{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:V6DGSM3PTUGSHJOVS25GP57XTW","short_pith_number":"pith:V6DGSM3P","canonical_record":{"source":{"id":"2205.13991","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-05-27T14:07:26Z","cross_cats_sorted":["math.GR","math.GT","math.NT"],"title_canon_sha256":"759f81ce27e1c0f18fb67c8fe121c5ceb57b992d2ae1e95aecf96bb34c7eff49","abstract_canon_sha256":"bfa214a32376e6c16a1905add64a9ef6e7cc8df3b184c907a4fd473d388327ec"},"schema_version":"1.0"},"canonical_sha256":"af8669336f9d0d23a5d596ba67f7f79d86c0dbab9c1c1bc13945e9e99084bdb9","source":{"kind":"arxiv","id":"2205.13991","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.13991","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"2205.13991v3","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.13991","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"V6DGSM3PTUGS","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_16","alias_value":"V6DGSM3PTUGSHJOV","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_8","alias_value":"V6DGSM3P","created_at":"2026-07-05T07:49:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:V6DGSM3PTUGSHJOVS25GP57XTW","target":"record","payload":{"canonical_record":{"source":{"id":"2205.13991","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-05-27T14:07:26Z","cross_cats_sorted":["math.GR","math.GT","math.NT"],"title_canon_sha256":"759f81ce27e1c0f18fb67c8fe121c5ceb57b992d2ae1e95aecf96bb34c7eff49","abstract_canon_sha256":"bfa214a32376e6c16a1905add64a9ef6e7cc8df3b184c907a4fd473d388327ec"},"schema_version":"1.0"},"canonical_sha256":"af8669336f9d0d23a5d596ba67f7f79d86c0dbab9c1c1bc13945e9e99084bdb9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:49:28.304848Z","signature_b64":"W9uYcFZhfDXgJbww7beeH6a0CKdGqj0u3MV4v1VYD4MicYQemJgr/2jlNyobISyJrLWbJ8L7bD/MZaisNY8MBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af8669336f9d0d23a5d596ba67f7f79d86c0dbab9c1c1bc13945e9e99084bdb9","last_reissued_at":"2026-07-05T07:49:28.304469Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:49:28.304469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.13991","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ulDHbUEiW0r5s0pfIDU3cvI/y1Q7uWS0+U573vTlpNAixLhFoYwbaT2U1AqQHICT6N36p7QL5YaJanSuD2gZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:12:32.467257Z"},"content_sha256":"55494e8ba054c3228ae5fa87d1ed77672c94987366ba7f476827ae06e3f9de17","schema_version":"1.0","event_id":"sha256:55494e8ba054c3228ae5fa87d1ed77672c94987366ba7f476827ae06e3f9de17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:V6DGSM3PTUGSHJOVS25GP57XTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic fundamental groups of fake projective planes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.GT","math.NT"],"primary_cat":"math.AG","authors_text":"Matthew Stover","submitted_at":"2022-05-27T14:07:26Z","abstract_excerpt":"Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebraic fundamental groups: there are only forty-six isomorphism classes. We show that there are four pairs of complex conjugate pairs of fake projective planes that are $\\mathrm{Aut}(\\mathbb{C})$-equivalent and hence have mutually isomorphic algebraic fundamental groups. All other pairs of algebraic fundamental groups are shown to be distinct through explicit finite \\'etale covers. As a by-product, this provides the firs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.13991","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.13991/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:49:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QEsCu2S4YBtP1vB7N34ZN6sEx+WN0kr8jSlj8Q1J4PkDUS/1HbqswROrsFxFWru+Ht5kabjimSde8nEGAar1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T03:12:32.468329Z"},"content_sha256":"00a586efe87986fcd30171e6a31b440b83602d57048820155d0daab301ca6de6","schema_version":"1.0","event_id":"sha256:00a586efe87986fcd30171e6a31b440b83602d57048820155d0daab301ca6de6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6DGSM3PTUGSHJOVS25GP57XTW/bundle.json","state_url":"https://pith.science/pith/V6DGSM3PTUGSHJOVS25GP57XTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6DGSM3PTUGSHJOVS25GP57XTW/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":"2026-08-12T03:12:32Z","links":{"resolver":"https://pith.science/pith/V6DGSM3PTUGSHJOVS25GP57XTW","bundle":"https://pith.science/pith/V6DGSM3PTUGSHJOVS25GP57XTW/bundle.json","state":"https://pith.science/pith/V6DGSM3PTUGSHJOVS25GP57XTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6DGSM3PTUGSHJOVS25GP57XTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:V6DGSM3PTUGSHJOVS25GP57XTW","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":"bfa214a32376e6c16a1905add64a9ef6e7cc8df3b184c907a4fd473d388327ec","cross_cats_sorted":["math.GR","math.GT","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-05-27T14:07:26Z","title_canon_sha256":"759f81ce27e1c0f18fb67c8fe121c5ceb57b992d2ae1e95aecf96bb34c7eff49"},"schema_version":"1.0","source":{"id":"2205.13991","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.13991","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"arxiv_version","alias_value":"2205.13991v3","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.13991","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_12","alias_value":"V6DGSM3PTUGS","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_16","alias_value":"V6DGSM3PTUGSHJOV","created_at":"2026-07-05T07:49:28Z"},{"alias_kind":"pith_short_8","alias_value":"V6DGSM3P","created_at":"2026-07-05T07:49:28Z"}],"graph_snapshots":[{"event_id":"sha256:00a586efe87986fcd30171e6a31b440b83602d57048820155d0daab301ca6de6","target":"graph","created_at":"2026-07-05T07:49:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2205.13991/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebraic fundamental groups: there are only forty-six isomorphism classes. We show that there are four pairs of complex conjugate pairs of fake projective planes that are $\\mathrm{Aut}(\\mathbb{C})$-equivalent and hence have mutually isomorphic algebraic fundamental groups. All other pairs of algebraic fundamental groups are shown to be distinct through explicit finite \\'etale covers. As a by-product, this provides the firs","authors_text":"Matthew Stover","cross_cats":["math.GR","math.GT","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-05-27T14:07:26Z","title":"Algebraic fundamental groups of fake projective planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.13991","kind":"arxiv","version":3},"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":"sha256:55494e8ba054c3228ae5fa87d1ed77672c94987366ba7f476827ae06e3f9de17","target":"record","created_at":"2026-07-05T07:49:28Z","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":"bfa214a32376e6c16a1905add64a9ef6e7cc8df3b184c907a4fd473d388327ec","cross_cats_sorted":["math.GR","math.GT","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-05-27T14:07:26Z","title_canon_sha256":"759f81ce27e1c0f18fb67c8fe121c5ceb57b992d2ae1e95aecf96bb34c7eff49"},"schema_version":"1.0","source":{"id":"2205.13991","kind":"arxiv","version":3}},"canonical_sha256":"af8669336f9d0d23a5d596ba67f7f79d86c0dbab9c1c1bc13945e9e99084bdb9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af8669336f9d0d23a5d596ba67f7f79d86c0dbab9c1c1bc13945e9e99084bdb9","first_computed_at":"2026-07-05T07:49:28.304469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:49:28.304469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W9uYcFZhfDXgJbww7beeH6a0CKdGqj0u3MV4v1VYD4MicYQemJgr/2jlNyobISyJrLWbJ8L7bD/MZaisNY8MBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:49:28.304848Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.13991","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55494e8ba054c3228ae5fa87d1ed77672c94987366ba7f476827ae06e3f9de17","sha256:00a586efe87986fcd30171e6a31b440b83602d57048820155d0daab301ca6de6"],"state_sha256":"599ca9312088a3dee458092d7dc68459cc027a6856804385fe6dc51dbcb6a90f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIB/SvfhV5Vvs6dtcBAUgVvt3gQYskxYoQy+0iC9mXbuzUJigD/dITx0SCG71kQX7aB4/67eHYzHBzEiu3d+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T03:12:32.475160Z","bundle_sha256":"c9147db03fa4690064c7e0754e6116fe124e5d0eb1a8f52c872b54be739e41bf"}}