{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:X22Q33ILBP75DULFVVCXCK2EU4","short_pith_number":"pith:X22Q33IL","canonical_record":{"source":{"id":"1706.09264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-28T13:03:30Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"0dbbc24aecc2b00098ce057cf4d6750b6d18838dffe70d128cdf5d42909cc10d","abstract_canon_sha256":"e5d7339f80049cbad9b472393e3742f066896c5173de6d0ed5c7aed9b2da986a"},"schema_version":"1.0"},"canonical_sha256":"beb50ded0b0bffd1d165ad45712b44a70077502b261a365e7a1580a5d29dac2e","source":{"kind":"arxiv","id":"1706.09264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09264","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09264v1","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09264","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"X22Q33ILBP75","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X22Q33ILBP75DULF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X22Q33IL","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:X22Q33ILBP75DULFVVCXCK2EU4","target":"record","payload":{"canonical_record":{"source":{"id":"1706.09264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-28T13:03:30Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"0dbbc24aecc2b00098ce057cf4d6750b6d18838dffe70d128cdf5d42909cc10d","abstract_canon_sha256":"e5d7339f80049cbad9b472393e3742f066896c5173de6d0ed5c7aed9b2da986a"},"schema_version":"1.0"},"canonical_sha256":"beb50ded0b0bffd1d165ad45712b44a70077502b261a365e7a1580a5d29dac2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:06.668846Z","signature_b64":"GZvOILmyErGf1Ab4mXJWu3OQQw+eIEsxjvEFTn1OX5aXArC5UD0BuVVyEwB9BlSZ7PmRDLZctkZLWeWWc4buCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"beb50ded0b0bffd1d165ad45712b44a70077502b261a365e7a1580a5d29dac2e","last_reissued_at":"2026-05-18T00:41:06.668177Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:06.668177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.09264","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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tU2oPYbHW76xa4+zpSn0+Z/rOxLG55s5x4M99MGVmxjVAUtLUAmqiScStRux7vor/sfHU+NkN74A2NNejNuiCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:40.762441Z"},"content_sha256":"cafcdb571a07429f06d08af8d7f8e34d87d7464ae7b2c42ceaf344e0e573dfab","schema_version":"1.0","event_id":"sha256:cafcdb571a07429f06d08af8d7f8e34d87d7464ae7b2c42ceaf344e0e573dfab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:X22Q33ILBP75DULFVVCXCK2EU4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simply Connected 3-Manifolds with a Dense Set of Ends of Specified Genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Dennis J. Garity, Du\\v{s}an D. Repov\\v{s}","submitted_at":"2017-06-28T13:03:30Z","abstract_excerpt":"We show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\\{e_i\\}$ so that, for every $i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in $S^3$. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09264","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":"2026-05-18T00:41:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"44kHpfES7mv4sBuWQ1XZYCDDOj0kaEuPCyaxy4x8bPn4FU+zbJB9miLwKywJebwCm6NOZKhR/XK/+OsVb46YDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:21:40.763218Z"},"content_sha256":"7c37cb9f9b3c6a545c3606b0747afcf37a9cf34f88d62f7573431693c47b73b6","schema_version":"1.0","event_id":"sha256:7c37cb9f9b3c6a545c3606b0747afcf37a9cf34f88d62f7573431693c47b73b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X22Q33ILBP75DULFVVCXCK2EU4/bundle.json","state_url":"https://pith.science/pith/X22Q33ILBP75DULFVVCXCK2EU4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X22Q33ILBP75DULFVVCXCK2EU4/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":"2026-05-31T09:21:40Z","links":{"resolver":"https://pith.science/pith/X22Q33ILBP75DULFVVCXCK2EU4","bundle":"https://pith.science/pith/X22Q33ILBP75DULFVVCXCK2EU4/bundle.json","state":"https://pith.science/pith/X22Q33ILBP75DULFVVCXCK2EU4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X22Q33ILBP75DULFVVCXCK2EU4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:X22Q33ILBP75DULFVVCXCK2EU4","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":"e5d7339f80049cbad9b472393e3742f066896c5173de6d0ed5c7aed9b2da986a","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-28T13:03:30Z","title_canon_sha256":"0dbbc24aecc2b00098ce057cf4d6750b6d18838dffe70d128cdf5d42909cc10d"},"schema_version":"1.0","source":{"id":"1706.09264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09264","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09264v1","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09264","created_at":"2026-05-18T00:41:06Z"},{"alias_kind":"pith_short_12","alias_value":"X22Q33ILBP75","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"X22Q33ILBP75DULF","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"X22Q33IL","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:7c37cb9f9b3c6a545c3606b0747afcf37a9cf34f88d62f7573431693c47b73b6","target":"graph","created_at":"2026-05-18T00:41:06Z","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 show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\\{e_i\\}$ so that, for every $i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in $S^3$. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.","authors_text":"Dennis J. Garity, Du\\v{s}an D. Repov\\v{s}","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-28T13:03:30Z","title":"Simply Connected 3-Manifolds with a Dense Set of Ends of Specified Genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09264","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:cafcdb571a07429f06d08af8d7f8e34d87d7464ae7b2c42ceaf344e0e573dfab","target":"record","created_at":"2026-05-18T00:41:06Z","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":"e5d7339f80049cbad9b472393e3742f066896c5173de6d0ed5c7aed9b2da986a","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-06-28T13:03:30Z","title_canon_sha256":"0dbbc24aecc2b00098ce057cf4d6750b6d18838dffe70d128cdf5d42909cc10d"},"schema_version":"1.0","source":{"id":"1706.09264","kind":"arxiv","version":1}},"canonical_sha256":"beb50ded0b0bffd1d165ad45712b44a70077502b261a365e7a1580a5d29dac2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"beb50ded0b0bffd1d165ad45712b44a70077502b261a365e7a1580a5d29dac2e","first_computed_at":"2026-05-18T00:41:06.668177Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:06.668177Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZvOILmyErGf1Ab4mXJWu3OQQw+eIEsxjvEFTn1OX5aXArC5UD0BuVVyEwB9BlSZ7PmRDLZctkZLWeWWc4buCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:06.668846Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cafcdb571a07429f06d08af8d7f8e34d87d7464ae7b2c42ceaf344e0e573dfab","sha256:7c37cb9f9b3c6a545c3606b0747afcf37a9cf34f88d62f7573431693c47b73b6"],"state_sha256":"35daf166c9dfd2ce713aa25579e707176ec3a336e4545db9cfbbcdac930cdf5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mErOMDpNAt9Ymbq7zrn98dRvwwtyr+i5VZA88b+sqDMWFCbI7MkgBRhLM4RA+fk3TF3d6CaHhsu/Ap7lrtOzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:21:40.767175Z","bundle_sha256":"0ad77f43116462f301ea112eec3d5e71a3276ea1c5af352355388d54d288fb7f"}}