{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GNHROP3BPINUKSMVV6JBJUJZDP","short_pith_number":"pith:GNHROP3B","canonical_record":{"source":{"id":"1508.04454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-18T20:38:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3fb4bac09ecc7633b14b14168d9577e82a9c2887e3d8578c86480726db02d8c7","abstract_canon_sha256":"d6039022f35708cb98e83cc2bb74a853993e9245f1517ce4599cbb8b8d6b4ac7"},"schema_version":"1.0"},"canonical_sha256":"334f173f617a1b454995af9214d1391bed2208450fcb36b2398084e4a2e0d46e","source":{"kind":"arxiv","id":"1508.04454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04454","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04454v2","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04454","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"GNHROP3BPINU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GNHROP3BPINUKSMV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GNHROP3B","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GNHROP3BPINUKSMVV6JBJUJZDP","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-18T20:38:50Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"3fb4bac09ecc7633b14b14168d9577e82a9c2887e3d8578c86480726db02d8c7","abstract_canon_sha256":"d6039022f35708cb98e83cc2bb74a853993e9245f1517ce4599cbb8b8d6b4ac7"},"schema_version":"1.0"},"canonical_sha256":"334f173f617a1b454995af9214d1391bed2208450fcb36b2398084e4a2e0d46e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:52.036772Z","signature_b64":"8AHjnKC+/ylM6tuXPPm5v83Jv5k4frygHQtr4K3f3uL7MtLltFMF3J6wzcX33LQmGj6QunXLsq4XCmGEbZVJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"334f173f617a1b454995af9214d1391bed2208450fcb36b2398084e4a2e0d46e","last_reissued_at":"2026-05-18T01:32:52.036079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:52.036079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04454","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":"2026-05-18T01:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chZecF+diPDlZNBABnPUO9u2tHNwZZRvXtyy2qYj1p/0inWfU/rRP/+0dLWgo4Y1LYQNWIL0uYvXcHgmXigbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:50:55.319743Z"},"content_sha256":"c46eaeb89d8f2e95b442bf907fa9b1ca9cbc9fd67f2632b716ffd636818b082a","schema_version":"1.0","event_id":"sha256:c46eaeb89d8f2e95b442bf907fa9b1ca9cbc9fd67f2632b716ffd636818b082a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GNHROP3BPINUKSMVV6JBJUJZDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Presentations of Topological Full Groups by Generators and Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GR","authors_text":"Konstantin Medynets, Rostislav Grigorchuk","submitted_at":"2015-08-18T20:38:50Z","abstract_excerpt":"We describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying subshift is recursive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04454","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":""},"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":"2026-05-18T01:32:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mb5iygsWI1KSm//P7D7IJbaQiGjNgMH1XbkXzuZAWTrSlF2PzC6I7XCz3ZQIXIha7myIx8v2jNMhbQRv3O7fCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:50:55.320469Z"},"content_sha256":"8ae1241d72671130be1820cb992fdda56c4d094442da9c0850db3874a9b727c5","schema_version":"1.0","event_id":"sha256:8ae1241d72671130be1820cb992fdda56c4d094442da9c0850db3874a9b727c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNHROP3BPINUKSMVV6JBJUJZDP/bundle.json","state_url":"https://pith.science/pith/GNHROP3BPINUKSMVV6JBJUJZDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNHROP3BPINUKSMVV6JBJUJZDP/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":"2026-06-09T03:50:55Z","links":{"resolver":"https://pith.science/pith/GNHROP3BPINUKSMVV6JBJUJZDP","bundle":"https://pith.science/pith/GNHROP3BPINUKSMVV6JBJUJZDP/bundle.json","state":"https://pith.science/pith/GNHROP3BPINUKSMVV6JBJUJZDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNHROP3BPINUKSMVV6JBJUJZDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GNHROP3BPINUKSMVV6JBJUJZDP","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":"d6039022f35708cb98e83cc2bb74a853993e9245f1517ce4599cbb8b8d6b4ac7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-18T20:38:50Z","title_canon_sha256":"3fb4bac09ecc7633b14b14168d9577e82a9c2887e3d8578c86480726db02d8c7"},"schema_version":"1.0","source":{"id":"1508.04454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04454","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04454v2","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04454","created_at":"2026-05-18T01:32:52Z"},{"alias_kind":"pith_short_12","alias_value":"GNHROP3BPINU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GNHROP3BPINUKSMV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GNHROP3B","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:8ae1241d72671130be1820cb992fdda56c4d094442da9c0850db3874a9b727c5","target":"graph","created_at":"2026-05-18T01:32:52Z","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 describe generators and defining relations for the commutator subgroup of topological full groups of minimal subshifts. We show that the word problem in a topological full group is solvable if and only if the language of the underlying subshift is recursive.","authors_text":"Konstantin Medynets, Rostislav Grigorchuk","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-18T20:38:50Z","title":"Presentations of Topological Full Groups by Generators and Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04454","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:c46eaeb89d8f2e95b442bf907fa9b1ca9cbc9fd67f2632b716ffd636818b082a","target":"record","created_at":"2026-05-18T01:32:52Z","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":"d6039022f35708cb98e83cc2bb74a853993e9245f1517ce4599cbb8b8d6b4ac7","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-08-18T20:38:50Z","title_canon_sha256":"3fb4bac09ecc7633b14b14168d9577e82a9c2887e3d8578c86480726db02d8c7"},"schema_version":"1.0","source":{"id":"1508.04454","kind":"arxiv","version":2}},"canonical_sha256":"334f173f617a1b454995af9214d1391bed2208450fcb36b2398084e4a2e0d46e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"334f173f617a1b454995af9214d1391bed2208450fcb36b2398084e4a2e0d46e","first_computed_at":"2026-05-18T01:32:52.036079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:52.036079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8AHjnKC+/ylM6tuXPPm5v83Jv5k4frygHQtr4K3f3uL7MtLltFMF3J6wzcX33LQmGj6QunXLsq4XCmGEbZVJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:52.036772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c46eaeb89d8f2e95b442bf907fa9b1ca9cbc9fd67f2632b716ffd636818b082a","sha256:8ae1241d72671130be1820cb992fdda56c4d094442da9c0850db3874a9b727c5"],"state_sha256":"8e6d117157625cabb6f6e20038101ac3594fbdac169478b2fdbd44523ce8ced7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhNGbA8MPJNqhsPXGfYKhi5VBUgsMVLKIaxdAwT0YBJkf1lCDWS9I+0JVf1/90ZabhvZMqgoMDkrMvQtZxPYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:50:55.325006Z","bundle_sha256":"e196ccabe5738c3f50623942929f6e31b24f209ca5d2665aa90d8b614bb4bef4"}}