{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:VFQPC3YI3DLCOOSO5RZRX3B7NN","short_pith_number":"pith:VFQPC3YI","canonical_record":{"source":{"id":"2306.00063","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-05-31T18:00:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"866fb2e61cc0bc15236f4dc0f0725828b4ede8be64413772d4f80e5a6a5581a3","abstract_canon_sha256":"69c2e05fa9c3fe29c864357a04ae3a9372ad1fd616f6ff3485185a81104c6dc6"},"schema_version":"1.0"},"canonical_sha256":"a960f16f08d8d6273a4eec731bec3f6b44181dd766338defb9ccae983965870b","source":{"kind":"arxiv","id":"2306.00063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.00063","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"2306.00063v1","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.00063","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"VFQPC3YI3DLC","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_16","alias_value":"VFQPC3YI3DLCOOSO","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_8","alias_value":"VFQPC3YI","created_at":"2026-07-05T06:16:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:VFQPC3YI3DLCOOSO5RZRX3B7NN","target":"record","payload":{"canonical_record":{"source":{"id":"2306.00063","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-05-31T18:00:03Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"866fb2e61cc0bc15236f4dc0f0725828b4ede8be64413772d4f80e5a6a5581a3","abstract_canon_sha256":"69c2e05fa9c3fe29c864357a04ae3a9372ad1fd616f6ff3485185a81104c6dc6"},"schema_version":"1.0"},"canonical_sha256":"a960f16f08d8d6273a4eec731bec3f6b44181dd766338defb9ccae983965870b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:16:21.000769Z","signature_b64":"V/un5VzoxIRGgqu5t+hKEjB4VsJuIbO+VfAjQICRqsMsXtKNb1fub/8RDQAHIYlFerH1U+4VbkjFVVvM2xWIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a960f16f08d8d6273a4eec731bec3f6b44181dd766338defb9ccae983965870b","last_reissued_at":"2026-07-05T06:16:21.000282Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:16:21.000282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.00063","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":"2026-07-05T06:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbsD2aenaH7rfYzixo/TH61uIwYaTnXmbcWLrkoNVaruFvcvM/0s6hYyrpc6m2Tq4uqSMXdOtd2f/pXqrMAnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:00:45.304210Z"},"content_sha256":"d17246a7e921a5f6afe5b1196d5260fa12bc7382303df67ea214d28bbdaf6f10","schema_version":"1.0","event_id":"sha256:d17246a7e921a5f6afe5b1196d5260fa12bc7382303df67ea214d28bbdaf6f10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:VFQPC3YI3DLCOOSO5RZRX3B7NN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological model for q-deformed rational number and categorification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Li Fan, Yu Qiu","submitted_at":"2023-05-31T18:00:03Z","abstract_excerpt":"Let $\\mathbf{D}_{3}$ be a bigraded 3-decorated disk with an arc system $\\mathbf{A}$. We associate a bigraded simple closed arc $\\widehat{\\eta}_{\\frac{r}{s}}$ on $\\mathbf{D}_{3}$ to any rational number $\\frac{r}{s}\\in\\overline{\\mathbb{Q}}=\\mathbb{Q}\\cup\\{\\infty\\}$. We show that the right (resp. left) $q$-deformed rational numbers associated to $\\frac{r}{s}$, in the sense of Morier-Genoud-Ovsienko (resp. Bapat-Becker-Licata) can be naturally calculated by the $\\mathfrak{q}$-intersection between $\\widehat{\\eta}_{\\frac{r}{s}}$ and $\\mathbf{A}$ (resp. dual arc system $\\mathbf{A}^*$). The Jones poly"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00063","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/2306.00063/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":"2026-07-05T06:16:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bJh1Q9kCR67GVwRS/xTV0DQQYSWfcVEqYCutjkVuywn5kkTDF9D9QO18EQd9wf8nbx3pFLSio9Wbk0onUpKDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T14:00:45.304556Z"},"content_sha256":"7f2da1fdb9da4f081637e868ccc0af04ac21fb7243d513cbe292231af9b9c782","schema_version":"1.0","event_id":"sha256:7f2da1fdb9da4f081637e868ccc0af04ac21fb7243d513cbe292231af9b9c782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/bundle.json","state_url":"https://pith.science/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/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":"2026-08-04T14:00:45Z","links":{"resolver":"https://pith.science/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN","bundle":"https://pith.science/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/bundle.json","state":"https://pith.science/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VFQPC3YI3DLCOOSO5RZRX3B7NN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:VFQPC3YI3DLCOOSO5RZRX3B7NN","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":"69c2e05fa9c3fe29c864357a04ae3a9372ad1fd616f6ff3485185a81104c6dc6","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-05-31T18:00:03Z","title_canon_sha256":"866fb2e61cc0bc15236f4dc0f0725828b4ede8be64413772d4f80e5a6a5581a3"},"schema_version":"1.0","source":{"id":"2306.00063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.00063","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"2306.00063v1","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.00063","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"VFQPC3YI3DLC","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_16","alias_value":"VFQPC3YI3DLCOOSO","created_at":"2026-07-05T06:16:21Z"},{"alias_kind":"pith_short_8","alias_value":"VFQPC3YI","created_at":"2026-07-05T06:16:21Z"}],"graph_snapshots":[{"event_id":"sha256:7f2da1fdb9da4f081637e868ccc0af04ac21fb7243d513cbe292231af9b9c782","target":"graph","created_at":"2026-07-05T06:16:21Z","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/2306.00063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbf{D}_{3}$ be a bigraded 3-decorated disk with an arc system $\\mathbf{A}$. We associate a bigraded simple closed arc $\\widehat{\\eta}_{\\frac{r}{s}}$ on $\\mathbf{D}_{3}$ to any rational number $\\frac{r}{s}\\in\\overline{\\mathbb{Q}}=\\mathbb{Q}\\cup\\{\\infty\\}$. We show that the right (resp. left) $q$-deformed rational numbers associated to $\\frac{r}{s}$, in the sense of Morier-Genoud-Ovsienko (resp. Bapat-Becker-Licata) can be naturally calculated by the $\\mathfrak{q}$-intersection between $\\widehat{\\eta}_{\\frac{r}{s}}$ and $\\mathbf{A}$ (resp. dual arc system $\\mathbf{A}^*$). The Jones poly","authors_text":"Li Fan, Yu Qiu","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-05-31T18:00:03Z","title":"Topological model for q-deformed rational number and categorification"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00063","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:d17246a7e921a5f6afe5b1196d5260fa12bc7382303df67ea214d28bbdaf6f10","target":"record","created_at":"2026-07-05T06:16:21Z","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":"69c2e05fa9c3fe29c864357a04ae3a9372ad1fd616f6ff3485185a81104c6dc6","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2023-05-31T18:00:03Z","title_canon_sha256":"866fb2e61cc0bc15236f4dc0f0725828b4ede8be64413772d4f80e5a6a5581a3"},"schema_version":"1.0","source":{"id":"2306.00063","kind":"arxiv","version":1}},"canonical_sha256":"a960f16f08d8d6273a4eec731bec3f6b44181dd766338defb9ccae983965870b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a960f16f08d8d6273a4eec731bec3f6b44181dd766338defb9ccae983965870b","first_computed_at":"2026-07-05T06:16:21.000282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:16:21.000282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/un5VzoxIRGgqu5t+hKEjB4VsJuIbO+VfAjQICRqsMsXtKNb1fub/8RDQAHIYlFerH1U+4VbkjFVVvM2xWIDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:16:21.000769Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.00063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d17246a7e921a5f6afe5b1196d5260fa12bc7382303df67ea214d28bbdaf6f10","sha256:7f2da1fdb9da4f081637e868ccc0af04ac21fb7243d513cbe292231af9b9c782"],"state_sha256":"ada66e4aa4aae119e645028e85de032a299e90a557139d1a409cdba658ca3663"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8eSaYwG/8AYwzI4DFpccPMuD6RSBf/R17xJOnkuHFoSGwVqlGRQTglTUVTCjl5Sp/gCywjFEwlquPha3H6ipBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T14:00:45.337768Z","bundle_sha256":"2e19310ddaaade5d74bb8ba8193d65984c45e9e88f0598e76473fd5752b417e8"}}