{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:GNRLMADA5FJXW6SNSB25KJNKAK","short_pith_number":"pith:GNRLMADA","canonical_record":{"source":{"id":"1904.09541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-21T04:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"2b00ba37c31f1ab7bd7caad70bd3d899882a97152aeaf6b00d7a7a984cb16ed6","abstract_canon_sha256":"a3dddb8bbcf597e3a8d82f83350f0ff4f2fc6936dfd8dd495907d9010264b4b0"},"schema_version":"1.0"},"canonical_sha256":"3362b60060e9537b7a4d9075d525aa02bfb0a5046b9f50f8aca69ed0707b1950","source":{"kind":"arxiv","id":"1904.09541","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09541","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09541v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09541","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"GNRLMADA5FJX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNRLMADA5FJXW6SN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNRLMADA","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:GNRLMADA5FJXW6SNSB25KJNKAK","target":"record","payload":{"canonical_record":{"source":{"id":"1904.09541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-21T04:36:03Z","cross_cats_sorted":[],"title_canon_sha256":"2b00ba37c31f1ab7bd7caad70bd3d899882a97152aeaf6b00d7a7a984cb16ed6","abstract_canon_sha256":"a3dddb8bbcf597e3a8d82f83350f0ff4f2fc6936dfd8dd495907d9010264b4b0"},"schema_version":"1.0"},"canonical_sha256":"3362b60060e9537b7a4d9075d525aa02bfb0a5046b9f50f8aca69ed0707b1950","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:03.946055Z","signature_b64":"FZHE4hXHse3GVzzdhC1/cHIHH+U7/at9g4Osi/z/vrxLriah+j0opqrqb+4WSQ+0mJb/DNtbwe0j/CX+YQybBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3362b60060e9537b7a4d9075d525aa02bfb0a5046b9f50f8aca69ed0707b1950","last_reissued_at":"2026-05-17T23:48:03.945618Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:03.945618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.09541","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":"2026-05-17T23:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YP8l1E+Pc1olQl3TS4apK+nAppC5Xn7UAK1j8HqsNdUYF+TtnI7mxynNlJh2jfLTYLexpH5Ki07k92D040w1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:41:41.169500Z"},"content_sha256":"ffa2c7cd95f982c15e30d93b05ef63dfb8de248ce08f923505353a17d1884049","schema_version":"1.0","event_id":"sha256:ffa2c7cd95f982c15e30d93b05ef63dfb8de248ce08f923505353a17d1884049"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:GNRLMADA5FJXW6SNSB25KJNKAK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite nonabelian corks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hiroto Masuda","submitted_at":"2019-04-21T04:36:03Z","abstract_excerpt":"We construct $G$-corks for any extension $G$ of $\\mathbb Z^m$ by any finite subgroup of $\\mathrm{SO}(4)$ and weakly equivariant $G$-corks for any extension $G$ of $\\mathbb Z^m$ by any finite solvable group. In particular, this is the first example of $G$-corks for an infinite nonabelian group $G$ and answers a question by Tange. The construction is a combination of previous results by Auckly-Kim-Melvin-Ruberman, Gompf, and Tange. Using Gompf's results about exotic $\\mathbb R^4$'s, we give an application to construct exotic $\\mathbb R^4$'s whose diffeotopy group contains all poly-cyclic groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09541","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":"2026-05-17T23:48:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErJybMREjJLaOsHeHTXBSfvA5zyRqU+kBI2HIXABom4TWhEzinmzKs/XT3iG86EQqiSRA+6QIPzDx89h9TXHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:41:41.170167Z"},"content_sha256":"39f47144d6d7a3a9dde23bf952be8beeb377c834c4cba509921fa3fa6cd3f10b","schema_version":"1.0","event_id":"sha256:39f47144d6d7a3a9dde23bf952be8beeb377c834c4cba509921fa3fa6cd3f10b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNRLMADA5FJXW6SNSB25KJNKAK/bundle.json","state_url":"https://pith.science/pith/GNRLMADA5FJXW6SNSB25KJNKAK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNRLMADA5FJXW6SNSB25KJNKAK/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":"2026-05-29T17:41:41Z","links":{"resolver":"https://pith.science/pith/GNRLMADA5FJXW6SNSB25KJNKAK","bundle":"https://pith.science/pith/GNRLMADA5FJXW6SNSB25KJNKAK/bundle.json","state":"https://pith.science/pith/GNRLMADA5FJXW6SNSB25KJNKAK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNRLMADA5FJXW6SNSB25KJNKAK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:GNRLMADA5FJXW6SNSB25KJNKAK","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":"a3dddb8bbcf597e3a8d82f83350f0ff4f2fc6936dfd8dd495907d9010264b4b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-21T04:36:03Z","title_canon_sha256":"2b00ba37c31f1ab7bd7caad70bd3d899882a97152aeaf6b00d7a7a984cb16ed6"},"schema_version":"1.0","source":{"id":"1904.09541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.09541","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"arxiv_version","alias_value":"1904.09541v1","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.09541","created_at":"2026-05-17T23:48:03Z"},{"alias_kind":"pith_short_12","alias_value":"GNRLMADA5FJX","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNRLMADA5FJXW6SN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNRLMADA","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:39f47144d6d7a3a9dde23bf952be8beeb377c834c4cba509921fa3fa6cd3f10b","target":"graph","created_at":"2026-05-17T23:48:03Z","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 construct $G$-corks for any extension $G$ of $\\mathbb Z^m$ by any finite subgroup of $\\mathrm{SO}(4)$ and weakly equivariant $G$-corks for any extension $G$ of $\\mathbb Z^m$ by any finite solvable group. In particular, this is the first example of $G$-corks for an infinite nonabelian group $G$ and answers a question by Tange. The construction is a combination of previous results by Auckly-Kim-Melvin-Ruberman, Gompf, and Tange. Using Gompf's results about exotic $\\mathbb R^4$'s, we give an application to construct exotic $\\mathbb R^4$'s whose diffeotopy group contains all poly-cyclic groups.","authors_text":"Hiroto Masuda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-21T04:36:03Z","title":"Infinite nonabelian corks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.09541","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:ffa2c7cd95f982c15e30d93b05ef63dfb8de248ce08f923505353a17d1884049","target":"record","created_at":"2026-05-17T23:48:03Z","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":"a3dddb8bbcf597e3a8d82f83350f0ff4f2fc6936dfd8dd495907d9010264b4b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-04-21T04:36:03Z","title_canon_sha256":"2b00ba37c31f1ab7bd7caad70bd3d899882a97152aeaf6b00d7a7a984cb16ed6"},"schema_version":"1.0","source":{"id":"1904.09541","kind":"arxiv","version":1}},"canonical_sha256":"3362b60060e9537b7a4d9075d525aa02bfb0a5046b9f50f8aca69ed0707b1950","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3362b60060e9537b7a4d9075d525aa02bfb0a5046b9f50f8aca69ed0707b1950","first_computed_at":"2026-05-17T23:48:03.945618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:03.945618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FZHE4hXHse3GVzzdhC1/cHIHH+U7/at9g4Osi/z/vrxLriah+j0opqrqb+4WSQ+0mJb/DNtbwe0j/CX+YQybBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:03.946055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.09541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ffa2c7cd95f982c15e30d93b05ef63dfb8de248ce08f923505353a17d1884049","sha256:39f47144d6d7a3a9dde23bf952be8beeb377c834c4cba509921fa3fa6cd3f10b"],"state_sha256":"73ad3d34eee7b5d9fc25026dd4a1179b22fae3bd418916f9e46b1196882ba8e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fV5GntBtN0fyaWfKQobphr6k4Uqr0vefpaLYUuOTi/rBQE4BOFRMtv33YhZKlw6gTDxVR8B37I22qSfTqNT2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:41:41.173992Z","bundle_sha256":"691c3a973903b8fc4136e07dae2fc5277586a8e09a5f9baf83d1bfafef8d6be6"}}