{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UZJQRJTARCIO3UDPKIL3SZVLXX","short_pith_number":"pith:UZJQRJTA","canonical_record":{"source":{"id":"1408.2254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-10T17:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"d8f8805a071ea6e3e15e44f22cf96fdfc3c403f16e3f25136b265bedc475a8ba","abstract_canon_sha256":"e6f426495fc74166fae12a7aa71a95739c06635877c40c8c4b6efa37ea4f2a24"},"schema_version":"1.0"},"canonical_sha256":"a65308a6608890edd06f5217b966abbdc1158d1b302c3633372c3176d4f895e0","source":{"kind":"arxiv","id":"1408.2254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2254","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2254v1","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2254","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"UZJQRJTARCIO","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UZJQRJTARCIO3UDP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UZJQRJTA","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UZJQRJTARCIO3UDPKIL3SZVLXX","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-10T17:01:22Z","cross_cats_sorted":[],"title_canon_sha256":"d8f8805a071ea6e3e15e44f22cf96fdfc3c403f16e3f25136b265bedc475a8ba","abstract_canon_sha256":"e6f426495fc74166fae12a7aa71a95739c06635877c40c8c4b6efa37ea4f2a24"},"schema_version":"1.0"},"canonical_sha256":"a65308a6608890edd06f5217b966abbdc1158d1b302c3633372c3176d4f895e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:29.884143Z","signature_b64":"7k/BL/06b5VQVkoAV8CgwXrx7LKYUDT5TkqIWYgltb9M4RilVVVgjdK/xUO3eNYTAehY+fy3MHXhSuTglOONDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a65308a6608890edd06f5217b966abbdc1158d1b302c3633372c3176d4f895e0","last_reissued_at":"2026-05-18T02:45:29.883565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:29.883565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2254","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":"2026-05-18T02:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTOyuPZgkB9ETKFFBDN48xrvYZOS70lIOPBJyXUZzDZ45bOnIQmVfCYFYDxCFSmkaJ/FQyFGm65IvcDObWJ5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:36:50.446002Z"},"content_sha256":"b65498391b422f7a5c11ea9a016d7b34a5303adb4c68ff3537c5bd23b35d1981","schema_version":"1.0","event_id":"sha256:b65498391b422f7a5c11ea9a016d7b34a5303adb4c68ff3537c5bd23b35d1981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UZJQRJTARCIO3UDPKIL3SZVLXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Notes on automorphisms of surfaces of general type with $p_g=0$ and $K^2=7$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yifan Chen","submitted_at":"2014-08-10T17:01:22Z","abstract_excerpt":"Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue surface with $K^2=7$ is isomorphic to $\\mathbb{Z}_2^2$ or $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$. We construct a $2$-dimensional family of Inoue surfaces with automorphism groups isomorphic to $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2254","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":"2026-05-18T02:45:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yOrpoPrwUhGf5rZcLcTDCkcDvUAKGyNX5cwUGte2n/vFmBmIZ5uATppntxFS/uGcb9dy0O0sNqUqqLMFZ/U2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T06:36:50.446669Z"},"content_sha256":"8a170910174b9cacb711cecd237625288c20120661dac41610f19f3a8e21264b","schema_version":"1.0","event_id":"sha256:8a170910174b9cacb711cecd237625288c20120661dac41610f19f3a8e21264b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/bundle.json","state_url":"https://pith.science/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/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":"2026-05-25T06:36:50Z","links":{"resolver":"https://pith.science/pith/UZJQRJTARCIO3UDPKIL3SZVLXX","bundle":"https://pith.science/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/bundle.json","state":"https://pith.science/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZJQRJTARCIO3UDPKIL3SZVLXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UZJQRJTARCIO3UDPKIL3SZVLXX","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":"e6f426495fc74166fae12a7aa71a95739c06635877c40c8c4b6efa37ea4f2a24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-10T17:01:22Z","title_canon_sha256":"d8f8805a071ea6e3e15e44f22cf96fdfc3c403f16e3f25136b265bedc475a8ba"},"schema_version":"1.0","source":{"id":"1408.2254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2254","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2254v1","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2254","created_at":"2026-05-18T02:45:29Z"},{"alias_kind":"pith_short_12","alias_value":"UZJQRJTARCIO","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UZJQRJTARCIO3UDP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UZJQRJTA","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:8a170910174b9cacb711cecd237625288c20120661dac41610f19f3a8e21264b","target":"graph","created_at":"2026-05-18T02:45:29Z","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 $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue surface with $K^2=7$ is isomorphic to $\\mathbb{Z}_2^2$ or $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$. We construct a $2$-dimensional family of Inoue surfaces with automorphism groups isomorphic to $\\mathbb{Z}_2 \\times \\mathbb{Z}_4$.","authors_text":"Yifan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-10T17:01:22Z","title":"Notes on automorphisms of surfaces of general type with $p_g=0$ and $K^2=7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2254","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:b65498391b422f7a5c11ea9a016d7b34a5303adb4c68ff3537c5bd23b35d1981","target":"record","created_at":"2026-05-18T02:45:29Z","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":"e6f426495fc74166fae12a7aa71a95739c06635877c40c8c4b6efa37ea4f2a24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-10T17:01:22Z","title_canon_sha256":"d8f8805a071ea6e3e15e44f22cf96fdfc3c403f16e3f25136b265bedc475a8ba"},"schema_version":"1.0","source":{"id":"1408.2254","kind":"arxiv","version":1}},"canonical_sha256":"a65308a6608890edd06f5217b966abbdc1158d1b302c3633372c3176d4f895e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a65308a6608890edd06f5217b966abbdc1158d1b302c3633372c3176d4f895e0","first_computed_at":"2026-05-18T02:45:29.883565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:29.883565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7k/BL/06b5VQVkoAV8CgwXrx7LKYUDT5TkqIWYgltb9M4RilVVVgjdK/xUO3eNYTAehY+fy3MHXhSuTglOONDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:29.884143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b65498391b422f7a5c11ea9a016d7b34a5303adb4c68ff3537c5bd23b35d1981","sha256:8a170910174b9cacb711cecd237625288c20120661dac41610f19f3a8e21264b"],"state_sha256":"7caf3130b7a632c164f20cd2afe4d82d69f2292d9ccd142d13ac7db2c6837918"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRoulg5DRO3zSf/KlpS+WQvVCmD/XTkhysyaRNAOqvNNZQ6dtG2yuBCCEjrdVn00nUPB0RyV3DrOyze2ezhcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T06:36:50.450434Z","bundle_sha256":"5c6f26628dc47d5a030512217f374248d8bab979ba47274280810151e34b1e2c"}}