{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HOOTEARPXSQ6A22UBROBA3N5UT","short_pith_number":"pith:HOOTEARP","canonical_record":{"source":{"id":"1312.5382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-19T00:56:14Z","cross_cats_sorted":[],"title_canon_sha256":"7d5371021b933d4411891673660be6405a94aafec9128c2140a3cb59419ba3a6","abstract_canon_sha256":"53ae2145f80396823fe58ef2e293e45865b643f5a16983e1f59c0b76aba10301"},"schema_version":"1.0"},"canonical_sha256":"3b9d32022fbca1e06b540c5c106dbda4ca0e1dfa9ddf8ff2968166c9d575af85","source":{"kind":"arxiv","id":"1312.5382","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5382","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5382v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5382","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"HOOTEARPXSQ6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HOOTEARPXSQ6A22U","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HOOTEARP","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HOOTEARPXSQ6A22UBROBA3N5UT","target":"record","payload":{"canonical_record":{"source":{"id":"1312.5382","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-19T00:56:14Z","cross_cats_sorted":[],"title_canon_sha256":"7d5371021b933d4411891673660be6405a94aafec9128c2140a3cb59419ba3a6","abstract_canon_sha256":"53ae2145f80396823fe58ef2e293e45865b643f5a16983e1f59c0b76aba10301"},"schema_version":"1.0"},"canonical_sha256":"3b9d32022fbca1e06b540c5c106dbda4ca0e1dfa9ddf8ff2968166c9d575af85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:15.952021Z","signature_b64":"jrhGuEl0ZCURJsVaCylyCqgIV+xQTqLDQx4knOkE2D6YxjBkEMJh/TB1ARD1GyhuDv8n01kc3z7zitX6zj3OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b9d32022fbca1e06b540c5c106dbda4ca0e1dfa9ddf8ff2968166c9d575af85","last_reissued_at":"2026-05-18T00:54:15.951582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:15.951582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.5382","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tV0rqkj21sFjlC/EvyofxA3K2r4Bp8Cm9W3fYq0KrJKHxCzFawArDSBLPn2fC+umxlPc/t1YxgotcCIFrVHGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:16:01.446909Z"},"content_sha256":"f3d52868ca2fba23c285800bc81992bb2f070b61df1935fda911e533c746b263","schema_version":"1.0","event_id":"sha256:f3d52868ca2fba23c285800bc81992bb2f070b61df1935fda911e533c746b263"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HOOTEARPXSQ6A22UBROBA3N5UT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Shift Dynamics For Cyclically Presented Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"William A. Bogley","submitted_at":"2013-12-19T00:56:14Z","abstract_excerpt":"For group presentations with cyclic symmetry, there is a connection between asphericity and the dynamics of the shift automorphism. For the class of groups $G_n(k,l)$ described by the cyclic presentations $\\mathcal{P}_n(k,l) = (x_i:x_ix_{i+k}x_{i+l}\\ (i \\mod n))$ and studied extensively by G. Williams and M. Edjvet \\cite{EdjvetWilliams}, the shift acts freely on the nonidentity elements of $G_n(k,l)$ if and only if the presentation $\\mathcal{P}_n(k,l)$ is combinatorially aspherical in the sense of \\cite{CCH}. The shift has a nonidentity fixed point precisely when $G_n(k,l)$ is finite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5382","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":"2026-05-18T00:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EsDBH4dZHhVpYQ8etXwbD3SSAV4f1nvgzLE8SrHc3aP844zijiUGQUzt3W4AH4QBmGhCULeXNjfiwEsN9nS9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T09:16:01.447242Z"},"content_sha256":"592d5f3c4fac22c2b29dac59d3559cd712bac98bb14e67bdc0b8d5088d243f93","schema_version":"1.0","event_id":"sha256:592d5f3c4fac22c2b29dac59d3559cd712bac98bb14e67bdc0b8d5088d243f93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOOTEARPXSQ6A22UBROBA3N5UT/bundle.json","state_url":"https://pith.science/pith/HOOTEARPXSQ6A22UBROBA3N5UT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOOTEARPXSQ6A22UBROBA3N5UT/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":"2026-06-21T09:16:01Z","links":{"resolver":"https://pith.science/pith/HOOTEARPXSQ6A22UBROBA3N5UT","bundle":"https://pith.science/pith/HOOTEARPXSQ6A22UBROBA3N5UT/bundle.json","state":"https://pith.science/pith/HOOTEARPXSQ6A22UBROBA3N5UT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOOTEARPXSQ6A22UBROBA3N5UT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HOOTEARPXSQ6A22UBROBA3N5UT","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":"53ae2145f80396823fe58ef2e293e45865b643f5a16983e1f59c0b76aba10301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-19T00:56:14Z","title_canon_sha256":"7d5371021b933d4411891673660be6405a94aafec9128c2140a3cb59419ba3a6"},"schema_version":"1.0","source":{"id":"1312.5382","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.5382","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1312.5382v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.5382","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"HOOTEARPXSQ6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HOOTEARPXSQ6A22U","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HOOTEARP","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:592d5f3c4fac22c2b29dac59d3559cd712bac98bb14e67bdc0b8d5088d243f93","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"For group presentations with cyclic symmetry, there is a connection between asphericity and the dynamics of the shift automorphism. For the class of groups $G_n(k,l)$ described by the cyclic presentations $\\mathcal{P}_n(k,l) = (x_i:x_ix_{i+k}x_{i+l}\\ (i \\mod n))$ and studied extensively by G. Williams and M. Edjvet \\cite{EdjvetWilliams}, the shift acts freely on the nonidentity elements of $G_n(k,l)$ if and only if the presentation $\\mathcal{P}_n(k,l)$ is combinatorially aspherical in the sense of \\cite{CCH}. The shift has a nonidentity fixed point precisely when $G_n(k,l)$ is finite.","authors_text":"William A. Bogley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-19T00:56:14Z","title":"On Shift Dynamics For Cyclically Presented Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.5382","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:f3d52868ca2fba23c285800bc81992bb2f070b61df1935fda911e533c746b263","target":"record","created_at":"2026-05-18T00:54:15Z","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":"53ae2145f80396823fe58ef2e293e45865b643f5a16983e1f59c0b76aba10301","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-12-19T00:56:14Z","title_canon_sha256":"7d5371021b933d4411891673660be6405a94aafec9128c2140a3cb59419ba3a6"},"schema_version":"1.0","source":{"id":"1312.5382","kind":"arxiv","version":1}},"canonical_sha256":"3b9d32022fbca1e06b540c5c106dbda4ca0e1dfa9ddf8ff2968166c9d575af85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b9d32022fbca1e06b540c5c106dbda4ca0e1dfa9ddf8ff2968166c9d575af85","first_computed_at":"2026-05-18T00:54:15.951582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.951582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jrhGuEl0ZCURJsVaCylyCqgIV+xQTqLDQx4knOkE2D6YxjBkEMJh/TB1ARD1GyhuDv8n01kc3z7zitX6zj3OCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.952021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.5382","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3d52868ca2fba23c285800bc81992bb2f070b61df1935fda911e533c746b263","sha256:592d5f3c4fac22c2b29dac59d3559cd712bac98bb14e67bdc0b8d5088d243f93"],"state_sha256":"e458c1ea9554247c9bdd839fefc5ccb322af7c75f8f7d582f579c88fe19c70fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S1qPjwvEYm80OoiSZw0TNW9c+8CBIvbsmxJnqQ1hTsi8K82vIwNkKy5Ybb1rhG1NDZyXiWvSM46yYqufuPe3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T09:16:01.449187Z","bundle_sha256":"701dd3978ac22821b425d99805115eaaed4a84d847610bdffb53785c0b1df748"}}