{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IZ3CZKH2MNRB3SEFJJM4K2ZF5L","short_pith_number":"pith:IZ3CZKH2","canonical_record":{"source":{"id":"1609.03371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-12T12:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"ae703264d650022fc12edf877b870d2e991fa0eb380e3ba79ce4ec4644d315a1","abstract_canon_sha256":"498ab45840424bb50432a869ed29285cf2d320bc7dc760b32967c58bbb150487"},"schema_version":"1.0"},"canonical_sha256":"46762ca8fa63621dc8854a59c56b25eac4dda003e585e04f825614c2284e27a9","source":{"kind":"arxiv","id":"1609.03371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03371","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03371v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03371","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"IZ3CZKH2MNRB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IZ3CZKH2MNRB3SEF","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IZ3CZKH2","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IZ3CZKH2MNRB3SEFJJM4K2ZF5L","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-12T12:38:46Z","cross_cats_sorted":[],"title_canon_sha256":"ae703264d650022fc12edf877b870d2e991fa0eb380e3ba79ce4ec4644d315a1","abstract_canon_sha256":"498ab45840424bb50432a869ed29285cf2d320bc7dc760b32967c58bbb150487"},"schema_version":"1.0"},"canonical_sha256":"46762ca8fa63621dc8854a59c56b25eac4dda003e585e04f825614c2284e27a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:47.099134Z","signature_b64":"7jjHl9aC5eFeqA3GkIK4YemrI38rbslZVeNjd53YcrH8OfNpiHtunx0t/cU75G18+rPSC9dhRwjZAypPnHAiAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46762ca8fa63621dc8854a59c56b25eac4dda003e585e04f825614c2284e27a9","last_reissued_at":"2026-05-18T01:04:47.098577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:47.098577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03371","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":"2026-05-18T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WA/bElA7g9WL07FpygXsU/L+VUTYojv6GGj4FESVcJDTRiWn93MBWKUPpSI01qlfTkCaDJh/Bj6BquTGVseDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:45:25.780424Z"},"content_sha256":"83bfd90fe3a2df69d7db2e1f6fc511c9f9024ee4cb1c9b45b0edf7a87c202bae","schema_version":"1.0","event_id":"sha256:83bfd90fe3a2df69d7db2e1f6fc511c9f9024ee4cb1c9b45b0edf7a87c202bae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IZ3CZKH2MNRB3SEFJJM4K2ZF5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Calibrating word problems of groups via the complexity of equivalence relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrea Sorbi, Andr\\'e Nies","submitted_at":"2016-09-12T12:38:46Z","abstract_excerpt":"(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal co-computably enumerable equivalence relation. (3) Each c.e. truth-table degree contains the word problem of a finitely generated group of computable permutations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03371","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":"2026-05-18T01:04:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YneAfg++Hsqr9yRJGWKeysP+fWC8yM1K1mkCl95L8TFLBy3ZtYT9QzED0Gf78qyLIQCgf3nz1aahBB2pV5YICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:45:25.781195Z"},"content_sha256":"0510e3464161c1346b1725c08ddf24bba98d63d8507e2a4e95080bb71232e98e","schema_version":"1.0","event_id":"sha256:0510e3464161c1346b1725c08ddf24bba98d63d8507e2a4e95080bb71232e98e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/bundle.json","state_url":"https://pith.science/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/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":"2026-05-25T23:45:25Z","links":{"resolver":"https://pith.science/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L","bundle":"https://pith.science/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/bundle.json","state":"https://pith.science/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZ3CZKH2MNRB3SEFJJM4K2ZF5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IZ3CZKH2MNRB3SEFJJM4K2ZF5L","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":"498ab45840424bb50432a869ed29285cf2d320bc7dc760b32967c58bbb150487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-12T12:38:46Z","title_canon_sha256":"ae703264d650022fc12edf877b870d2e991fa0eb380e3ba79ce4ec4644d315a1"},"schema_version":"1.0","source":{"id":"1609.03371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03371","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03371v1","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03371","created_at":"2026-05-18T01:04:47Z"},{"alias_kind":"pith_short_12","alias_value":"IZ3CZKH2MNRB","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IZ3CZKH2MNRB3SEF","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IZ3CZKH2","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:0510e3464161c1346b1725c08ddf24bba98d63d8507e2a4e95080bb71232e98e","target":"graph","created_at":"2026-05-18T01:04:47Z","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":"(1) There is a finitely presented group with a word problem which is a uniformly effectively inseparable equivalence relation. (2) There is a finitely generated group of computable permutations with a word problem which is a universal co-computably enumerable equivalence relation. (3) Each c.e. truth-table degree contains the word problem of a finitely generated group of computable permutations.","authors_text":"Andrea Sorbi, Andr\\'e Nies","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-12T12:38:46Z","title":"Calibrating word problems of groups via the complexity of equivalence relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03371","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":"sha256:83bfd90fe3a2df69d7db2e1f6fc511c9f9024ee4cb1c9b45b0edf7a87c202bae","target":"record","created_at":"2026-05-18T01:04:47Z","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":"498ab45840424bb50432a869ed29285cf2d320bc7dc760b32967c58bbb150487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-09-12T12:38:46Z","title_canon_sha256":"ae703264d650022fc12edf877b870d2e991fa0eb380e3ba79ce4ec4644d315a1"},"schema_version":"1.0","source":{"id":"1609.03371","kind":"arxiv","version":1}},"canonical_sha256":"46762ca8fa63621dc8854a59c56b25eac4dda003e585e04f825614c2284e27a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46762ca8fa63621dc8854a59c56b25eac4dda003e585e04f825614c2284e27a9","first_computed_at":"2026-05-18T01:04:47.098577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:47.098577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7jjHl9aC5eFeqA3GkIK4YemrI38rbslZVeNjd53YcrH8OfNpiHtunx0t/cU75G18+rPSC9dhRwjZAypPnHAiAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:47.099134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83bfd90fe3a2df69d7db2e1f6fc511c9f9024ee4cb1c9b45b0edf7a87c202bae","sha256:0510e3464161c1346b1725c08ddf24bba98d63d8507e2a4e95080bb71232e98e"],"state_sha256":"f8b5b5dcae4a7728766eeb1e91dd8e038fa89fa98b9cd2abbea4076a31461356"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Jk8rcFUyMrYRVqm5kRFbwMETnclN+7OLdvja92rzW1S8MG1uMQREJmMf8Wnslcx1WV0Bdq8QS2BuIuB0wvuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:45:25.785077Z","bundle_sha256":"42d2ed95cb1534f54894314d69353aae3aa0c594b13c1a45193e6b3136c1a4f2"}}