{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:SVBRPOW6HXFCBPPLYBTI7VFTYW","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":"b9a728543fa77e779284a2f9a09602ec44c863ceeac816e978d7c7c0c19ab7c4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-09T08:22:38Z","title_canon_sha256":"6a2583d5169646c9a1ef1ea7e47ce212e705472f90261d8a38318180f7fab5da"},"schema_version":"1.0","source":{"id":"1905.03483","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.03483","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"arxiv_version","alias_value":"1905.03483v1","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03483","created_at":"2026-05-17T23:46:39Z"},{"alias_kind":"pith_short_12","alias_value":"SVBRPOW6HXFC","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"SVBRPOW6HXFCBPPL","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"SVBRPOW6","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:daa12bbb9b9aa7da4720327d1f9ba43e24191e6c18e4005c89ddc6c0eee2b82d","target":"graph","created_at":"2026-05-17T23:46:39Z","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":"Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will focus on their algebraic-geometric aspects, explaining how the representation theory of higher genus braid groups can be used to produce interesting examples of projective surfaces defined over the field of complex numbers.","authors_text":"Francesco Polizzi","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-09T08:22:38Z","title":"Representations of braid groups and construction of projective surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03483","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":"sha256:7c9a62528537994a6423ef7a602833489d9ada824e5f9faba291acb4d674bef8","target":"record","created_at":"2026-05-17T23:46:39Z","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":"b9a728543fa77e779284a2f9a09602ec44c863ceeac816e978d7c7c0c19ab7c4","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-05-09T08:22:38Z","title_canon_sha256":"6a2583d5169646c9a1ef1ea7e47ce212e705472f90261d8a38318180f7fab5da"},"schema_version":"1.0","source":{"id":"1905.03483","kind":"arxiv","version":1}},"canonical_sha256":"954317bade3dca20bdebc0668fd4b3c5b4c51ac8308559079deb007fb2976979","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"954317bade3dca20bdebc0668fd4b3c5b4c51ac8308559079deb007fb2976979","first_computed_at":"2026-05-17T23:46:39.742407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:39.742407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G8XxCXExzUbFNUe2c0B7ld3ar28L37N1fUt6kOvonv10g6QtsSEI0dRwpn7BPRhM4Tllnj29nNMJaXjyZaVuDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:39.743125Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.03483","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c9a62528537994a6423ef7a602833489d9ada824e5f9faba291acb4d674bef8","sha256:daa12bbb9b9aa7da4720327d1f9ba43e24191e6c18e4005c89ddc6c0eee2b82d"],"state_sha256":"76e1185d3f9708d84bec9cd986e190526b98c9b7859ee4311a4ef31bf6ba504e"}