{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:NMZOLUZKM56JH2F7ZGTNT7BO3Z","short_pith_number":"pith:NMZOLUZK","canonical_record":{"source":{"id":"0705.3453","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-05-23T19:50:53Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"168138e662dbf34a399141d2cb981028ef1c97c7589ddc95c3e000995ea55eef","abstract_canon_sha256":"b4832adab9a8c378011f5ad44e73e10b5dca48699beb6558c83a142243692c97"},"schema_version":"1.0"},"canonical_sha256":"6b32e5d32a677c93e8bfc9a6d9fc2ede5cddaf6ef7f05d07ece9db4fec07d245","source":{"kind":"arxiv","id":"0705.3453","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3453","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3453v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3453","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"NMZOLUZKM56J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"NMZOLUZKM56JH2F7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"NMZOLUZK","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:NMZOLUZKM56JH2F7ZGTNT7BO3Z","target":"record","payload":{"canonical_record":{"source":{"id":"0705.3453","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2007-05-23T19:50:53Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"168138e662dbf34a399141d2cb981028ef1c97c7589ddc95c3e000995ea55eef","abstract_canon_sha256":"b4832adab9a8c378011f5ad44e73e10b5dca48699beb6558c83a142243692c97"},"schema_version":"1.0"},"canonical_sha256":"6b32e5d32a677c93e8bfc9a6d9fc2ede5cddaf6ef7f05d07ece9db4fec07d245","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:31.250388Z","signature_b64":"bEhGqxUSGjUeqcsQQk2/KudrGt2szWphX5SCrxYJkqPLpUMaPMjmwel6NNzCLz2WRgcYCkY24/S/8R9QUXmPBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b32e5d32a677c93e8bfc9a6d9fc2ede5cddaf6ef7f05d07ece9db4fec07d245","last_reissued_at":"2026-05-18T01:22:31.249881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:31.249881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0705.3453","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":"2026-05-18T01:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B8RI0yGNNpelQZunISextOzqZBva51YJYy0lBCqXdRPPf/w7XJ+ccg9shZEmU/2nu2m1BxgnjNQuW78Fje2oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:27:43.404412Z"},"content_sha256":"4c78ad6de953da6c2200a6fcfb54f4e3457cc65696398644683de904e7e19912","schema_version":"1.0","event_id":"sha256:4c78ad6de953da6c2200a6fcfb54f4e3457cc65696398644683de904e7e19912"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:NMZOLUZKM56JH2F7ZGTNT7BO3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graphs on surfaces and Khovanov homology","license":"","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.GT","authors_text":"Abhijit Champanerkar, Ilya Kofman, Neal Stoltzfus","submitted_at":"2007-05-23T19:50:53Z","abstract_excerpt":"Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram $L$, there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring $L$. This correspondence preserves the bigrading used for the spanning tree model of Khovanov homology, whose Euler characteristic is the Jones polynomial of $L$. Thus, Khovanov homology can be expressed in terms of ri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3453","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":"2026-05-18T01:22:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/UttUtuE0jpSQi3KvP2wzqH5s4WfznAC+OAmt8Circpgel00lS3neAdpv/UYAHpovmzUKLO0j/QvKHYcfeeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:27:43.404766Z"},"content_sha256":"6ec9ec4a6dd5cbbdf850b8834f75e8ce0e650ac244d2096b7253b05b661193cc","schema_version":"1.0","event_id":"sha256:6ec9ec4a6dd5cbbdf850b8834f75e8ce0e650ac244d2096b7253b05b661193cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/bundle.json","state_url":"https://pith.science/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/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":"2026-06-11T14:27:43Z","links":{"resolver":"https://pith.science/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z","bundle":"https://pith.science/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/bundle.json","state":"https://pith.science/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NMZOLUZKM56JH2F7ZGTNT7BO3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:NMZOLUZKM56JH2F7ZGTNT7BO3Z","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":"b4832adab9a8c378011f5ad44e73e10b5dca48699beb6558c83a142243692c97","cross_cats_sorted":["math.CO","math.QA"],"license":"","primary_cat":"math.GT","submitted_at":"2007-05-23T19:50:53Z","title_canon_sha256":"168138e662dbf34a399141d2cb981028ef1c97c7589ddc95c3e000995ea55eef"},"schema_version":"1.0","source":{"id":"0705.3453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.3453","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"0705.3453v1","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.3453","created_at":"2026-05-18T01:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"NMZOLUZKM56J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"NMZOLUZKM56JH2F7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"NMZOLUZK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:6ec9ec4a6dd5cbbdf850b8834f75e8ce0e650ac244d2096b7253b05b661193cc","target":"graph","created_at":"2026-05-18T01:22:31Z","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":"Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram $L$, there is an associated ribbon graph whose quasi-trees correspond bijectively to spanning trees of the graph obtained by checkerboard coloring $L$. This correspondence preserves the bigrading used for the spanning tree model of Khovanov homology, whose Euler characteristic is the Jones polynomial of $L$. Thus, Khovanov homology can be expressed in terms of ri","authors_text":"Abhijit Champanerkar, Ilya Kofman, Neal Stoltzfus","cross_cats":["math.CO","math.QA"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-05-23T19:50:53Z","title":"Graphs on surfaces and Khovanov homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.3453","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":"sha256:4c78ad6de953da6c2200a6fcfb54f4e3457cc65696398644683de904e7e19912","target":"record","created_at":"2026-05-18T01:22:31Z","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":"b4832adab9a8c378011f5ad44e73e10b5dca48699beb6558c83a142243692c97","cross_cats_sorted":["math.CO","math.QA"],"license":"","primary_cat":"math.GT","submitted_at":"2007-05-23T19:50:53Z","title_canon_sha256":"168138e662dbf34a399141d2cb981028ef1c97c7589ddc95c3e000995ea55eef"},"schema_version":"1.0","source":{"id":"0705.3453","kind":"arxiv","version":1}},"canonical_sha256":"6b32e5d32a677c93e8bfc9a6d9fc2ede5cddaf6ef7f05d07ece9db4fec07d245","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b32e5d32a677c93e8bfc9a6d9fc2ede5cddaf6ef7f05d07ece9db4fec07d245","first_computed_at":"2026-05-18T01:22:31.249881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:31.249881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bEhGqxUSGjUeqcsQQk2/KudrGt2szWphX5SCrxYJkqPLpUMaPMjmwel6NNzCLz2WRgcYCkY24/S/8R9QUXmPBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:31.250388Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.3453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c78ad6de953da6c2200a6fcfb54f4e3457cc65696398644683de904e7e19912","sha256:6ec9ec4a6dd5cbbdf850b8834f75e8ce0e650ac244d2096b7253b05b661193cc"],"state_sha256":"d5e34d9c2a855251480d0b2b7f31b5d5e0cbdbbbb24ff83109c2739222382581"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLME71gxDRUU81ttZ+UTV2Z3H9LKdeM/uPsLUfHDhjAFbNbb+hitQAJhIYGCGicb2oXYRQLIplUnlpQ5z5mnBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:27:43.406929Z","bundle_sha256":"e423102146720f22b5d1c7939aafc21d7e17611f43d0f76c41a1e818b01af601"}}