{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:VPP67HIG2LS2ESV2ZMBNPT6HK2","short_pith_number":"pith:VPP67HIG","canonical_record":{"source":{"id":"2608.06761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:28:01Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"1ef85e5cca867cf2567061a3c7a9921f29b60e8ccfe706cd59a0ba2b4f9d99ae","abstract_canon_sha256":"22ec8060fe8ffb38328474c6191194752cd3b2fddfe38597311ed30d94b81374"},"schema_version":"1.0"},"canonical_sha256":"abdfef9d06d2e5a24abacb02d7cfc756b499393f312f05eaa61d4563202fe7f7","source":{"kind":"arxiv","id":"2608.06761","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06761","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06761v1","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06761","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"VPP67HIG2LS2","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"VPP67HIG2LS2ESV2","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"VPP67HIG","created_at":"2026-08-10T01:11:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:VPP67HIG2LS2ESV2ZMBNPT6HK2","target":"record","payload":{"canonical_record":{"source":{"id":"2608.06761","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:28:01Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"1ef85e5cca867cf2567061a3c7a9921f29b60e8ccfe706cd59a0ba2b4f9d99ae","abstract_canon_sha256":"22ec8060fe8ffb38328474c6191194752cd3b2fddfe38597311ed30d94b81374"},"schema_version":"1.0"},"canonical_sha256":"abdfef9d06d2e5a24abacb02d7cfc756b499393f312f05eaa61d4563202fe7f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-10T01:11:57.715783Z","signature_b64":"rR7YrL9+2me7QbuL6sjnKu6GE1J0JPnVvKNloh9sNa70FulvHJMoLNpwEeplqCEVlHoUCDU+riTgJpuFo6KDBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abdfef9d06d2e5a24abacb02d7cfc756b499393f312f05eaa61d4563202fe7f7","last_reissued_at":"2026-08-10T01:11:57.713464Z","signature_status":"signed_v1","first_computed_at":"2026-08-10T01:11:57.713464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.06761","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":"2026-08-10T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kICbBnIRCxAodW9VVKIi2QPpvxGRgoVoHWBALhvPWRem7Y1gLm6Z67jelsExgY45K8SKlg1YoJQkqat22PXxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:17:42.023539Z"},"content_sha256":"3d53f974882cfecae5fe34cdfde13fa8878d0e960f0cf0e42c3fe66b750efc61","schema_version":"1.0","event_id":"sha256:3d53f974882cfecae5fe34cdfde13fa8878d0e960f0cf0e42c3fe66b750efc61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:VPP67HIG2LS2ESV2ZMBNPT6HK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coefficients of $q$-real numbers: their combinatorial meaning and growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.CO","authors_text":"Pavel Etingof, Valentin Ovsienko","submitted_at":"2026-08-07T03:28:01Z","abstract_excerpt":"A $q$-deformed real number, or ``$q$-real'', was defined by Morier-Genoud and the second author. When $x\\in\\mathbb{R}$ such that $x\\geq0$, the $q$-analogue $[x]_q$ is a power series with integer coefficients in one formal variable~$q$. In general a $q$-real is a formal Laurent series. The main goal of this paper is to study the coefficients of $q$-reals as functions on~$\\mathbb{R}$ and give a combinatorial interpretation of these coefficients. This allows us to prove a conjecture studied by several authors stating that the $q$-deformed golden ratio has the smallest radius of convergence among "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06761","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/2608.06761/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":"2026-08-10T01:11:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hSPxaBmbYBvxBW/UdaEjEDEqS0UJaltLfRnaDmYhV5dkzi2/lQrfxMLuacYR0oHHa+cARIj4LmmNqrP1vaGMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T04:17:42.024122Z"},"content_sha256":"a32e3bd9c42695368bbf901427925ac61f95423961d1f33b9d3d5bbbbb8e6a27","schema_version":"1.0","event_id":"sha256:a32e3bd9c42695368bbf901427925ac61f95423961d1f33b9d3d5bbbbb8e6a27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/bundle.json","state_url":"https://pith.science/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/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":"2026-08-12T04:17:42Z","links":{"resolver":"https://pith.science/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2","bundle":"https://pith.science/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/bundle.json","state":"https://pith.science/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VPP67HIG2LS2ESV2ZMBNPT6HK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VPP67HIG2LS2ESV2ZMBNPT6HK2","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":"22ec8060fe8ffb38328474c6191194752cd3b2fddfe38597311ed30d94b81374","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:28:01Z","title_canon_sha256":"1ef85e5cca867cf2567061a3c7a9921f29b60e8ccfe706cd59a0ba2b4f9d99ae"},"schema_version":"1.0","source":{"id":"2608.06761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.06761","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2608.06761v1","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06761","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"VPP67HIG2LS2","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"VPP67HIG2LS2ESV2","created_at":"2026-08-10T01:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"VPP67HIG","created_at":"2026-08-10T01:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:a32e3bd9c42695368bbf901427925ac61f95423961d1f33b9d3d5bbbbb8e6a27","target":"graph","created_at":"2026-08-10T01:11:57Z","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/2608.06761/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A $q$-deformed real number, or ``$q$-real'', was defined by Morier-Genoud and the second author. When $x\\in\\mathbb{R}$ such that $x\\geq0$, the $q$-analogue $[x]_q$ is a power series with integer coefficients in one formal variable~$q$. In general a $q$-real is a formal Laurent series. The main goal of this paper is to study the coefficients of $q$-reals as functions on~$\\mathbb{R}$ and give a combinatorial interpretation of these coefficients. This allows us to prove a conjecture studied by several authors stating that the $q$-deformed golden ratio has the smallest radius of convergence among ","authors_text":"Pavel Etingof, Valentin Ovsienko","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:28:01Z","title":"Coefficients of $q$-real numbers: their combinatorial meaning and growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06761","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":"sha256:3d53f974882cfecae5fe34cdfde13fa8878d0e960f0cf0e42c3fe66b750efc61","target":"record","created_at":"2026-08-10T01:11:57Z","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":"22ec8060fe8ffb38328474c6191194752cd3b2fddfe38597311ed30d94b81374","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-08-07T03:28:01Z","title_canon_sha256":"1ef85e5cca867cf2567061a3c7a9921f29b60e8ccfe706cd59a0ba2b4f9d99ae"},"schema_version":"1.0","source":{"id":"2608.06761","kind":"arxiv","version":1}},"canonical_sha256":"abdfef9d06d2e5a24abacb02d7cfc756b499393f312f05eaa61d4563202fe7f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abdfef9d06d2e5a24abacb02d7cfc756b499393f312f05eaa61d4563202fe7f7","first_computed_at":"2026-08-10T01:11:57.713464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-10T01:11:57.713464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rR7YrL9+2me7QbuL6sjnKu6GE1J0JPnVvKNloh9sNa70FulvHJMoLNpwEeplqCEVlHoUCDU+riTgJpuFo6KDBA==","signature_status":"signed_v1","signed_at":"2026-08-10T01:11:57.715783Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.06761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d53f974882cfecae5fe34cdfde13fa8878d0e960f0cf0e42c3fe66b750efc61","sha256:a32e3bd9c42695368bbf901427925ac61f95423961d1f33b9d3d5bbbbb8e6a27"],"state_sha256":"1c70ff1c8eddcb750e0945d439f1319f86608befd91b15149e0a10e666a2fb9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdb1VF0cGWKvf8DGn1vFlzGE16NGabuUSuFsypNFHDHItbgJYThf1P71Tar7nrYDSgbPZFMHhTtWSb1Rx0GvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T04:17:42.029574Z","bundle_sha256":"a22998b4cbec9c397d301eed39467c6490d6b31d5275da87f0e8fabc0b6d38bc"}}