{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FAZ7Q3VZGXWBWEVLBSFGTUXOB2","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":"743445e7fa8e0cff2e293243486153d97e788ee2583d97a00b7b5517c6291326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-28T23:05:53Z","title_canon_sha256":"8aa3986c5668b028af3c9aaae3664957f73605c76fdcbab2d8fe7a6afe4bd164"},"schema_version":"1.0","source":{"id":"1201.6000","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6000","created_at":"2026-05-18T04:03:34Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6000v1","created_at":"2026-05-18T04:03:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6000","created_at":"2026-05-18T04:03:34Z"},{"alias_kind":"pith_short_12","alias_value":"FAZ7Q3VZGXWB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"FAZ7Q3VZGXWBWEVL","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"FAZ7Q3VZ","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:e245a3f0b0595faabc6d35fb0de972e65b1388a6563ebb52d2b77d87a4563475","target":"graph","created_at":"2026-05-18T04:03:34Z","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":"Every exotic pair in 4-dimension is obtained each other by twisting a {\\it cork} or {\\it plug} which are codimension 0 submanifolds embedded in the 4-manifolds. The twist was an involution on the boundary of the submanifold. We define cork (or plug) with order $p\\in {\\Bbb N}\\cup \\{\\infty\\}$ and show there exists a plug with infinite order. Furthermore we show twisting $(P,\\varphi^2)$ gives to enlargements of $P$ compact exotic manifolds with boundary.","authors_text":"Motoo Tange","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-28T23:05:53Z","title":"A plug with infinite order and some exotic 4-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6000","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":"sha256:47a1506bedfe01a2e1a9c81ddf72062be956bc073fb487fa82710b6687e3d3fa","target":"record","created_at":"2026-05-18T04:03:34Z","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":"743445e7fa8e0cff2e293243486153d97e788ee2583d97a00b7b5517c6291326","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-01-28T23:05:53Z","title_canon_sha256":"8aa3986c5668b028af3c9aaae3664957f73605c76fdcbab2d8fe7a6afe4bd164"},"schema_version":"1.0","source":{"id":"1201.6000","kind":"arxiv","version":1}},"canonical_sha256":"2833f86eb935ec1b12ab0c8a69d2ee0e97bbc795fd8321dec0a46d6cd045dc97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2833f86eb935ec1b12ab0c8a69d2ee0e97bbc795fd8321dec0a46d6cd045dc97","first_computed_at":"2026-05-18T04:03:34.021772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:34.021772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P7KBPITxBdkCGT/zOXpzRYBKBSzlUn1VzVDCoNDG401JnYPKoQZq8wzUFt6VUgnxhVMxskYgCsNhlacX2hd6Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:34.022365Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6000","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a1506bedfe01a2e1a9c81ddf72062be956bc073fb487fa82710b6687e3d3fa","sha256:e245a3f0b0595faabc6d35fb0de972e65b1388a6563ebb52d2b77d87a4563475"],"state_sha256":"b2f6f769ed5bd3f1cb961e709b8614430a1efc6208cb253f99d25117e894dba2"}