3BL","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"Y2NUL2X5","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:76f52dbd0c640ecb4927891bf1d5d597d26b11359a4f4b2880fb6c066e8eeb60","target":"graph","created_at":"2026-05-18T01:19:15Z","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 analyses the construction of the kernel graph of a non-synchronizing transformation semigroup and introduces the inverse synchronization problem. Given a transformation semigroup $S\\leq T_n$, we construct the kernel graph $\\text{Gr}(S)$ by saying $v$ and $w$ are adjacent, if there is no $f\\in S$ with $vf=wf$. The kernel graph is trivial or complete if the semigroup is a synchronizing semigroup or a permutation group, respectively. The connection between graphs and synchronizing (semi-) groups was established by Cameron and Kazanidis, and it has led to many results regarding the clas","authors_text":"Artur Schaefer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-17T13:46:17Z","title":"Generating Sets of the Kernel Graph and the Inverse Problem in Synchronization Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04295","kind":"arxiv","version":2},"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:a61f010c3651634bce356e51df7eeb35319b02890bdb4bf53f724c242672d4f0","target":"record","created_at":"2026-05-18T01:19:15Z","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":"41e6069d41bb2b58b53cf09deffcffa93e360fbc59d9f732c333e67d851b1ed1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-17T13:46:17Z","title_canon_sha256":"126b726a436d885569fd3e1634a3cdf814a6230fb22adabdb32c8043462ea909"},"schema_version":"1.0","source":{"id":"1601.04295","kind":"arxiv","version":2}},"canonical_sha256":"c69b45eafdd785e0ec2b812da492491665f70446752b722b1f906d4694072989","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c69b45eafdd785e0ec2b812da492491665f70446752b722b1f906d4694072989","first_computed_at":"2026-05-18T01:19:15.731542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:15.731542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pc09yO4VGeHpIDgdN9zfuel7zXqGX6EHCoangJzBAImLHMeda4HqxkbHUeyBDi6PhjckKqLjuDKtbxLVcGGsBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:15.731877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.04295","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a61f010c3651634bce356e51df7eeb35319b02890bdb4bf53f724c242672d4f0","sha256:76f52dbd0c640ecb4927891bf1d5d597d26b11359a4f4b2880fb6c066e8eeb60"],"state_sha256":"65dc4b5ab352c385aba33a48f59cbde86282038db864ea6d99c714a3a25ea334"}