{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LQATKRPIM7AM4DUUPJJKBIHQA6","short_pith_number":"pith:LQATKRPI","canonical_record":{"source":{"id":"1209.0966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-05T13:27:08Z","cross_cats_sorted":[],"title_canon_sha256":"443d56a559253a3bd673d3a4c917a4a6a0b202dbe3cba6abb92cb38055ebd06c","abstract_canon_sha256":"878e4ef90cc1a46b386fc8a746274e8870d60fb8fb4e17af4ece44315f4ba1be"},"schema_version":"1.0"},"canonical_sha256":"5c013545e867c0ce0e947a52a0a0f007802e0dd362c3036ed945993bc85c8726","source":{"kind":"arxiv","id":"1209.0966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0966","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0966v1","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0966","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"LQATKRPIM7AM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LQATKRPIM7AM4DUU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LQATKRPI","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LQATKRPIM7AM4DUUPJJKBIHQA6","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0966","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-05T13:27:08Z","cross_cats_sorted":[],"title_canon_sha256":"443d56a559253a3bd673d3a4c917a4a6a0b202dbe3cba6abb92cb38055ebd06c","abstract_canon_sha256":"878e4ef90cc1a46b386fc8a746274e8870d60fb8fb4e17af4ece44315f4ba1be"},"schema_version":"1.0"},"canonical_sha256":"5c013545e867c0ce0e947a52a0a0f007802e0dd362c3036ed945993bc85c8726","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:12.075680Z","signature_b64":"9DN9BMRb8dtOa+2SYAN519jRiWzOKS7p2BSnhVlN+CgXk5Ijo55GLm/cUqsrBWWiRZfGoSC1agPph5NiuzqUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c013545e867c0ce0e947a52a0a0f007802e0dd362c3036ed945993bc85c8726","last_reissued_at":"2026-05-18T03:45:12.074861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:12.074861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0966","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":"2026-05-18T03:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6eQbkdszolYR4rq1ZINvW6oKF/dxhwfMpWRyRXqzNxOUiCP5rtdDjHTzgJAvXk5fuQaCyOqfAS8Dz4FaOHhbAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:02:12.130835Z"},"content_sha256":"0c9433109f2e99668eaa72230b0c163190342a17e17dcb8bbd9ff3fced1aad9d","schema_version":"1.0","event_id":"sha256:0c9433109f2e99668eaa72230b0c163190342a17e17dcb8bbd9ff3fced1aad9d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LQATKRPIM7AM4DUUPJJKBIHQA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Gerald Williams, James Howie","submitted_at":"2012-09-05T13:27:08Z","abstract_excerpt":"We study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented group implies solvability of the conjugacy problem for the LOG group. In the case where the label on the tail of the LOG spells a positive word in the vertices in the circuit we show that the LOGs and gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0966","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":"2026-05-18T03:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDOY8CUd7f83tSqKiIboQGCPtpSf6y/7WD3UB9Jzppndp7yDQB2sGsRtGkeNqQtdErnAYkaGOv7pBUTDXihxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:02:12.131177Z"},"content_sha256":"9fd31b7710bf44709cb0c940dcf7c36c8ff1605c4c0cfd3bddd3d5d14c0fbc0f","schema_version":"1.0","event_id":"sha256:9fd31b7710bf44709cb0c940dcf7c36c8ff1605c4c0cfd3bddd3d5d14c0fbc0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/bundle.json","state_url":"https://pith.science/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/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":"2026-06-20T23:02:12Z","links":{"resolver":"https://pith.science/pith/LQATKRPIM7AM4DUUPJJKBIHQA6","bundle":"https://pith.science/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/bundle.json","state":"https://pith.science/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LQATKRPIM7AM4DUUPJJKBIHQA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LQATKRPIM7AM4DUUPJJKBIHQA6","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":"878e4ef90cc1a46b386fc8a746274e8870d60fb8fb4e17af4ece44315f4ba1be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-05T13:27:08Z","title_canon_sha256":"443d56a559253a3bd673d3a4c917a4a6a0b202dbe3cba6abb92cb38055ebd06c"},"schema_version":"1.0","source":{"id":"1209.0966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0966","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0966v1","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0966","created_at":"2026-05-18T03:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"LQATKRPIM7AM","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LQATKRPIM7AM4DUU","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LQATKRPI","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:9fd31b7710bf44709cb0c940dcf7c36c8ff1605c4c0cfd3bddd3d5d14c0fbc0f","target":"graph","created_at":"2026-05-18T03:45:12Z","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 study a class of Labelled Oriented Graph (LOG) group where the underlying graph is a tadpole graph. We show that such a group is the natural HNN extension of a cyclically presented group and investigate the relationship between the LOG group and the cyclically presented group. We relate the second homotopy groups of their presentations and show that hyperbolicity of the cyclically presented group implies solvability of the conjugacy problem for the LOG group. In the case where the label on the tail of the LOG spells a positive word in the vertices in the circuit we show that the LOGs and gr","authors_text":"Gerald Williams, James Howie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-05T13:27:08Z","title":"Tadpole Labelled Oriented Graph Groups and Cyclically Presented Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0966","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":"sha256:0c9433109f2e99668eaa72230b0c163190342a17e17dcb8bbd9ff3fced1aad9d","target":"record","created_at":"2026-05-18T03:45:12Z","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":"878e4ef90cc1a46b386fc8a746274e8870d60fb8fb4e17af4ece44315f4ba1be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-09-05T13:27:08Z","title_canon_sha256":"443d56a559253a3bd673d3a4c917a4a6a0b202dbe3cba6abb92cb38055ebd06c"},"schema_version":"1.0","source":{"id":"1209.0966","kind":"arxiv","version":1}},"canonical_sha256":"5c013545e867c0ce0e947a52a0a0f007802e0dd362c3036ed945993bc85c8726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c013545e867c0ce0e947a52a0a0f007802e0dd362c3036ed945993bc85c8726","first_computed_at":"2026-05-18T03:45:12.074861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:12.074861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9DN9BMRb8dtOa+2SYAN519jRiWzOKS7p2BSnhVlN+CgXk5Ijo55GLm/cUqsrBWWiRZfGoSC1agPph5NiuzqUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:12.075680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c9433109f2e99668eaa72230b0c163190342a17e17dcb8bbd9ff3fced1aad9d","sha256:9fd31b7710bf44709cb0c940dcf7c36c8ff1605c4c0cfd3bddd3d5d14c0fbc0f"],"state_sha256":"28f34ecd5a42630c25ca910ac72502e479abb42b1c0f28a0204b6ed1bada606d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RUv1kI4HZ3PE1PZKaLyMpTm3uVtRALd6MUL+tUIr0ycxHhoSBOoA+SRMnX/pJeEuATGYhcHGMCcu/2IA/mLfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:02:12.133111Z","bundle_sha256":"09ec9e8b03c39d752a59eaa6c62a92e92c554b5d8a25e7bcb3cd3227a0a962d1"}}