{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PZTXJVNS3GTHRYIYDFIQVQ4ZCT","short_pith_number":"pith:PZTXJVNS","canonical_record":{"source":{"id":"1608.00617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-01T21:02:05Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4268cdba1d393fd519e80f68d9172762be1b30a13af68bab894146e417e4c08f","abstract_canon_sha256":"e1fdff7565fbf6caa402b6526153a7a7e1eca5f51fff37a799d67007c659a55b"},"schema_version":"1.0"},"canonical_sha256":"7e6774d5b2d9a678e11819510ac39914dbe5a7da126967e9ba375521fb6c6c20","source":{"kind":"arxiv","id":"1608.00617","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00617","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00617v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00617","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"PZTXJVNS3GTH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PZTXJVNS3GTHRYIY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PZTXJVNS","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PZTXJVNS3GTHRYIYDFIQVQ4ZCT","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00617","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-01T21:02:05Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"4268cdba1d393fd519e80f68d9172762be1b30a13af68bab894146e417e4c08f","abstract_canon_sha256":"e1fdff7565fbf6caa402b6526153a7a7e1eca5f51fff37a799d67007c659a55b"},"schema_version":"1.0"},"canonical_sha256":"7e6774d5b2d9a678e11819510ac39914dbe5a7da126967e9ba375521fb6c6c20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:11.372717Z","signature_b64":"a8T6UnsGPSKB1rPoAiFQHu+RwRfQvH2Dc+uuQkW6YpNOsLgo034oVhqJHCRIaQxvDVBLrtdUG/vtGRihY8ouAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e6774d5b2d9a678e11819510ac39914dbe5a7da126967e9ba375521fb6c6c20","last_reissued_at":"2026-05-18T01:10:11.372299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:11.372299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00617","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rmwm7cMyhUOvUHM08KDfLAOWGWO2JZsFKd8z11zwOn0HGNonDcdKEHbMBKJV+RUc4U1fS/4IQ9rIqHRLeTcnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:18:24.831085Z"},"content_sha256":"2234d54e2293fe3851a1e20d7bfe63e8bc10fb43c40a1d64f94d28dbde54bcd8","schema_version":"1.0","event_id":"sha256:2234d54e2293fe3851a1e20d7bfe63e8bc10fb43c40a1d64f94d28dbde54bcd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PZTXJVNS3GTHRYIYDFIQVQ4ZCT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On rank of the join of two subgroups in a free group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Sergei V. Ivanov","submitted_at":"2016-08-01T21:02:05Z","abstract_excerpt":"Let $H, K$ be two finitely generated subgroups of a free group, let $\\langle H, K \\rangle$ denote the subgroup generated by $H, K$, called the join of $H, K$, and let neither of $H$, $K$ have finite index in $\\langle H, K \\rangle$. We prove the existence of an epimorphism $\\zeta : \\langle H, K \\rangle \\to F_2$, where $F_2$ is a free group of rank 2, such that the restriction of $\\zeta$ on both $H$ and $K$ is injective and the restriction $\\zeta_0 : H \\cap K \\to \\zeta (H) \\cap \\zeta (K) $ of $\\zeta$ on $H \\cap K $ to $\\zeta (H) \\cap \\zeta (K)$ is surjective. This is obtained as a corollary of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00617","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":"2026-05-18T01:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M3KoA+bpPA7mL45L6X6aOQxqSOwHLZrTmvCU5oWX91WOBfuszaGgEPEGukg6Dx5IhN+CwubEVhieH7PZKQ/8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:18:24.831444Z"},"content_sha256":"d4b09787268e3123b9ba9c6ca4cb5581d6b3c45ca706c11074723d54daa1fb95","schema_version":"1.0","event_id":"sha256:d4b09787268e3123b9ba9c6ca4cb5581d6b3c45ca706c11074723d54daa1fb95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/bundle.json","state_url":"https://pith.science/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/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":"2026-06-23T02:18:24Z","links":{"resolver":"https://pith.science/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT","bundle":"https://pith.science/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/bundle.json","state":"https://pith.science/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZTXJVNS3GTHRYIYDFIQVQ4ZCT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PZTXJVNS3GTHRYIYDFIQVQ4ZCT","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":"e1fdff7565fbf6caa402b6526153a7a7e1eca5f51fff37a799d67007c659a55b","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-01T21:02:05Z","title_canon_sha256":"4268cdba1d393fd519e80f68d9172762be1b30a13af68bab894146e417e4c08f"},"schema_version":"1.0","source":{"id":"1608.00617","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00617","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00617v1","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00617","created_at":"2026-05-18T01:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"PZTXJVNS3GTH","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PZTXJVNS3GTHRYIY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PZTXJVNS","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:d4b09787268e3123b9ba9c6ca4cb5581d6b3c45ca706c11074723d54daa1fb95","target":"graph","created_at":"2026-05-18T01:10:11Z","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":"Let $H, K$ be two finitely generated subgroups of a free group, let $\\langle H, K \\rangle$ denote the subgroup generated by $H, K$, called the join of $H, K$, and let neither of $H$, $K$ have finite index in $\\langle H, K \\rangle$. We prove the existence of an epimorphism $\\zeta : \\langle H, K \\rangle \\to F_2$, where $F_2$ is a free group of rank 2, such that the restriction of $\\zeta$ on both $H$ and $K$ is injective and the restriction $\\zeta_0 : H \\cap K \\to \\zeta (H) \\cap \\zeta (K) $ of $\\zeta$ on $H \\cap K $ to $\\zeta (H) \\cap \\zeta (K)$ is surjective. This is obtained as a corollary of a","authors_text":"Sergei V. Ivanov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-01T21:02:05Z","title":"On rank of the join of two subgroups in a free group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00617","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":"sha256:2234d54e2293fe3851a1e20d7bfe63e8bc10fb43c40a1d64f94d28dbde54bcd8","target":"record","created_at":"2026-05-18T01:10:11Z","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":"e1fdff7565fbf6caa402b6526153a7a7e1eca5f51fff37a799d67007c659a55b","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-01T21:02:05Z","title_canon_sha256":"4268cdba1d393fd519e80f68d9172762be1b30a13af68bab894146e417e4c08f"},"schema_version":"1.0","source":{"id":"1608.00617","kind":"arxiv","version":1}},"canonical_sha256":"7e6774d5b2d9a678e11819510ac39914dbe5a7da126967e9ba375521fb6c6c20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e6774d5b2d9a678e11819510ac39914dbe5a7da126967e9ba375521fb6c6c20","first_computed_at":"2026-05-18T01:10:11.372299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:11.372299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a8T6UnsGPSKB1rPoAiFQHu+RwRfQvH2Dc+uuQkW6YpNOsLgo034oVhqJHCRIaQxvDVBLrtdUG/vtGRihY8ouAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:11.372717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00617","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2234d54e2293fe3851a1e20d7bfe63e8bc10fb43c40a1d64f94d28dbde54bcd8","sha256:d4b09787268e3123b9ba9c6ca4cb5581d6b3c45ca706c11074723d54daa1fb95"],"state_sha256":"39119f71af3dfc58ed255ace3a37685a012ef413ddc871d70cd33ff620de68be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dz4IIggCpxedAq+W0jxw6Nlsk6rajlN8D9f4h8qNlaIYt7yYpezJ+kxqiOQN0aZsGqfRrQ7xJL00rUe7GXX+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:18:24.833368Z","bundle_sha256":"3106a667458f91dfde08512f86d40426d73d8f44927f4d980537e9f988566a42"}}