{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NAP7GEA4R6ZLDTDSGCK2X5BKCH","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":"b0dc7cf994e59a0687856510ce95a599866b6ef651e7a824d9cb961266af854a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:52:12Z","title_canon_sha256":"69c21f02578cfccad6663585c8a17f32cd3fdd9b2112fd7b7ced29cb4d6fab83"},"schema_version":"1.0","source":{"id":"2606.01035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01035","created_at":"2026-06-02T01:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01035v1","created_at":"2026-06-02T01:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01035","created_at":"2026-06-02T01:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"NAP7GEA4R6ZL","created_at":"2026-06-02T01:04:19Z"},{"alias_kind":"pith_short_16","alias_value":"NAP7GEA4R6ZLDTDS","created_at":"2026-06-02T01:04:19Z"},{"alias_kind":"pith_short_8","alias_value":"NAP7GEA4","created_at":"2026-06-02T01:04:19Z"}],"graph_snapshots":[{"event_id":"sha256:ef794288503b30c4edd70b0dfe7b3abde4d209fa0bdf656cded660cc712edd32","target":"graph","created_at":"2026-06-02T01:04:19Z","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/2606.01035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We utilize multi-virtual knot theory where there are a multiplicity of virtual crossings to study strict virtual linkoids. In strict virtual linkoid theory, local moves define all virtual moves and Reidemeister moves. In the strict equivalence, no moves, classical or virtual, can transfer an arc across a linkoid endpoint. By taking closures of strict virtual linkoids that are multi-virtual knots and links, we obtain new invariants for strict virtual linkoids. Generalized bracket polynomial invariants and generalized loop bracket polynomial invariants (for planar strict virtual linkoids) are st","authors_text":"Louis H Kauffman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:52:12Z","title":"Strict Equivalence of Multi-Virtual Linkoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01035","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":"sha256:92a87256dc4bf9f1ec6ab86d4ff01befd88b51bf50c78b960a984c9fdc2f9a75","target":"record","created_at":"2026-06-02T01:04:19Z","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":"b0dc7cf994e59a0687856510ce95a599866b6ef651e7a824d9cb961266af854a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:52:12Z","title_canon_sha256":"69c21f02578cfccad6663585c8a17f32cd3fdd9b2112fd7b7ced29cb4d6fab83"},"schema_version":"1.0","source":{"id":"2606.01035","kind":"arxiv","version":1}},"canonical_sha256":"681ff3101c8fb2b1cc723095abf42a11d90aafad28ab224b8eb9823b584c269a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"681ff3101c8fb2b1cc723095abf42a11d90aafad28ab224b8eb9823b584c269a","first_computed_at":"2026-06-02T01:04:19.133753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:19.133753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y+hK+ctxKOyQ+2BagTaArS4C1ytnUa8URfVD/Fi9ST3TMPa65S/CvKP/TqVNEBgZw5GPpLPkKl5JfnaclTh/CQ==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:19.134255Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92a87256dc4bf9f1ec6ab86d4ff01befd88b51bf50c78b960a984c9fdc2f9a75","sha256:ef794288503b30c4edd70b0dfe7b3abde4d209fa0bdf656cded660cc712edd32"],"state_sha256":"1d71e5c62e53a53fba14ff3402319132ebeb0ac164b3c31aa4bc4a21bc7f6374"}