{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OQ4B6U3DEFEWCH645OWS36YZ7U","short_pith_number":"pith:OQ4B6U3D","canonical_record":{"source":{"id":"1310.3245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5ab1292e61923c6542dcc8843ecd3ec269f6a2771fdbc80165e7d7705a376bb","abstract_canon_sha256":"815d685b5ede55a1779d5742a61c6d6a550165068f10801ff79a4730b1665362"},"schema_version":"1.0"},"canonical_sha256":"74381f53632149611fdcebad2dfb19fd20ef49d2d2f72b024abb09b2f1f576e5","source":{"kind":"arxiv","id":"1310.3245","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3245","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3245v1","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3245","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"OQ4B6U3DEFEW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OQ4B6U3DEFEWCH64","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OQ4B6U3D","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OQ4B6U3DEFEWCH645OWS36YZ7U","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3245","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:06:57Z","cross_cats_sorted":[],"title_canon_sha256":"a5ab1292e61923c6542dcc8843ecd3ec269f6a2771fdbc80165e7d7705a376bb","abstract_canon_sha256":"815d685b5ede55a1779d5742a61c6d6a550165068f10801ff79a4730b1665362"},"schema_version":"1.0"},"canonical_sha256":"74381f53632149611fdcebad2dfb19fd20ef49d2d2f72b024abb09b2f1f576e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:44.526617Z","signature_b64":"FEm5Y1O1vFCkOGzrY17C+832GnAbsnKV3FxR9AkPpRJtUYAij2WxbTdH2Ae9A8g+w0z6r1OZeoFNBHzbbO6wCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"74381f53632149611fdcebad2dfb19fd20ef49d2d2f72b024abb09b2f1f576e5","last_reissued_at":"2026-05-18T03:10:44.526018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:44.526018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3245","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":"2026-05-18T03:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdrJF8eJfuS/o/4hiR25fwyg12jADk2j+cvR7+J/epieF9L0j6u3+PwuViVGK0VrfYbHi7yv6a6eIIbzPRQEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:38:00.294946Z"},"content_sha256":"0aa51e95f3617ef2e68d930b72826e62a8d4282c67d4b00efba854fc92caf13b","schema_version":"1.0","event_id":"sha256:0aa51e95f3617ef2e68d930b72826e62a8d4282c67d4b00efba854fc92caf13b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OQ4B6U3DEFEWCH645OWS36YZ7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Template iterations and maximal cofinitary groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Asger T\\\"ornquist, Vera Fischer","submitted_at":"2013-10-11T19:06:57Z","abstract_excerpt":"The main result of the present paper is that $\\mathfrak a_g$, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial properties allowing it to be used within a similar template forcing construction. Additionally we obtain that $\\mathfrak a_p$, the minimal size of a maximal family of almost disjoint permutations, and $\\mathfrak a_e$, the minimal size of a maximal eventually different family, can be of countable cofinality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3245","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":"2026-05-18T03:10:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"693eOiz7ySGzkMvyFBEULPlv5pII3uoIVF9sDMq4uVxaah23FajMhhgHETssnrMKVQmx6Zgz6iZJ2oqEKQYMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:38:00.295624Z"},"content_sha256":"a2c7aa3ded4fb1688c0cb893d733432cd37301d08f34f2e7fa844f80a3ec1e8d","schema_version":"1.0","event_id":"sha256:a2c7aa3ded4fb1688c0cb893d733432cd37301d08f34f2e7fa844f80a3ec1e8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/bundle.json","state_url":"https://pith.science/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/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":"2026-05-27T05:38:00Z","links":{"resolver":"https://pith.science/pith/OQ4B6U3DEFEWCH645OWS36YZ7U","bundle":"https://pith.science/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/bundle.json","state":"https://pith.science/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQ4B6U3DEFEWCH645OWS36YZ7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OQ4B6U3DEFEWCH645OWS36YZ7U","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":"815d685b5ede55a1779d5742a61c6d6a550165068f10801ff79a4730b1665362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:06:57Z","title_canon_sha256":"a5ab1292e61923c6542dcc8843ecd3ec269f6a2771fdbc80165e7d7705a376bb"},"schema_version":"1.0","source":{"id":"1310.3245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3245","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3245v1","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3245","created_at":"2026-05-18T03:10:44Z"},{"alias_kind":"pith_short_12","alias_value":"OQ4B6U3DEFEW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OQ4B6U3DEFEWCH64","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OQ4B6U3D","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:a2c7aa3ded4fb1688c0cb893d733432cd37301d08f34f2e7fa844f80a3ec1e8d","target":"graph","created_at":"2026-05-18T03:10:44Z","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":"The main result of the present paper is that $\\mathfrak a_g$, the minimal size of maximal cofinitary group, can be of countable cofinality. To prove this we define a natural poset for adding a maximal cofinitary group of a given cardinality, which enjoys certain combinatorial properties allowing it to be used within a similar template forcing construction. Additionally we obtain that $\\mathfrak a_p$, the minimal size of a maximal family of almost disjoint permutations, and $\\mathfrak a_e$, the minimal size of a maximal eventually different family, can be of countable cofinality.","authors_text":"Asger T\\\"ornquist, Vera Fischer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:06:57Z","title":"Template iterations and maximal cofinitary groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3245","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":"sha256:0aa51e95f3617ef2e68d930b72826e62a8d4282c67d4b00efba854fc92caf13b","target":"record","created_at":"2026-05-18T03:10:44Z","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":"815d685b5ede55a1779d5742a61c6d6a550165068f10801ff79a4730b1665362","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T19:06:57Z","title_canon_sha256":"a5ab1292e61923c6542dcc8843ecd3ec269f6a2771fdbc80165e7d7705a376bb"},"schema_version":"1.0","source":{"id":"1310.3245","kind":"arxiv","version":1}},"canonical_sha256":"74381f53632149611fdcebad2dfb19fd20ef49d2d2f72b024abb09b2f1f576e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74381f53632149611fdcebad2dfb19fd20ef49d2d2f72b024abb09b2f1f576e5","first_computed_at":"2026-05-18T03:10:44.526018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:44.526018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEm5Y1O1vFCkOGzrY17C+832GnAbsnKV3FxR9AkPpRJtUYAij2WxbTdH2Ae9A8g+w0z6r1OZeoFNBHzbbO6wCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:44.526617Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0aa51e95f3617ef2e68d930b72826e62a8d4282c67d4b00efba854fc92caf13b","sha256:a2c7aa3ded4fb1688c0cb893d733432cd37301d08f34f2e7fa844f80a3ec1e8d"],"state_sha256":"597f75197a9f9dd1a60c9a8d0b2a1560547c406cf94ec60aa8d6d4e1f3cdf485"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"byNm/Zq4itrIjQqvJ93LDKAIHOtk50QPPXLEiKB9geqeet+sb0h9zYOWg+eZdxbhguaB6Wqfz9SlAtEU+9uKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:38:00.299034Z","bundle_sha256":"d3184c71b83d63d83689957927af37aa44a69f9e5d0236761e5ac5c5f9e90bcb"}}