{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KIVBQCMGHOUV3RGBID6JKFHW5X","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":"8e3f2251f989618bfef5fec1c5668756ad31b022414188714dcbf35cc0d53d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-13T16:24:41Z","title_canon_sha256":"680b7381ed83eb11934462a62a7ee58474aa0396a042db941f8fe12d02287237"},"schema_version":"1.0","source":{"id":"1210.3717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3717","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3717v1","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3717","created_at":"2026-05-18T03:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"KIVBQCMGHOUV","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KIVBQCMGHOUV3RGB","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KIVBQCMG","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:7c2225ed4cf95188b68f6ca35c2d9f83a32a2bfa7992810e67e580181ec02ac6","target":"graph","created_at":"2026-05-18T03:43:17Z","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":"For a $C^{1}$ degree two latitude preserving endomorphism $f$ of the 2-sphere, we show that $f$ has $2^{n}$ periodic points.","authors_text":"Charles Pugh, Michael Shub","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-13T16:24:41Z","title":"Periodic Points on the 2-sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3717","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":"sha256:736ad9aa219bee43e12acc1baee17890aa035bfef2a4315fba8cce0f8c56334e","target":"record","created_at":"2026-05-18T03:43:17Z","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":"8e3f2251f989618bfef5fec1c5668756ad31b022414188714dcbf35cc0d53d12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-13T16:24:41Z","title_canon_sha256":"680b7381ed83eb11934462a62a7ee58474aa0396a042db941f8fe12d02287237"},"schema_version":"1.0","source":{"id":"1210.3717","kind":"arxiv","version":1}},"canonical_sha256":"522a1809863ba95dc4c140fc9514f6edcad5c830796d1ad08dfd55489f0546a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"522a1809863ba95dc4c140fc9514f6edcad5c830796d1ad08dfd55489f0546a0","first_computed_at":"2026-05-18T03:43:17.288920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:17.288920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oIRjHWjpCTExqJzKjPc2nr0L8CkROh2k8zqcnTdorA5gjOamovzwA9E4nx0yGdN5ORSG8QcDS141LG9CfBlAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:17.290422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:736ad9aa219bee43e12acc1baee17890aa035bfef2a4315fba8cce0f8c56334e","sha256:7c2225ed4cf95188b68f6ca35c2d9f83a32a2bfa7992810e67e580181ec02ac6"],"state_sha256":"33c9ee49143aa2909f6ca77bbb5ca4cadcf5dadd24c7070856fde62298d6bb7e"}