{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QOPWCLDHD4NNEVOBY47X3OV4G6","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":"4bb27c0337005180e7ea56896f3993e20cbf2f1e289dc5def845fcdea18ed753","cross_cats_sorted":["math.AG","math.HO"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-18T14:12:46Z","title_canon_sha256":"808cd997986162cf3bef4aaeb64eca6867d83412f1b314416086d06302002181"},"schema_version":"1.0","source":{"id":"1612.06373","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06373","created_at":"2026-05-18T00:36:52Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06373v4","created_at":"2026-05-18T00:36:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06373","created_at":"2026-05-18T00:36:52Z"},{"alias_kind":"pith_short_12","alias_value":"QOPWCLDHD4NN","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOPWCLDHD4NNEVOB","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOPWCLDH","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:8bd3bccf0a65be237df8eddb19bf4264dc83a27b12cbe6f35564750f099397c8","target":"graph","created_at":"2026-05-18T00:36:52Z","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":"This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus, Newton and Gauss, but also to many contemporary mathematicians. We play with a bit of algebra, topology, geometry, complex analysis and computer science. Hopefully, some motivated undergraduates and some more advanced mathematicians will enjoy some of these panoramas.","authors_text":"Etienne Ghys","cross_cats":["math.AG","math.HO"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-18T14:12:46Z","title":"A Singular Mathematical Promenade"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06373","kind":"arxiv","version":4},"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":"sha256:676a61f40a1e7e6412f0068af78b44d9304023648e357af5965e39617dbf6629","target":"record","created_at":"2026-05-18T00:36:52Z","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":"4bb27c0337005180e7ea56896f3993e20cbf2f1e289dc5def845fcdea18ed753","cross_cats_sorted":["math.AG","math.HO"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-18T14:12:46Z","title_canon_sha256":"808cd997986162cf3bef4aaeb64eca6867d83412f1b314416086d06302002181"},"schema_version":"1.0","source":{"id":"1612.06373","kind":"arxiv","version":4}},"canonical_sha256":"839f612c671f1ad255c1c73f7dbabc37918e3a655e873e2f83e954e0e3e43aa5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"839f612c671f1ad255c1c73f7dbabc37918e3a655e873e2f83e954e0e3e43aa5","first_computed_at":"2026-05-18T00:36:52.207161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:52.207161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"189IAiKBGVaXSZXbI0GkRxtC2aTIj0pyTGLArXaI9GS1z+MGn6ZDVYjF4NUT9s5mxOcF9SIL0+H56lSWJTXmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:52.207732Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06373","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:676a61f40a1e7e6412f0068af78b44d9304023648e357af5965e39617dbf6629","sha256:8bd3bccf0a65be237df8eddb19bf4264dc83a27b12cbe6f35564750f099397c8"],"state_sha256":"5feafa329fd340f34595f242a76b15d362d455c00dc191eaef2f86b9c0382ff8"}