{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:JXIX63PTTZVPUG2RSDYEZGRCRW","short_pith_number":"pith:JXIX63PT","canonical_record":{"source":{"id":"2302.08988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-02-17T16:44:10Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"61872fd040f8484032604fee48a35f9eee1d11a1e9a8aba012013eef32aa8047","abstract_canon_sha256":"e13833f748864803130e95abcbb430f62bf80cbca94bae777c6d547da7170f34"},"schema_version":"1.0"},"canonical_sha256":"4dd17f6df39e6afa1b5190f04c9a228da90a2942f0fddfcf62bbeec5d587d833","source":{"kind":"arxiv","id":"2302.08988","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08988","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08988v2","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08988","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"JXIX63PTTZVP","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_16","alias_value":"JXIX63PTTZVPUG2R","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_8","alias_value":"JXIX63PT","created_at":"2026-06-23T01:12:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:JXIX63PTTZVPUG2RSDYEZGRCRW","target":"record","payload":{"canonical_record":{"source":{"id":"2302.08988","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-02-17T16:44:10Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"61872fd040f8484032604fee48a35f9eee1d11a1e9a8aba012013eef32aa8047","abstract_canon_sha256":"e13833f748864803130e95abcbb430f62bf80cbca94bae777c6d547da7170f34"},"schema_version":"1.0"},"canonical_sha256":"4dd17f6df39e6afa1b5190f04c9a228da90a2942f0fddfcf62bbeec5d587d833","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T01:12:43.382401Z","signature_b64":"j5bWBkz56v0UKDHbN4MeUbwODZYrIEhM1rNw25VHVCLoPQvZ2ToUfxMV10LtuLykdUaLzZoAv71ZZEETbSCoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4dd17f6df39e6afa1b5190f04c9a228da90a2942f0fddfcf62bbeec5d587d833","last_reissued_at":"2026-06-23T01:12:43.381886Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T01:12:43.381886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.08988","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-23T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Whaisz93QJtnJ9FFZnI45vgN6wvev72RmrA/rZ1A+0NVrB1vjW5Eog5JWXikfPRwUmHZQpasLGzrpwIhs1YrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:29:34.170692Z"},"content_sha256":"415508c748688b950f71804f60879a48b4ceb4d43b80e25c17fd312fb31b8c45","schema_version":"1.0","event_id":"sha256:415508c748688b950f71804f60879a48b4ceb4d43b80e25c17fd312fb31b8c45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:JXIX63PTTZVPUG2RSDYEZGRCRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological embeddings into transformation monoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"J. D. Mitchell, L. Elliott, S. Bardyla, Y. Peresse","submitted_at":"2023-02-17T16:44:10Z","abstract_excerpt":"In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid $\\mathbb{N} ^ \\mathbb{N}$ or the symmetric inverse monoid $I_{\\mathbb{N}}$ with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into $\\mathbb{N} ^ \\mathbb{N}$ and belong to any of the following classes: commutative semigroups; compact semigroups; groups; and certain Clifford semigroups. We prove analogous characterisations for topological inverse semigroups and $I_{\\mathbb{N}}$. We construct"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08988","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.08988/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-23T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGB/KdPMFBbBn2XBkXEeRLdWF90XjR+ptQHYe201F9eYsxDJ/CiGIZwicdxaNYrg6RzpvcLPs/r7Q/QnOnXRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:29:34.171087Z"},"content_sha256":"fef5a34eff1abf686ef6e24586c424dd61ec9345ea1e51119057992c96d680ba","schema_version":"1.0","event_id":"sha256:fef5a34eff1abf686ef6e24586c424dd61ec9345ea1e51119057992c96d680ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/bundle.json","state_url":"https://pith.science/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/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":"2026-07-07T10:29:34Z","links":{"resolver":"https://pith.science/pith/JXIX63PTTZVPUG2RSDYEZGRCRW","bundle":"https://pith.science/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/bundle.json","state":"https://pith.science/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JXIX63PTTZVPUG2RSDYEZGRCRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:JXIX63PTTZVPUG2RSDYEZGRCRW","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":"e13833f748864803130e95abcbb430f62bf80cbca94bae777c6d547da7170f34","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-02-17T16:44:10Z","title_canon_sha256":"61872fd040f8484032604fee48a35f9eee1d11a1e9a8aba012013eef32aa8047"},"schema_version":"1.0","source":{"id":"2302.08988","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.08988","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"2302.08988v2","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.08988","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"JXIX63PTTZVP","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_16","alias_value":"JXIX63PTTZVPUG2R","created_at":"2026-06-23T01:12:43Z"},{"alias_kind":"pith_short_8","alias_value":"JXIX63PT","created_at":"2026-06-23T01:12:43Z"}],"graph_snapshots":[{"event_id":"sha256:fef5a34eff1abf686ef6e24586c424dd61ec9345ea1e51119057992c96d680ba","target":"graph","created_at":"2026-06-23T01:12:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.08988/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we consider the questions of which topological semigroups embed topologically into the full transformation monoid $\\mathbb{N} ^ \\mathbb{N}$ or the symmetric inverse monoid $I_{\\mathbb{N}}$ with their respective canonical Polish semigroup topologies. We characterise those topological semigroups that embed topologically into $\\mathbb{N} ^ \\mathbb{N}$ and belong to any of the following classes: commutative semigroups; compact semigroups; groups; and certain Clifford semigroups. We prove analogous characterisations for topological inverse semigroups and $I_{\\mathbb{N}}$. We construct","authors_text":"J. D. Mitchell, L. Elliott, S. Bardyla, Y. Peresse","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-02-17T16:44:10Z","title":"Topological embeddings into transformation monoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.08988","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":"sha256:415508c748688b950f71804f60879a48b4ceb4d43b80e25c17fd312fb31b8c45","target":"record","created_at":"2026-06-23T01:12:43Z","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":"e13833f748864803130e95abcbb430f62bf80cbca94bae777c6d547da7170f34","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2023-02-17T16:44:10Z","title_canon_sha256":"61872fd040f8484032604fee48a35f9eee1d11a1e9a8aba012013eef32aa8047"},"schema_version":"1.0","source":{"id":"2302.08988","kind":"arxiv","version":2}},"canonical_sha256":"4dd17f6df39e6afa1b5190f04c9a228da90a2942f0fddfcf62bbeec5d587d833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dd17f6df39e6afa1b5190f04c9a228da90a2942f0fddfcf62bbeec5d587d833","first_computed_at":"2026-06-23T01:12:43.381886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T01:12:43.381886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j5bWBkz56v0UKDHbN4MeUbwODZYrIEhM1rNw25VHVCLoPQvZ2ToUfxMV10LtuLykdUaLzZoAv71ZZEETbSCoBg==","signature_status":"signed_v1","signed_at":"2026-06-23T01:12:43.382401Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.08988","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:415508c748688b950f71804f60879a48b4ceb4d43b80e25c17fd312fb31b8c45","sha256:fef5a34eff1abf686ef6e24586c424dd61ec9345ea1e51119057992c96d680ba"],"state_sha256":"12f3098b38774f6a5a6fe54b7e5eb35cc7bd078be4c4cb6b3648b1c538014994"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W2+aPo1AQHwJxOPsiUl8a3e3DpFlkJRZvcrA1/WCLekgoj0onOL1qDA9pRKKXyz138ey0k6ooiRC0x+RpE1lAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:29:34.173055Z","bundle_sha256":"9a5bd0fe09b392bbf3e046bbaac533e421aa7af61740e1f52bd6df45fa15a6a1"}}