{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UR7KHESE7V25MLJI2BUDTUP3AM","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":"811c6fc370d8acb92c760455475dac50800c0051bc7459c6b5956b33412182e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-07-21T09:00:14Z","title_canon_sha256":"5673737abecd6aaa5c7f85c66106278cd720411f9d1e052ecbbd5064de1aed8f"},"schema_version":"1.0","source":{"id":"1907.10359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.10359","created_at":"2026-05-17T23:39:38Z"},{"alias_kind":"arxiv_version","alias_value":"1907.10359v1","created_at":"2026-05-17T23:39:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.10359","created_at":"2026-05-17T23:39:38Z"},{"alias_kind":"pith_short_12","alias_value":"UR7KHESE7V25","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UR7KHESE7V25MLJI","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UR7KHESE","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2d3f03c7ca64840a45fbe781b4cea9ce79a40cdcf543f780b1147fa6fa92fc78","target":"graph","created_at":"2026-05-17T23:39:38Z","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":"We define an equivalence relation on graphs with signed edges, such that the associated adjacency matrices of two equivalent graphs are congruent over $\\mathbb{Z}$. We show that signed graphs whose eigenvalues are larger than $-2$ are equivalent to one of the simply laced Dynkin diagrams: $A_{n}$, $D_{n}$, $E_{6}$, $E_{7}$ and $E_{8}$. Checkerboard graph links are a class of fibred strongly quasipositive links which include positive braid links. We use the previous result to prove that a checkerboard graph link with maximal signature is isotopic to one of the links realized by the simply laced","authors_text":"Lucas Fernandez Vilanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-07-21T09:00:14Z","title":"Checkerboard graph links and simply laced Dynkin diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10359","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":"sha256:7462363938b2bbe6156ebe21b00d8017dd639744f7ed0753f09d622b5e8d252b","target":"record","created_at":"2026-05-17T23:39:38Z","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":"811c6fc370d8acb92c760455475dac50800c0051bc7459c6b5956b33412182e2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2019-07-21T09:00:14Z","title_canon_sha256":"5673737abecd6aaa5c7f85c66106278cd720411f9d1e052ecbbd5064de1aed8f"},"schema_version":"1.0","source":{"id":"1907.10359","kind":"arxiv","version":1}},"canonical_sha256":"a47ea39244fd75d62d28d06839d1fb033b682da746d799df03865d126fe7e4d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a47ea39244fd75d62d28d06839d1fb033b682da746d799df03865d126fe7e4d1","first_computed_at":"2026-05-17T23:39:38.184721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:38.184721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OIcGyIFNmpCaD1AuXz1R1G6S4cG9X8hF0fK5ByKzgd2e0+lQmtTL0A+esMfmKjH1SEpBusTsmfSQeBoBaw0TCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:38.185281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.10359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7462363938b2bbe6156ebe21b00d8017dd639744f7ed0753f09d622b5e8d252b","sha256:2d3f03c7ca64840a45fbe781b4cea9ce79a40cdcf543f780b1147fa6fa92fc78"],"state_sha256":"84daed03aa00d6ece83f7799af10d4fb249ae23c6b5eac3d6214037b3726c6ef"}