{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q4Q23TMMTQSZVKMP3VHGLLYRBW","short_pith_number":"pith:Q4Q23TMM","canonical_record":{"source":{"id":"1409.1085","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-03T13:44:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"be39b1d655a803da4d647518ceeb74c339e3f3e4989d6866f2d05fdd90b0222a","abstract_canon_sha256":"806efe5d529c7250aca15953acec4d78b99b49805d72ce27631d27fdf2aadbcb"},"schema_version":"1.0"},"canonical_sha256":"8721adcd8c9c259aa98fdd4e65af110da19426340a93b514b381cec11aaa1e9a","source":{"kind":"arxiv","id":"1409.1085","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1085","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1085v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1085","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q4Q23TMMTQSZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q4Q23TMMTQSZVKMP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q4Q23TMM","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q4Q23TMMTQSZVKMP3VHGLLYRBW","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1085","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-03T13:44:12Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"be39b1d655a803da4d647518ceeb74c339e3f3e4989d6866f2d05fdd90b0222a","abstract_canon_sha256":"806efe5d529c7250aca15953acec4d78b99b49805d72ce27631d27fdf2aadbcb"},"schema_version":"1.0"},"canonical_sha256":"8721adcd8c9c259aa98fdd4e65af110da19426340a93b514b381cec11aaa1e9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:53.270796Z","signature_b64":"khbxHsPGCqi3i9BQiygLk99mL5RXppWHmDTLUh2tmrDOwJq5RxX7E5pSviustabbo0v0Ut4MGFHnonPaOLnvDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8721adcd8c9c259aa98fdd4e65af110da19426340a93b514b381cec11aaa1e9a","last_reissued_at":"2026-05-18T01:17:53.270153Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:53.270153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1085","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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qgRDsZPsBd8bV0T32wXQRv6WqnOvfcWariXRMrqt8vB1jc5GDjFmHu/+pgwAs6JQJA3uXFuD84CdHIsFfr/EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:20:19.664581Z"},"content_sha256":"2b6042d8713e03ea12696e9593eec2e59b5a7b716a0a0efb75d5b0f187de88e0","schema_version":"1.0","event_id":"sha256:2b6042d8713e03ea12696e9593eec2e59b5a7b716a0a0efb75d5b0f187de88e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q4Q23TMMTQSZVKMP3VHGLLYRBW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operad groups and their finiteness properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Werner Thumann","submitted_at":"2014-09-03T13:44:12Z","abstract_excerpt":"We propose a new unifying framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application, we proof a theorem which implies that planar or symmetric or braided operads with transformations satisfying some finiteness conditions yield operad groups of type $F_\\infty$. This unifies and extends existing proofs that certain Thompson-like groups are of type $F_\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1085","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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UidiFUV7mJdAx0NfBvjjKps84nQb5vvSYww0Pag3hUVSASxnM1WAx06JPiQ4qSgEPlrwt0d4HH2bo2tT3O79BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:20:19.664961Z"},"content_sha256":"b66e67727f84fd86c5aab3bab8c2f40b841bed7049c26ad8ec4130b7b2016f2e","schema_version":"1.0","event_id":"sha256:b66e67727f84fd86c5aab3bab8c2f40b841bed7049c26ad8ec4130b7b2016f2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/bundle.json","state_url":"https://pith.science/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/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":"2026-06-04T06:20:19Z","links":{"resolver":"https://pith.science/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW","bundle":"https://pith.science/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/bundle.json","state":"https://pith.science/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4Q23TMMTQSZVKMP3VHGLLYRBW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q4Q23TMMTQSZVKMP3VHGLLYRBW","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":"806efe5d529c7250aca15953acec4d78b99b49805d72ce27631d27fdf2aadbcb","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-03T13:44:12Z","title_canon_sha256":"be39b1d655a803da4d647518ceeb74c339e3f3e4989d6866f2d05fdd90b0222a"},"schema_version":"1.0","source":{"id":"1409.1085","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1085","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1085v3","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1085","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q4Q23TMMTQSZ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q4Q23TMMTQSZVKMP","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q4Q23TMM","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:b66e67727f84fd86c5aab3bab8c2f40b841bed7049c26ad8ec4130b7b2016f2e","target":"graph","created_at":"2026-05-18T01:17:53Z","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":"We propose a new unifying framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application, we proof a theorem which implies that planar or symmetric or braided operads with transformations satisfying some finiteness conditions yield operad groups of type $F_\\infty$. This unifies and extends existing proofs that certain Thompson-like groups are of type $F_\\infty$.","authors_text":"Werner Thumann","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-03T13:44:12Z","title":"Operad groups and their finiteness properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1085","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":"sha256:2b6042d8713e03ea12696e9593eec2e59b5a7b716a0a0efb75d5b0f187de88e0","target":"record","created_at":"2026-05-18T01:17:53Z","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":"806efe5d529c7250aca15953acec4d78b99b49805d72ce27631d27fdf2aadbcb","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-09-03T13:44:12Z","title_canon_sha256":"be39b1d655a803da4d647518ceeb74c339e3f3e4989d6866f2d05fdd90b0222a"},"schema_version":"1.0","source":{"id":"1409.1085","kind":"arxiv","version":3}},"canonical_sha256":"8721adcd8c9c259aa98fdd4e65af110da19426340a93b514b381cec11aaa1e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8721adcd8c9c259aa98fdd4e65af110da19426340a93b514b381cec11aaa1e9a","first_computed_at":"2026-05-18T01:17:53.270153Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.270153Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"khbxHsPGCqi3i9BQiygLk99mL5RXppWHmDTLUh2tmrDOwJq5RxX7E5pSviustabbo0v0Ut4MGFHnonPaOLnvDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.270796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1085","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b6042d8713e03ea12696e9593eec2e59b5a7b716a0a0efb75d5b0f187de88e0","sha256:b66e67727f84fd86c5aab3bab8c2f40b841bed7049c26ad8ec4130b7b2016f2e"],"state_sha256":"601d32df5e4b9c8aaa7a110e1b8abb39ced205801fc131041816b0b1f5013265"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"StgfcArPqLHv+4fjtNjkwSDAvSObjKGfjggo55dD5RYxBA3JW21jW6ASujB8Pf/9JB8xhPRiEWpr5QeB/AxxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:20:19.667271Z","bundle_sha256":"1c66ba88b8019fb906dac9d440fe326e44ab0e537a7e02d56bff26026534d914"}}