{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VLK57RLRTJVUDDBPAJWK7K623T","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":"0929a93d37c1d6d71e63d1984c840d511837e6c122d2b84a542b14d7129cbdf5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-12T16:24:11Z","title_canon_sha256":"b964b5587b1510d76623fcab90d09f140cfe53090a0d8ad7bd8e6c1c8a3b16cb"},"schema_version":"1.0","source":{"id":"1802.04166","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04166","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04166v2","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04166","created_at":"2026-05-17T23:54:26Z"},{"alias_kind":"pith_short_12","alias_value":"VLK57RLRTJVU","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VLK57RLRTJVUDDBP","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VLK57RLR","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:b32b9bb4e24167653f101ff2ef6c9dcfe7c465b80fdef5db574368f4e6b77d2b","target":"graph","created_at":"2026-05-17T23:54:26Z","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 investigate the connection between infinite permutation monoids and bimorphism monoids of first-order structures. Taking our lead from the study of automorphism groups of structures as infinite permutation groups and the more recent developments in the field of homomorphism-homogeneous structures, we establish a series of results that underline this connection. Of particular interest is the idea of MB-homogeneity; a relational structure $\\mathcal{M}$ is MB-homogeneous if every monomorphism between finite substructures of $\\mathcal{M}$ extends to a bimorphism of $\\mathcal{M}$.","authors_text":"David M. Evans, Robert D. Gray, Thomas D. H. Coleman","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-12T16:24:11Z","title":"Permutation monoids and MB-homogeneity for graphs and relational structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04166","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:c2559d99f573486798705004c34d0576f0f023d267166da98d55adb680568d75","target":"record","created_at":"2026-05-17T23:54:26Z","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":"0929a93d37c1d6d71e63d1984c840d511837e6c122d2b84a542b14d7129cbdf5","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-02-12T16:24:11Z","title_canon_sha256":"b964b5587b1510d76623fcab90d09f140cfe53090a0d8ad7bd8e6c1c8a3b16cb"},"schema_version":"1.0","source":{"id":"1802.04166","kind":"arxiv","version":2}},"canonical_sha256":"aad5dfc5719a6b418c2f026cafabdadcf450a14832b17d8f9fdd6bed9df6a28f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aad5dfc5719a6b418c2f026cafabdadcf450a14832b17d8f9fdd6bed9df6a28f","first_computed_at":"2026-05-17T23:54:26.347282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:26.347282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hzP/HFB4da7XGfuaISErCtl/XgA/y+7nnd0IYTHYeU+qm7qfdkySDXQtbS/WCR7yQYGWYY+I1zdTXChwXKj7Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:26.347981Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04166","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2559d99f573486798705004c34d0576f0f023d267166da98d55adb680568d75","sha256:b32b9bb4e24167653f101ff2ef6c9dcfe7c465b80fdef5db574368f4e6b77d2b"],"state_sha256":"4702480c6c05ed829d6e6f82d96d715ebc3f34d5c9f6a9bee80021bd68b53052"}