{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5LFUVN4READMD7CWQ7IFDIYCTN","short_pith_number":"pith:5LFUVN4R","canonical_record":{"source":{"id":"1512.09162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-30T21:58:12Z","cross_cats_sorted":[],"title_canon_sha256":"9123b5e078164bda912ad58f7d28ce0c617b6485f411d3bfa4cd51a980ab903c","abstract_canon_sha256":"357f605400217368d5e3df2f61f99462c362eea480053af9fd11eb6cb55c1131"},"schema_version":"1.0"},"canonical_sha256":"eacb4ab7912006c1fc5687d051a3029b4652c7f74d40943c01e62c4c193b9a43","source":{"kind":"arxiv","id":"1512.09162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09162","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09162v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09162","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"5LFUVN4READM","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5LFUVN4READMD7CW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5LFUVN4R","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5LFUVN4READMD7CWQ7IFDIYCTN","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-30T21:58:12Z","cross_cats_sorted":[],"title_canon_sha256":"9123b5e078164bda912ad58f7d28ce0c617b6485f411d3bfa4cd51a980ab903c","abstract_canon_sha256":"357f605400217368d5e3df2f61f99462c362eea480053af9fd11eb6cb55c1131"},"schema_version":"1.0"},"canonical_sha256":"eacb4ab7912006c1fc5687d051a3029b4652c7f74d40943c01e62c4c193b9a43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:33.149092Z","signature_b64":"yoQzK795T5tYcXFBHjeQ9n0d5In8//obq31c6EioOTHiPoX3yR/HEi0q0y6STuOjzR9KcDt5V/qjZFdhbytLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eacb4ab7912006c1fc5687d051a3029b4652c7f74d40943c01e62c4c193b9a43","last_reissued_at":"2026-05-18T01:23:33.148440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:33.148440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09162","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ycW4vRJXCqkKxQhrNdNS4EtygREMnQopepxxFQCANtmMrfFD2n0na3zHMJGI6DHEbJxxBOsGBVGxWh6HPfjBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:49:42.794044Z"},"content_sha256":"73e0e2766d6f32ea02bba1dba6b8ffdfe74e8ffe372f5113d26203733207af29","schema_version":"1.0","event_id":"sha256:73e0e2766d6f32ea02bba1dba6b8ffdfe74e8ffe372f5113d26203733207af29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5LFUVN4READMD7CWQ7IFDIYCTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Slavik Jablan's work on 4-moves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jozef H. Przytycki","submitted_at":"2015-12-30T21:58:12Z","abstract_excerpt":"We show that every alternating link of 2-components and 12 crossings can be reduced by 4-moves to the trivial link or the Hopf link. It answers the question asked in one of the last papers by Slavik Jablan."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09162","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ffHTuJFwPgwyFpi5gpARbUJT5VKHkAn2Gk3qQ5+fqLPYUrv5c4nY8m0KxOEWlR4XrNPOtkKi5GZrdZnSn9zAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:49:42.794401Z"},"content_sha256":"dee20fd781a8c9a24e061ec1473fce5c78eda772c0c475ec28fd8472c39dbef9","schema_version":"1.0","event_id":"sha256:dee20fd781a8c9a24e061ec1473fce5c78eda772c0c475ec28fd8472c39dbef9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5LFUVN4READMD7CWQ7IFDIYCTN/bundle.json","state_url":"https://pith.science/pith/5LFUVN4READMD7CWQ7IFDIYCTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5LFUVN4READMD7CWQ7IFDIYCTN/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":"2026-06-24T06:49:42Z","links":{"resolver":"https://pith.science/pith/5LFUVN4READMD7CWQ7IFDIYCTN","bundle":"https://pith.science/pith/5LFUVN4READMD7CWQ7IFDIYCTN/bundle.json","state":"https://pith.science/pith/5LFUVN4READMD7CWQ7IFDIYCTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5LFUVN4READMD7CWQ7IFDIYCTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5LFUVN4READMD7CWQ7IFDIYCTN","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":"357f605400217368d5e3df2f61f99462c362eea480053af9fd11eb6cb55c1131","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-30T21:58:12Z","title_canon_sha256":"9123b5e078164bda912ad58f7d28ce0c617b6485f411d3bfa4cd51a980ab903c"},"schema_version":"1.0","source":{"id":"1512.09162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09162","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09162v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09162","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"5LFUVN4READM","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5LFUVN4READMD7CW","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5LFUVN4R","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:dee20fd781a8c9a24e061ec1473fce5c78eda772c0c475ec28fd8472c39dbef9","target":"graph","created_at":"2026-05-18T01:23:33Z","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 show that every alternating link of 2-components and 12 crossings can be reduced by 4-moves to the trivial link or the Hopf link. It answers the question asked in one of the last papers by Slavik Jablan.","authors_text":"Jozef H. Przytycki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-30T21:58:12Z","title":"On Slavik Jablan's work on 4-moves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09162","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":"sha256:73e0e2766d6f32ea02bba1dba6b8ffdfe74e8ffe372f5113d26203733207af29","target":"record","created_at":"2026-05-18T01:23:33Z","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":"357f605400217368d5e3df2f61f99462c362eea480053af9fd11eb6cb55c1131","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-12-30T21:58:12Z","title_canon_sha256":"9123b5e078164bda912ad58f7d28ce0c617b6485f411d3bfa4cd51a980ab903c"},"schema_version":"1.0","source":{"id":"1512.09162","kind":"arxiv","version":1}},"canonical_sha256":"eacb4ab7912006c1fc5687d051a3029b4652c7f74d40943c01e62c4c193b9a43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eacb4ab7912006c1fc5687d051a3029b4652c7f74d40943c01e62c4c193b9a43","first_computed_at":"2026-05-18T01:23:33.148440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:33.148440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoQzK795T5tYcXFBHjeQ9n0d5In8//obq31c6EioOTHiPoX3yR/HEi0q0y6STuOjzR9KcDt5V/qjZFdhbytLBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:33.149092Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73e0e2766d6f32ea02bba1dba6b8ffdfe74e8ffe372f5113d26203733207af29","sha256:dee20fd781a8c9a24e061ec1473fce5c78eda772c0c475ec28fd8472c39dbef9"],"state_sha256":"fb89ff7bffc627c361bf8324265b04037718c61a8da551ec5bb4e991dfa9b7cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWINGnLhKg5fOzvmvlwhbMbgP0ylEh6yMBwrPm96dEiH/bbekXbH5BlpdfClR98Y5iK+/K2fVGLjKYy9kletAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:49:42.796382Z","bundle_sha256":"41f44bf7061c55cda40be086f31d583fcdb5e1414198b9b31f8929ca9379410d"}}