{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MU3F6SYA2HDN5P62YKXRFS5S5P","short_pith_number":"pith:MU3F6SYA","canonical_record":{"source":{"id":"2607.22308","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-24T13:48:18Z","cross_cats_sorted":["math.CO","math.GT"],"title_canon_sha256":"6d2735fde856b0e29c62fe879fadaf581b5b7a10a2eb5f59ca394b14c602dcb3","abstract_canon_sha256":"57af9314a31f3f79bff51e162cb2927df3fbea27f12c24d537271a7606aaa4dd"},"schema_version":"1.0"},"canonical_sha256":"65365f4b00d1c6debfdac2af12cbb2ebcaf4b474be9948b05fbe693178987efa","source":{"kind":"arxiv","id":"2607.22308","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22308","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22308v1","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22308","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"MU3F6SYA2HDN","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_16","alias_value":"MU3F6SYA2HDN5P62","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_8","alias_value":"MU3F6SYA","created_at":"2026-07-27T01:20:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MU3F6SYA2HDN5P62YKXRFS5S5P","target":"record","payload":{"canonical_record":{"source":{"id":"2607.22308","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-24T13:48:18Z","cross_cats_sorted":["math.CO","math.GT"],"title_canon_sha256":"6d2735fde856b0e29c62fe879fadaf581b5b7a10a2eb5f59ca394b14c602dcb3","abstract_canon_sha256":"57af9314a31f3f79bff51e162cb2927df3fbea27f12c24d537271a7606aaa4dd"},"schema_version":"1.0"},"canonical_sha256":"65365f4b00d1c6debfdac2af12cbb2ebcaf4b474be9948b05fbe693178987efa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-27T01:20:59.072823Z","signature_b64":"krxyVuz5JMio51CrQYiw03jPNpCEdCsaIsujuPqiZc9N4fEM9fV3m57iN1gQqMgZD3DxbMpJ0j4MBzeLaxq7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"65365f4b00d1c6debfdac2af12cbb2ebcaf4b474be9948b05fbe693178987efa","last_reissued_at":"2026-07-27T01:20:59.071972Z","signature_status":"signed_v1","first_computed_at":"2026-07-27T01:20:59.071972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.22308","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":"2026-07-27T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v17DY1/tGniKmmUvYQvfNNPFzaG8/bwwdO3xaIi/iL+5PYeEzSfGuTVafShpixPrwJEg8SW7QbsVR0CuKUpUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:12:05.951490Z"},"content_sha256":"bf6dc43ff90bde3d7a7804d0de43ac73fe6038641c9bec8e6b74cc94b511f2c6","schema_version":"1.0","event_id":"sha256:bf6dc43ff90bde3d7a7804d0de43ac73fe6038641c9bec8e6b74cc94b511f2c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MU3F6SYA2HDN5P62YKXRFS5S5P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nuancing the unicity of $q$-rationals","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.CO","math.GT"],"primary_cat":"math.QA","authors_text":"Alexander Thomas, Olga Paris-Romaskevich, Perrine Jouteur","submitted_at":"2026-07-24T13:48:18Z","abstract_excerpt":"We prove unicity of $q$-rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modular symmetry. We prove that there are exactly two deformations which deliver the usual $q$-integers: the original $q$-rationals defined by Morier-Genoud and Ovsienko, and another new one. Although the new family can be obtained by conjugacy from the old one, new positivity properties appear. In addition, this new family provides a direct computation of the Jones polynomial of rational knots."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22308","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/2607.22308/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":"2026-07-27T01:20:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3SQcOcVsXhhe+N5V4aOSLXFk9W4pQnmP7goPupW9ijblBtjeGKos+Hw6Ntnq59drN2BDJCCStKJ2JVLCHt5oBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T14:12:05.952401Z"},"content_sha256":"2cb777e812a58ffa72b251fce9b3eea6a31bc02310e64a6535a0d8b64efc2cfe","schema_version":"1.0","event_id":"sha256:2cb777e812a58ffa72b251fce9b3eea6a31bc02310e64a6535a0d8b64efc2cfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/bundle.json","state_url":"https://pith.science/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/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":"2026-08-11T14:12:05Z","links":{"resolver":"https://pith.science/pith/MU3F6SYA2HDN5P62YKXRFS5S5P","bundle":"https://pith.science/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/bundle.json","state":"https://pith.science/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MU3F6SYA2HDN5P62YKXRFS5S5P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MU3F6SYA2HDN5P62YKXRFS5S5P","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":"57af9314a31f3f79bff51e162cb2927df3fbea27f12c24d537271a7606aaa4dd","cross_cats_sorted":["math.CO","math.GT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-24T13:48:18Z","title_canon_sha256":"6d2735fde856b0e29c62fe879fadaf581b5b7a10a2eb5f59ca394b14c602dcb3"},"schema_version":"1.0","source":{"id":"2607.22308","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.22308","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.22308v1","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.22308","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_12","alias_value":"MU3F6SYA2HDN","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_16","alias_value":"MU3F6SYA2HDN5P62","created_at":"2026-07-27T01:20:59Z"},{"alias_kind":"pith_short_8","alias_value":"MU3F6SYA","created_at":"2026-07-27T01:20:59Z"}],"graph_snapshots":[{"event_id":"sha256:2cb777e812a58ffa72b251fce9b3eea6a31bc02310e64a6535a0d8b64efc2cfe","target":"graph","created_at":"2026-07-27T01:20:59Z","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/2607.22308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove unicity of $q$-rational numbers up to conjugacy, using character varieties. Despite the unicity, we exhibit a two-parameter family of deformations of rationals with a modular symmetry. We prove that there are exactly two deformations which deliver the usual $q$-integers: the original $q$-rationals defined by Morier-Genoud and Ovsienko, and another new one. Although the new family can be obtained by conjugacy from the old one, new positivity properties appear. In addition, this new family provides a direct computation of the Jones polynomial of rational knots.","authors_text":"Alexander Thomas, Olga Paris-Romaskevich, Perrine Jouteur","cross_cats":["math.CO","math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-24T13:48:18Z","title":"Nuancing the unicity of $q$-rationals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22308","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:bf6dc43ff90bde3d7a7804d0de43ac73fe6038641c9bec8e6b74cc94b511f2c6","target":"record","created_at":"2026-07-27T01:20:59Z","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":"57af9314a31f3f79bff51e162cb2927df3fbea27f12c24d537271a7606aaa4dd","cross_cats_sorted":["math.CO","math.GT"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2026-07-24T13:48:18Z","title_canon_sha256":"6d2735fde856b0e29c62fe879fadaf581b5b7a10a2eb5f59ca394b14c602dcb3"},"schema_version":"1.0","source":{"id":"2607.22308","kind":"arxiv","version":1}},"canonical_sha256":"65365f4b00d1c6debfdac2af12cbb2ebcaf4b474be9948b05fbe693178987efa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65365f4b00d1c6debfdac2af12cbb2ebcaf4b474be9948b05fbe693178987efa","first_computed_at":"2026-07-27T01:20:59.071972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-27T01:20:59.071972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"krxyVuz5JMio51CrQYiw03jPNpCEdCsaIsujuPqiZc9N4fEM9fV3m57iN1gQqMgZD3DxbMpJ0j4MBzeLaxq7Aw==","signature_status":"signed_v1","signed_at":"2026-07-27T01:20:59.072823Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.22308","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf6dc43ff90bde3d7a7804d0de43ac73fe6038641c9bec8e6b74cc94b511f2c6","sha256:2cb777e812a58ffa72b251fce9b3eea6a31bc02310e64a6535a0d8b64efc2cfe"],"state_sha256":"537adea09b82463f341eae13bc0d88f69da607a0d05f39dab75b180050392867"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ULPx7pEoZcWTQF4jIjFESAns7e5KhHBzmpkmSgwLVb3+hLDOEsnk6Wirvv7+AAMMimJZ0QgYW0c3X+UMulx3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T14:12:05.959685Z","bundle_sha256":"ef4f884dcebfb02ede823ef4975aaee6d96e66722c570cc59e335eadf30a97ba"}}