{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NAP7GEA4R6ZLDTDSGCK2X5BKCH","short_pith_number":"pith:NAP7GEA4","canonical_record":{"source":{"id":"2606.01035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"69c21f02578cfccad6663585c8a17f32cd3fdd9b2112fd7b7ced29cb4d6fab83","abstract_canon_sha256":"b0dc7cf994e59a0687856510ce95a599866b6ef651e7a824d9cb961266af854a"},"schema_version":"1.0"},"canonical_sha256":"681ff3101c8fb2b1cc723095abf42a11d90aafad28ab224b8eb9823b584c269a","source":{"kind":"arxiv","id":"2606.01035","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NAP7GEA4R6ZLDTDSGCK2X5BKCH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.01035","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"69c21f02578cfccad6663585c8a17f32cd3fdd9b2112fd7b7ced29cb4d6fab83","abstract_canon_sha256":"b0dc7cf994e59a0687856510ce95a599866b6ef651e7a824d9cb961266af854a"},"schema_version":"1.0"},"canonical_sha256":"681ff3101c8fb2b1cc723095abf42a11d90aafad28ab224b8eb9823b584c269a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:19.134255Z","signature_b64":"Y+hK+ctxKOyQ+2BagTaArS4C1ytnUa8URfVD/Fi9ST3TMPa65S/CvKP/TqVNEBgZw5GPpLPkKl5JfnaclTh/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"681ff3101c8fb2b1cc723095abf42a11d90aafad28ab224b8eb9823b584c269a","last_reissued_at":"2026-06-02T01:04:19.133753Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:19.133753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.01035","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T01:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gj+J0qg9BQRYOzz7TAaCLfyoW973y76uwRVWf/DLpyPyCElA/MazuXIiSXQIBj2Ya4P31XKmfAWvAnffpgidAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:54:27.563234Z"},"content_sha256":"92a87256dc4bf9f1ec6ab86d4ff01befd88b51bf50c78b960a984c9fdc2f9a75","schema_version":"1.0","event_id":"sha256:92a87256dc4bf9f1ec6ab86d4ff01befd88b51bf50c78b960a984c9fdc2f9a75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NAP7GEA4R6ZLDTDSGCK2X5BKCH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strict Equivalence of Multi-Virtual Linkoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Louis H Kauffman","submitted_at":"2026-05-31T05:52:12Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01035","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T01:04:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ykYita/GCOVAcxuMO4uBwLxcRc7qU6wqNDEuxXOv/8oOBsI30SUzMTmywf9+rY0YEzt1A+CEc12Obh7iAIvXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:54:27.563627Z"},"content_sha256":"ef794288503b30c4edd70b0dfe7b3abde4d209fa0bdf656cded660cc712edd32","schema_version":"1.0","event_id":"sha256:ef794288503b30c4edd70b0dfe7b3abde4d209fa0bdf656cded660cc712edd32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/bundle.json","state_url":"https://pith.science/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-23T16:54:27Z","links":{"resolver":"https://pith.science/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH","bundle":"https://pith.science/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/bundle.json","state":"https://pith.science/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NAP7GEA4R6ZLDTDSGCK2X5BKCH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+ncxLCGyby6VunFkUhi0l9dDWrBiMzIKx/WL+TrrDGWQGS8K5o134kEkwix99dUxm8qaJw4hRAMyAi2FYEGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:54:27.565663Z","bundle_sha256":"7fdc833adfa57ff9c78883dee26dcfdf55a7720d26e7ecb344b6820f2670ac49"}}