{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7PEE5OSDNBVZ5RMBP5CVOS2JMN","short_pith_number":"pith:7PEE5OSD","canonical_record":{"source":{"id":"1201.6616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-01-31T16:58:54Z","cross_cats_sorted":[],"title_canon_sha256":"9f25dac9b8972eadf7ea6203790665d34300420f621294e3aae1d5f70efff145","abstract_canon_sha256":"7e08b6f343d4d0ebe5649301e702fe3c7772d6a2205d8175abdb39697e5f274e"},"schema_version":"1.0"},"canonical_sha256":"fbc84eba43686b9ec5817f45574b49635b8f1475e310a93787b71e1de737e937","source":{"kind":"arxiv","id":"1201.6616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6616","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6616v1","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6616","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"7PEE5OSDNBVZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PEE5OSDNBVZ5RMB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PEE5OSD","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7PEE5OSDNBVZ5RMBP5CVOS2JMN","target":"record","payload":{"canonical_record":{"source":{"id":"1201.6616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-01-31T16:58:54Z","cross_cats_sorted":[],"title_canon_sha256":"9f25dac9b8972eadf7ea6203790665d34300420f621294e3aae1d5f70efff145","abstract_canon_sha256":"7e08b6f343d4d0ebe5649301e702fe3c7772d6a2205d8175abdb39697e5f274e"},"schema_version":"1.0"},"canonical_sha256":"fbc84eba43686b9ec5817f45574b49635b8f1475e310a93787b71e1de737e937","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:51.769462Z","signature_b64":"fB0qfnUjugZXmU2klfoMH5R68i1z3OyrlBl+QTyyYxNkSto6VCCRcbTuKBpXloz0DoJ0jjGB01gXI64Z1vjWDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fbc84eba43686b9ec5817f45574b49635b8f1475e310a93787b71e1de737e937","last_reissued_at":"2026-05-18T01:29:51.768927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:51.768927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.6616","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":"2026-05-18T01:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NiPt90pzO5wnlPG+zH5Nuz+m+fBLAHnjKfuuf83JDik6LORHAlbHylJ2xWuTotEf5xc8FqMmCejP+I3h+qP5DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:44:13.989232Z"},"content_sha256":"5b8cc02aa5f47ca338d714339451446ef19085da28fbebd25d4db3c772e16d08","schema_version":"1.0","event_id":"sha256:5b8cc02aa5f47ca338d714339451446ef19085da28fbebd25d4db3c772e16d08"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7PEE5OSDNBVZ5RMBP5CVOS2JMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Context-free rewriting systems and word-hyperbolic structures with uniqueness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alan J. Cain, Victor Maltcev","submitted_at":"2012-01-31T16:58:54Z","abstract_excerpt":"This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan & Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6616","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":"2026-05-18T01:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5cARAoiO1vyx/SE6bJ8RO8hQ3PWqdoo7N09/v2XxnjotmOqTem9pMy2EUXHX+2DeDh2aD3WIHLZ0ONDjEjzuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:44:13.990001Z"},"content_sha256":"fba2feb507f0cfc813580f3d76c725b2b87f23bb45e56efa804bbded7f47004b","schema_version":"1.0","event_id":"sha256:fba2feb507f0cfc813580f3d76c725b2b87f23bb45e56efa804bbded7f47004b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/bundle.json","state_url":"https://pith.science/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/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":"2026-05-31T20:44:13Z","links":{"resolver":"https://pith.science/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN","bundle":"https://pith.science/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/bundle.json","state":"https://pith.science/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7PEE5OSDNBVZ5RMBP5CVOS2JMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7PEE5OSDNBVZ5RMBP5CVOS2JMN","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":"7e08b6f343d4d0ebe5649301e702fe3c7772d6a2205d8175abdb39697e5f274e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-01-31T16:58:54Z","title_canon_sha256":"9f25dac9b8972eadf7ea6203790665d34300420f621294e3aae1d5f70efff145"},"schema_version":"1.0","source":{"id":"1201.6616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6616","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6616v1","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6616","created_at":"2026-05-18T01:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"7PEE5OSDNBVZ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7PEE5OSDNBVZ5RMB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7PEE5OSD","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:fba2feb507f0cfc813580f3d76c725b2b87f23bb45e56efa804bbded7f47004b","target":"graph","created_at":"2026-05-18T01:29:51Z","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":"This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan & Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid).","authors_text":"Alan J. Cain, Victor Maltcev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-01-31T16:58:54Z","title":"Context-free rewriting systems and word-hyperbolic structures with uniqueness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6616","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":"sha256:5b8cc02aa5f47ca338d714339451446ef19085da28fbebd25d4db3c772e16d08","target":"record","created_at":"2026-05-18T01:29:51Z","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":"7e08b6f343d4d0ebe5649301e702fe3c7772d6a2205d8175abdb39697e5f274e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-01-31T16:58:54Z","title_canon_sha256":"9f25dac9b8972eadf7ea6203790665d34300420f621294e3aae1d5f70efff145"},"schema_version":"1.0","source":{"id":"1201.6616","kind":"arxiv","version":1}},"canonical_sha256":"fbc84eba43686b9ec5817f45574b49635b8f1475e310a93787b71e1de737e937","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbc84eba43686b9ec5817f45574b49635b8f1475e310a93787b71e1de737e937","first_computed_at":"2026-05-18T01:29:51.768927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:51.768927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fB0qfnUjugZXmU2klfoMH5R68i1z3OyrlBl+QTyyYxNkSto6VCCRcbTuKBpXloz0DoJ0jjGB01gXI64Z1vjWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:51.769462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b8cc02aa5f47ca338d714339451446ef19085da28fbebd25d4db3c772e16d08","sha256:fba2feb507f0cfc813580f3d76c725b2b87f23bb45e56efa804bbded7f47004b"],"state_sha256":"bea4917f2361d02576c90d22d69abfdfeb1dde3c98e718286a6d005018ecea3c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOiTWdK1I4xYr0Srv2UizYADUWDOrGpvAAx4md+2UFIP7gRMa8Pw2aB8xytOolsw1wIqa1bLQnOUlMJRz0+VCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:44:13.993179Z","bundle_sha256":"386fbeaeb5340d44ca040825a11dc961d7cb11f3e4611073197c0fca625331fd"}}