{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:35GVX6TN4LWFSZLHIVSFG57MXD","short_pith_number":"pith:35GVX6TN","canonical_record":{"source":{"id":"1412.5357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-17T12:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"0dcd3bfe1f3f6f30fe5321ffdca46d96758efc777b97a4d518945e08062b2fc8","abstract_canon_sha256":"107380535b8d04c03ec8af36f41f547a97d20a1c05cb8f47c23288e9d757ea0c"},"schema_version":"1.0"},"canonical_sha256":"df4d5bfa6de2ec59656745645377ecb8ea09e7e345d1577849a3ce8b12ac57cc","source":{"kind":"arxiv","id":"1412.5357","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5357","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5357v2","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5357","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"35GVX6TN4LWF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"35GVX6TN4LWFSZLH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"35GVX6TN","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:35GVX6TN4LWFSZLHIVSFG57MXD","target":"record","payload":{"canonical_record":{"source":{"id":"1412.5357","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-17T12:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"0dcd3bfe1f3f6f30fe5321ffdca46d96758efc777b97a4d518945e08062b2fc8","abstract_canon_sha256":"107380535b8d04c03ec8af36f41f547a97d20a1c05cb8f47c23288e9d757ea0c"},"schema_version":"1.0"},"canonical_sha256":"df4d5bfa6de2ec59656745645377ecb8ea09e7e345d1577849a3ce8b12ac57cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:28.549405Z","signature_b64":"fai0l4XDtrisn/nMjza+4HDx2sVC02hvorq7/+WpJy1kdOtoj0pUVNOCH2juectHUFXqyNxY62EFtqi3UEbGDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df4d5bfa6de2ec59656745645377ecb8ea09e7e345d1577849a3ce8b12ac57cc","last_reissued_at":"2026-05-18T00:02:28.548919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:28.548919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.5357","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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSRWaJy8/Fxwk0yVardJjwG6/+7Uy8HxGFKSD7mnZmDiU0RZWQKLFuqC31tKhQ7+JMFK86uzyB0lufsWWlvyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:33:23.713626Z"},"content_sha256":"0b8277e1e2bb032567a16586a10bf70f37204ee47c1b35afb70bf6ed0f5bba3b","schema_version":"1.0","event_id":"sha256:0b8277e1e2bb032567a16586a10bf70f37204ee47c1b35afb70bf6ed0f5bba3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:35GVX6TN4LWFSZLHIVSFG57MXD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The JSJ-decompositions of one-relator groups with torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alan D. Logan","submitted_at":"2014-12-17T12:11:12Z","abstract_excerpt":"In this paper we use JSJ-decompositions to formalise a folk conjecture recorded by Pride on the structure of one-relator groups with torsion. We prove a slightly weaker version of the conjecture, which implies that the structure of one-relator groups with torsion closely resemble the structure of torsion-free hyperbolic groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5357","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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uxGDS0We7euSOGhxMkCgQBHMoK/8Xj7jl/ZmWno/9W+9d4xfBErVuM9c+rEEgRY+85MA1t7lulba99Jug8D7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:33:23.714064Z"},"content_sha256":"61dbbbe0f42bf2a0a5a578b5e72e54bef8c182c2c52572bb1c11892565a66f98","schema_version":"1.0","event_id":"sha256:61dbbbe0f42bf2a0a5a578b5e72e54bef8c182c2c52572bb1c11892565a66f98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/35GVX6TN4LWFSZLHIVSFG57MXD/bundle.json","state_url":"https://pith.science/pith/35GVX6TN4LWFSZLHIVSFG57MXD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/35GVX6TN4LWFSZLHIVSFG57MXD/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":"2026-05-26T08:33:23Z","links":{"resolver":"https://pith.science/pith/35GVX6TN4LWFSZLHIVSFG57MXD","bundle":"https://pith.science/pith/35GVX6TN4LWFSZLHIVSFG57MXD/bundle.json","state":"https://pith.science/pith/35GVX6TN4LWFSZLHIVSFG57MXD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/35GVX6TN4LWFSZLHIVSFG57MXD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:35GVX6TN4LWFSZLHIVSFG57MXD","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":"107380535b8d04c03ec8af36f41f547a97d20a1c05cb8f47c23288e9d757ea0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-17T12:11:12Z","title_canon_sha256":"0dcd3bfe1f3f6f30fe5321ffdca46d96758efc777b97a4d518945e08062b2fc8"},"schema_version":"1.0","source":{"id":"1412.5357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5357","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5357v2","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5357","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"35GVX6TN4LWF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"35GVX6TN4LWFSZLH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"35GVX6TN","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:61dbbbe0f42bf2a0a5a578b5e72e54bef8c182c2c52572bb1c11892565a66f98","target":"graph","created_at":"2026-05-18T00:02:28Z","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":"In this paper we use JSJ-decompositions to formalise a folk conjecture recorded by Pride on the structure of one-relator groups with torsion. We prove a slightly weaker version of the conjecture, which implies that the structure of one-relator groups with torsion closely resemble the structure of torsion-free hyperbolic groups.","authors_text":"Alan D. Logan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-17T12:11:12Z","title":"The JSJ-decompositions of one-relator groups with torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5357","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":"sha256:0b8277e1e2bb032567a16586a10bf70f37204ee47c1b35afb70bf6ed0f5bba3b","target":"record","created_at":"2026-05-18T00:02:28Z","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":"107380535b8d04c03ec8af36f41f547a97d20a1c05cb8f47c23288e9d757ea0c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-12-17T12:11:12Z","title_canon_sha256":"0dcd3bfe1f3f6f30fe5321ffdca46d96758efc777b97a4d518945e08062b2fc8"},"schema_version":"1.0","source":{"id":"1412.5357","kind":"arxiv","version":2}},"canonical_sha256":"df4d5bfa6de2ec59656745645377ecb8ea09e7e345d1577849a3ce8b12ac57cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df4d5bfa6de2ec59656745645377ecb8ea09e7e345d1577849a3ce8b12ac57cc","first_computed_at":"2026-05-18T00:02:28.548919Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:28.548919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fai0l4XDtrisn/nMjza+4HDx2sVC02hvorq7/+WpJy1kdOtoj0pUVNOCH2juectHUFXqyNxY62EFtqi3UEbGDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:28.549405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b8277e1e2bb032567a16586a10bf70f37204ee47c1b35afb70bf6ed0f5bba3b","sha256:61dbbbe0f42bf2a0a5a578b5e72e54bef8c182c2c52572bb1c11892565a66f98"],"state_sha256":"50856f55ca5526771dd255fb9b4888de1239088306f15c492ef2b5b5408aa2d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s8KLUy8WtJk2zE61k2iTLOngz6+E27BHnDUEqrNVy9Mn9g3J54G+QNqQKW/QaF7K1lXGZkxEqm/tQFh8PRXMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:33:23.717052Z","bundle_sha256":"f4db54882cb4fad36838131adcc33b7a163c6a4b4b13923ae017738398f80ff0"}}