{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CKY7YFZEMMV7ONXR7HJYYVMN6Z","short_pith_number":"pith:CKY7YFZE","canonical_record":{"source":{"id":"1302.2455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-11T11:33:10Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"f2760576777290783e863400575bba3c2a51308ef89f81b3ab92a16e490ab871","abstract_canon_sha256":"e5034558567c5b6c5986ec588b8addc6a6daf818ad9368dc4e5a9fe7b3b02659"},"schema_version":"1.0"},"canonical_sha256":"12b1fc1724632bf736f1f9d38c558df6542c598dca6c708c12d9d84c36087096","source":{"kind":"arxiv","id":"1302.2455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2455","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2455v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2455","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"CKY7YFZEMMV7","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CKY7YFZEMMV7ONXR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CKY7YFZE","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CKY7YFZEMMV7ONXR7HJYYVMN6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-11T11:33:10Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"f2760576777290783e863400575bba3c2a51308ef89f81b3ab92a16e490ab871","abstract_canon_sha256":"e5034558567c5b6c5986ec588b8addc6a6daf818ad9368dc4e5a9fe7b3b02659"},"schema_version":"1.0"},"canonical_sha256":"12b1fc1724632bf736f1f9d38c558df6542c598dca6c708c12d9d84c36087096","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:01.063230Z","signature_b64":"z5XTnLJEEq8pdSv6muz3LlsxmDa3fSxc8LVyuE+U9M0SWIxqs+joNh4OjMidUf+Zbit+Qari+oFYftrnn1mdAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b1fc1724632bf736f1f9d38c558df6542c598dca6c708c12d9d84c36087096","last_reissued_at":"2026-05-18T03:34:01.062531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:01.062531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2455","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ul6VgYSLX1/0dQ+upKb0kHC9OZNxJodmEn5JyFFl0sbtwGNRXvFvDKR2TXgJUV4oiK+qWNNeyfwc+I4WFx/3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:44:14.618648Z"},"content_sha256":"6448780037801bd3ceb7c1294b7c3545145da60b4dc315e1be7eda34df3cccf3","schema_version":"1.0","event_id":"sha256:6448780037801bd3ceb7c1294b7c3545145da60b4dc315e1be7eda34df3cccf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CKY7YFZEMMV7ONXR7HJYYVMN6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational Subsets and Submonoids of Wreath Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.GR","authors_text":"Benjamin Steinberg, Georg Zetzsche, Markus Lohrey","submitted_at":"2013-02-11T11:33:10Z","abstract_excerpt":"It is shown that membership in rational subsets of wreath products H \\wr V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z \\wr Z with an undecidable membership problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2455","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q25UPz+1AAjQtrAhXgEyDh9i+OPVNq1dAb9VzC6s/MsxO1RuIcxn3q0uDpsPW6Egw3HTCWRs8jw4IRKDIHdbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:44:14.619243Z"},"content_sha256":"843737b8f656a333205b2c3b1252d27be679f102e9ac1b436a9620b5e34c7ed2","schema_version":"1.0","event_id":"sha256:843737b8f656a333205b2c3b1252d27be679f102e9ac1b436a9620b5e34c7ed2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/bundle.json","state_url":"https://pith.science/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/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":"2026-05-26T15:44:14Z","links":{"resolver":"https://pith.science/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z","bundle":"https://pith.science/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/bundle.json","state":"https://pith.science/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKY7YFZEMMV7ONXR7HJYYVMN6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CKY7YFZEMMV7ONXR7HJYYVMN6Z","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":"e5034558567c5b6c5986ec588b8addc6a6daf818ad9368dc4e5a9fe7b3b02659","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-11T11:33:10Z","title_canon_sha256":"f2760576777290783e863400575bba3c2a51308ef89f81b3ab92a16e490ab871"},"schema_version":"1.0","source":{"id":"1302.2455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2455","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2455v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2455","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"CKY7YFZEMMV7","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CKY7YFZEMMV7ONXR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CKY7YFZE","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:843737b8f656a333205b2c3b1252d27be679f102e9ac1b436a9620b5e34c7ed2","target":"graph","created_at":"2026-05-18T03:34:01Z","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":"It is shown that membership in rational subsets of wreath products H \\wr V with H a finite group and V a virtually free group is decidable. On the other hand, it is shown that there exists a fixed finitely generated submonoid in the wreath product Z \\wr Z with an undecidable membership problem.","authors_text":"Benjamin Steinberg, Georg Zetzsche, Markus Lohrey","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-11T11:33:10Z","title":"Rational Subsets and Submonoids of Wreath Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2455","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":"sha256:6448780037801bd3ceb7c1294b7c3545145da60b4dc315e1be7eda34df3cccf3","target":"record","created_at":"2026-05-18T03:34:01Z","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":"e5034558567c5b6c5986ec588b8addc6a6daf818ad9368dc4e5a9fe7b3b02659","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-02-11T11:33:10Z","title_canon_sha256":"f2760576777290783e863400575bba3c2a51308ef89f81b3ab92a16e490ab871"},"schema_version":"1.0","source":{"id":"1302.2455","kind":"arxiv","version":1}},"canonical_sha256":"12b1fc1724632bf736f1f9d38c558df6542c598dca6c708c12d9d84c36087096","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b1fc1724632bf736f1f9d38c558df6542c598dca6c708c12d9d84c36087096","first_computed_at":"2026-05-18T03:34:01.062531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:01.062531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z5XTnLJEEq8pdSv6muz3LlsxmDa3fSxc8LVyuE+U9M0SWIxqs+joNh4OjMidUf+Zbit+Qari+oFYftrnn1mdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:01.063230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6448780037801bd3ceb7c1294b7c3545145da60b4dc315e1be7eda34df3cccf3","sha256:843737b8f656a333205b2c3b1252d27be679f102e9ac1b436a9620b5e34c7ed2"],"state_sha256":"5c3454a4e1ad25be829f6ba97a04d6a766c5c7f3ba2adcb7f73fd073e0fb88d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fOqm+df94uiGDgcAwBvPbz1ypPCt3sQIf5j0UYX4mAMamyGt1FFNBi67Qfmt2FZ/rjnHG/QD1Ojhmd6mL62JCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:44:14.622291Z","bundle_sha256":"ceae0b4624257d90726a4cde96a603126048e00e61ca25ea1ff960b14a52b020"}}