{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:XI3K33K44JTBDIE47BUO6EJAKL","short_pith_number":"pith:XI3K33K4","canonical_record":{"source":{"id":"1701.03999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-01-15T07:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"2154f4be9ace2fa733bb6ba91a6fa63a66c2c10bb8e2cd621f559991e64e6b97","abstract_canon_sha256":"7e7c6307668fae6cdeeb772eb903f3e2023def3704d2008d5ad4589498d2d013"},"schema_version":"1.0"},"canonical_sha256":"ba36aded5ce26611a09cf868ef112052d1e7dd5fd4345975ea28cc9464e626fc","source":{"kind":"arxiv","id":"1701.03999","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03999","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03999v1","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03999","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"XI3K33K44JTB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XI3K33K44JTBDIE4","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XI3K33K4","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:XI3K33K44JTBDIE47BUO6EJAKL","target":"record","payload":{"canonical_record":{"source":{"id":"1701.03999","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-01-15T07:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"2154f4be9ace2fa733bb6ba91a6fa63a66c2c10bb8e2cd621f559991e64e6b97","abstract_canon_sha256":"7e7c6307668fae6cdeeb772eb903f3e2023def3704d2008d5ad4589498d2d013"},"schema_version":"1.0"},"canonical_sha256":"ba36aded5ce26611a09cf868ef112052d1e7dd5fd4345975ea28cc9464e626fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:48.157104Z","signature_b64":"iBrYZzJ1gLGdidoifOxJRm7xemlQRncx8djc/gakXDFEbifuAdI3qFbGqBPSWD/9/sxXTR4l2U2JoFxOe1GUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba36aded5ce26611a09cf868ef112052d1e7dd5fd4345975ea28cc9464e626fc","last_reissued_at":"2026-05-18T00:52:48.156480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:48.156480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.03999","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":"2026-05-18T00:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ewH+cZkNtdwFOWjziiOpHTGh7FHY+mz4XzJA1Q9dc/WLTxlEaQgLSutGe4PJeJ+sfRUhJlBsNDUgE04mDANTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:11:02.004002Z"},"content_sha256":"f89193c42e025ec18490e287e1ae41514241751d2f98fad3628e8384b3070386","schema_version":"1.0","event_id":"sha256:f89193c42e025ec18490e287e1ae41514241751d2f98fad3628e8384b3070386"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:XI3K33K44JTBDIE47BUO6EJAKL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Virtual unknotting numbers of certain virtual torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Hirokazu Yanagi, Masaharu Ishikawa","submitted_at":"2017-01-15T07:23:46Z","abstract_excerpt":"The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the $(p,q)$-torus knot, i.e. it is (p-1)(q-1)/2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03999","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":""},"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":"2026-05-18T00:52:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b+hrBjJQvNkeMBAiFqwSLRl/yueTVPswa4cVpslSz3LIjpY0UOFTqQvHG8C7evPm2uqX8HQJZ2+RHSDpeqdrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:11:02.004388Z"},"content_sha256":"3fde3cc1308a21b8177cab3d7e09b4f183aa4450b17c3a6b24263a34d742d122","schema_version":"1.0","event_id":"sha256:3fde3cc1308a21b8177cab3d7e09b4f183aa4450b17c3a6b24263a34d742d122"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XI3K33K44JTBDIE47BUO6EJAKL/bundle.json","state_url":"https://pith.science/pith/XI3K33K44JTBDIE47BUO6EJAKL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XI3K33K44JTBDIE47BUO6EJAKL/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":"2026-06-20T17:11:02Z","links":{"resolver":"https://pith.science/pith/XI3K33K44JTBDIE47BUO6EJAKL","bundle":"https://pith.science/pith/XI3K33K44JTBDIE47BUO6EJAKL/bundle.json","state":"https://pith.science/pith/XI3K33K44JTBDIE47BUO6EJAKL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XI3K33K44JTBDIE47BUO6EJAKL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XI3K33K44JTBDIE47BUO6EJAKL","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":"7e7c6307668fae6cdeeb772eb903f3e2023def3704d2008d5ad4589498d2d013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-01-15T07:23:46Z","title_canon_sha256":"2154f4be9ace2fa733bb6ba91a6fa63a66c2c10bb8e2cd621f559991e64e6b97"},"schema_version":"1.0","source":{"id":"1701.03999","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03999","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03999v1","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03999","created_at":"2026-05-18T00:52:48Z"},{"alias_kind":"pith_short_12","alias_value":"XI3K33K44JTB","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"XI3K33K44JTBDIE4","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"XI3K33K4","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:3fde3cc1308a21b8177cab3d7e09b4f183aa4450b17c3a6b24263a34d742d122","target":"graph","created_at":"2026-05-18T00:52:48Z","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":"The virtual unknotting number of a virtual knot is the minimal number of crossing changes that makes the virtual knot to be the unknot, which is defined only for virtual knots virtually homotopic to the unknot. We focus on the virtual knot obtained from the standard (p,q)-torus knot diagram by replacing all crossings on one overstrand into virtual crossings and prove that its virtual unknotting number is equal to the unknotting number of the $(p,q)$-torus knot, i.e. it is (p-1)(q-1)/2.","authors_text":"Hirokazu Yanagi, Masaharu Ishikawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-01-15T07:23:46Z","title":"Virtual unknotting numbers of certain virtual torus knots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03999","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:f89193c42e025ec18490e287e1ae41514241751d2f98fad3628e8384b3070386","target":"record","created_at":"2026-05-18T00:52:48Z","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":"7e7c6307668fae6cdeeb772eb903f3e2023def3704d2008d5ad4589498d2d013","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-01-15T07:23:46Z","title_canon_sha256":"2154f4be9ace2fa733bb6ba91a6fa63a66c2c10bb8e2cd621f559991e64e6b97"},"schema_version":"1.0","source":{"id":"1701.03999","kind":"arxiv","version":1}},"canonical_sha256":"ba36aded5ce26611a09cf868ef112052d1e7dd5fd4345975ea28cc9464e626fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba36aded5ce26611a09cf868ef112052d1e7dd5fd4345975ea28cc9464e626fc","first_computed_at":"2026-05-18T00:52:48.156480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:48.156480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iBrYZzJ1gLGdidoifOxJRm7xemlQRncx8djc/gakXDFEbifuAdI3qFbGqBPSWD/9/sxXTR4l2U2JoFxOe1GUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:48.157104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03999","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f89193c42e025ec18490e287e1ae41514241751d2f98fad3628e8384b3070386","sha256:3fde3cc1308a21b8177cab3d7e09b4f183aa4450b17c3a6b24263a34d742d122"],"state_sha256":"37446daa71a3d433ed798bcfdb701113fc059e8c71237cc8216051aeee6d468f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cA16ep7UZQL+lGYhEfQb5tKW8zsQEfQwiKOAsHDH9Nkz09u344MLBc63q6YEdJpnV7qyI15BLChSMnfT1d6uAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T17:11:02.006286Z","bundle_sha256":"fd76b231c889a4933537b24abe191d21bf8029f27b436178dfb6370c492c5312"}}