{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:D6JRYWNUWOA5QENQAPVS4PT6TZ","short_pith_number":"pith:D6JRYWNU","canonical_record":{"source":{"id":"1309.3288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-12T20:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"3d5b28cf083f7fe539366122341f5c953a291f61c318da9f940fd7fcdbb64d40","abstract_canon_sha256":"8ffb23eafc7bc2ed725ff8ab81a72c20457dd1881310e5d1c3c10486340a839f"},"schema_version":"1.0"},"canonical_sha256":"1f931c59b4b381d811b003eb2e3e7e9e7109f8bfd7a66473942af73e29e25da1","source":{"kind":"arxiv","id":"1309.3288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3288","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3288v1","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3288","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"D6JRYWNUWOA5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D6JRYWNUWOA5QENQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D6JRYWNU","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:D6JRYWNUWOA5QENQAPVS4PT6TZ","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-12T20:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"3d5b28cf083f7fe539366122341f5c953a291f61c318da9f940fd7fcdbb64d40","abstract_canon_sha256":"8ffb23eafc7bc2ed725ff8ab81a72c20457dd1881310e5d1c3c10486340a839f"},"schema_version":"1.0"},"canonical_sha256":"1f931c59b4b381d811b003eb2e3e7e9e7109f8bfd7a66473942af73e29e25da1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:23.052255Z","signature_b64":"PK8OTpGCRLq+Ur4/aeUHksvMhnoJKHOqxoNvA1ZndPCe1pKMhYOPqTGOcPEbgQdeyhbE9yCTzNRAl3VEFiP0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f931c59b4b381d811b003eb2e3e7e9e7109f8bfd7a66473942af73e29e25da1","last_reissued_at":"2026-05-18T03:13:23.051298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:23.051298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3288","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":"2026-05-18T03:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j6wxOPzpEpFifQBvPvXUl1+h7WJywEIwWnUntYHWtndF4r7q8EAa+7q0YhBch0o16OoDyipLmiUn+THX/uR4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:37:35.808306Z"},"content_sha256":"d34fbed76151cc824a0dd52a99918d93bb75de918f955585e0337e11f64c26fe","schema_version":"1.0","event_id":"sha256:d34fbed76151cc824a0dd52a99918d93bb75de918f955585e0337e11f64c26fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:D6JRYWNUWOA5QENQAPVS4PT6TZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Links and Planar Diagram Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Matt Mastin","submitted_at":"2013-09-12T20:07:32Z","abstract_excerpt":"In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit algorithm for reconstructing a knot diagram on a surface from a PD-code. We also discuss the intrinsic symmetries of PD-codes (i.e., invertibility and chirality). The moves analogous to the Reidemeister moves are also explored, and we show that the given set of PD-codes modulo th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3288","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":"2026-05-18T03:13:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSKngZcELaf9n4qOOF0b0jqA5Tp/I05fNpwPqSvhlBIKBv9t8WbWl7JKdkZeBPH1eWiKKxr8WT5vGH9y26cYBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:37:35.808683Z"},"content_sha256":"1d2cae91fa264e32ac4231938e9bba2bf0bf1ab7f6637ae86fe91cf0e38e2340","schema_version":"1.0","event_id":"sha256:1d2cae91fa264e32ac4231938e9bba2bf0bf1ab7f6637ae86fe91cf0e38e2340"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/bundle.json","state_url":"https://pith.science/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/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":"2026-06-22T17:37:35Z","links":{"resolver":"https://pith.science/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ","bundle":"https://pith.science/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/bundle.json","state":"https://pith.science/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6JRYWNUWOA5QENQAPVS4PT6TZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D6JRYWNUWOA5QENQAPVS4PT6TZ","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":"8ffb23eafc7bc2ed725ff8ab81a72c20457dd1881310e5d1c3c10486340a839f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-12T20:07:32Z","title_canon_sha256":"3d5b28cf083f7fe539366122341f5c953a291f61c318da9f940fd7fcdbb64d40"},"schema_version":"1.0","source":{"id":"1309.3288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3288","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3288v1","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3288","created_at":"2026-05-18T03:13:23Z"},{"alias_kind":"pith_short_12","alias_value":"D6JRYWNUWOA5","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D6JRYWNUWOA5QENQ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D6JRYWNU","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:1d2cae91fa264e32ac4231938e9bba2bf0bf1ab7f6637ae86fe91cf0e38e2340","target":"graph","created_at":"2026-05-18T03:13:23Z","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":"In this paper we formalize a combinatorial object for describing link diagrams called a Planar Diagram Code. PD-codes are used by the KnotTheory Mathematica package developed by Bar-Natan, et al. We present the set of PD-codes as a stand alone object and discuss its relationship with link diagrams. We give an explicit algorithm for reconstructing a knot diagram on a surface from a PD-code. We also discuss the intrinsic symmetries of PD-codes (i.e., invertibility and chirality). The moves analogous to the Reidemeister moves are also explored, and we show that the given set of PD-codes modulo th","authors_text":"Matt Mastin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-12T20:07:32Z","title":"Links and Planar Diagram Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3288","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:d34fbed76151cc824a0dd52a99918d93bb75de918f955585e0337e11f64c26fe","target":"record","created_at":"2026-05-18T03:13:23Z","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":"8ffb23eafc7bc2ed725ff8ab81a72c20457dd1881310e5d1c3c10486340a839f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-09-12T20:07:32Z","title_canon_sha256":"3d5b28cf083f7fe539366122341f5c953a291f61c318da9f940fd7fcdbb64d40"},"schema_version":"1.0","source":{"id":"1309.3288","kind":"arxiv","version":1}},"canonical_sha256":"1f931c59b4b381d811b003eb2e3e7e9e7109f8bfd7a66473942af73e29e25da1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f931c59b4b381d811b003eb2e3e7e9e7109f8bfd7a66473942af73e29e25da1","first_computed_at":"2026-05-18T03:13:23.051298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:23.051298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PK8OTpGCRLq+Ur4/aeUHksvMhnoJKHOqxoNvA1ZndPCe1pKMhYOPqTGOcPEbgQdeyhbE9yCTzNRAl3VEFiP0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:23.052255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d34fbed76151cc824a0dd52a99918d93bb75de918f955585e0337e11f64c26fe","sha256:1d2cae91fa264e32ac4231938e9bba2bf0bf1ab7f6637ae86fe91cf0e38e2340"],"state_sha256":"c409ecbcd6e53f6a4559adcb4536f647dbb087cc6ae234e4d72d2f55526048ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BzsEtm2h698XFjIcuKbrzt3+Khwi+DR8KisHcDuGCQKlWGWbqi/OAwolKkeBOVdUhZiWRYoQ/mFcE+/CZo9iDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:37:35.810706Z","bundle_sha256":"86c54b2a0c43266310d62f3f14eb1551566ed3f9e12a30954e4c919329e72078"}}