{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:WA5RZC7Q7GO6H5F6RA6HJQZ7PH","short_pith_number":"pith:WA5RZC7Q","canonical_record":{"source":{"id":"2606.18110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T16:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"3bc41e275d3dfbeb4ade6000bae0011702ba1ac58ea2c6c5ad8fc6e081f2afe8","abstract_canon_sha256":"6fcfd4343763a4ad0ec73560cb8eb5725c4eaf758bd489b7eebfb123c4b47778"},"schema_version":"1.0"},"canonical_sha256":"b03b1c8bf0f99de3f4be883c74c33f79d1869029c60b41f8f9264c19fd4b0b2a","source":{"kind":"arxiv","id":"2606.18110","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18110","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18110v1","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18110","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"WA5RZC7Q7GO6","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_16","alias_value":"WA5RZC7Q7GO6H5F6","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_8","alias_value":"WA5RZC7Q","created_at":"2026-06-19T16:10:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:WA5RZC7Q7GO6H5F6RA6HJQZ7PH","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18110","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T16:15:28Z","cross_cats_sorted":[],"title_canon_sha256":"3bc41e275d3dfbeb4ade6000bae0011702ba1ac58ea2c6c5ad8fc6e081f2afe8","abstract_canon_sha256":"6fcfd4343763a4ad0ec73560cb8eb5725c4eaf758bd489b7eebfb123c4b47778"},"schema_version":"1.0"},"canonical_sha256":"b03b1c8bf0f99de3f4be883c74c33f79d1869029c60b41f8f9264c19fd4b0b2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:48.728856Z","signature_b64":"PA9dGATltZQpAlL8Tx9q+9gjdlbIJlWHrjsMolaCGTeucvSgHlaMeeHUcVcBsEciOiTkXVBDgNceciGeVKtMDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b03b1c8bf0f99de3f4be883c74c33f79d1869029c60b41f8f9264c19fd4b0b2a","last_reissued_at":"2026-06-19T16:10:48.728512Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:48.728512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18110","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":"2026-06-19T16:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJrrMqmREcwW3ZcrVgsllAN2crBy+ahzQLDj0qkTNpvvoMyXNH7JnZMn3uXL1QNn9Blk5osCCf9Yj5Sj3GVkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:43:19.841593Z"},"content_sha256":"393703d15b844771a4e6cd633d1e446e9ec943032f04d4f0f4d0043741f2e60b","schema_version":"1.0","event_id":"sha256:393703d15b844771a4e6cd633d1e446e9ec943032f04d4f0f4d0043741f2e60b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:WA5RZC7Q7GO6H5F6RA6HJQZ7PH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recursions for Mock Theta Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Martin Raum, Matthew Ortiz, Olav K. Richter","submitted_at":"2026-06-16T16:15:28Z","abstract_excerpt":"We establish weighted recursions for the coefficients of Ramanujan's third order mock theta functions $f$ and $\\omega$. Specifically, we apply a holomorphic projection operator to vector-valued Rankin-Cohen brackets of completed mock theta series and their shadows. By employing a vector-valued framework, we exploit the vanishing of certain spaces of vector-valued cusp forms. Our proof is AI-assisted and prioritizes accessibility, allowing for straightforward customization and replication within the broader research community."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18110","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/2606.18110/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":"2026-06-19T16:10:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R8ZYa20h7gm+7lMRIvDbgXNT+wnekWik7dn5eofjDaYxq/1CPnhpkSNhwjizZMY/n/xbeuLjFK4v6smuCpxDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:43:19.841975Z"},"content_sha256":"05ac6cc40ee7c62a66f5ce879db91679f358c2a0d98d66864b0c6967aee8ce85","schema_version":"1.0","event_id":"sha256:05ac6cc40ee7c62a66f5ce879db91679f358c2a0d98d66864b0c6967aee8ce85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/bundle.json","state_url":"https://pith.science/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/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":"2026-06-25T05:43:19Z","links":{"resolver":"https://pith.science/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH","bundle":"https://pith.science/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/bundle.json","state":"https://pith.science/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WA5RZC7Q7GO6H5F6RA6HJQZ7PH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WA5RZC7Q7GO6H5F6RA6HJQZ7PH","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":"6fcfd4343763a4ad0ec73560cb8eb5725c4eaf758bd489b7eebfb123c4b47778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T16:15:28Z","title_canon_sha256":"3bc41e275d3dfbeb4ade6000bae0011702ba1ac58ea2c6c5ad8fc6e081f2afe8"},"schema_version":"1.0","source":{"id":"2606.18110","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18110","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18110v1","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18110","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"WA5RZC7Q7GO6","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_16","alias_value":"WA5RZC7Q7GO6H5F6","created_at":"2026-06-19T16:10:48Z"},{"alias_kind":"pith_short_8","alias_value":"WA5RZC7Q","created_at":"2026-06-19T16:10:48Z"}],"graph_snapshots":[{"event_id":"sha256:05ac6cc40ee7c62a66f5ce879db91679f358c2a0d98d66864b0c6967aee8ce85","target":"graph","created_at":"2026-06-19T16:10:48Z","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/2606.18110/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish weighted recursions for the coefficients of Ramanujan's third order mock theta functions $f$ and $\\omega$. Specifically, we apply a holomorphic projection operator to vector-valued Rankin-Cohen brackets of completed mock theta series and their shadows. By employing a vector-valued framework, we exploit the vanishing of certain spaces of vector-valued cusp forms. Our proof is AI-assisted and prioritizes accessibility, allowing for straightforward customization and replication within the broader research community.","authors_text":"Martin Raum, Matthew Ortiz, Olav K. Richter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T16:15:28Z","title":"Recursions for Mock Theta Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18110","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":"sha256:393703d15b844771a4e6cd633d1e446e9ec943032f04d4f0f4d0043741f2e60b","target":"record","created_at":"2026-06-19T16:10:48Z","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":"6fcfd4343763a4ad0ec73560cb8eb5725c4eaf758bd489b7eebfb123c4b47778","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-16T16:15:28Z","title_canon_sha256":"3bc41e275d3dfbeb4ade6000bae0011702ba1ac58ea2c6c5ad8fc6e081f2afe8"},"schema_version":"1.0","source":{"id":"2606.18110","kind":"arxiv","version":1}},"canonical_sha256":"b03b1c8bf0f99de3f4be883c74c33f79d1869029c60b41f8f9264c19fd4b0b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b03b1c8bf0f99de3f4be883c74c33f79d1869029c60b41f8f9264c19fd4b0b2a","first_computed_at":"2026-06-19T16:10:48.728512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:48.728512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PA9dGATltZQpAlL8Tx9q+9gjdlbIJlWHrjsMolaCGTeucvSgHlaMeeHUcVcBsEciOiTkXVBDgNceciGeVKtMDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:48.728856Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18110","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:393703d15b844771a4e6cd633d1e446e9ec943032f04d4f0f4d0043741f2e60b","sha256:05ac6cc40ee7c62a66f5ce879db91679f358c2a0d98d66864b0c6967aee8ce85"],"state_sha256":"6a37cd5a1be9d4b601c995c54ce06446f3a49c5d6bb8dce6d64020a569ed1cc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NvTtTPgMz315JaqKOnfJCdg3zRQHTPz932bhcT+XYuOAwnnwvrduwT+dKl5Cob52u+VBW9l+c2gG84kTmOYbAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:43:19.844062Z","bundle_sha256":"1d2973e17151630dbdee9b30b665182ec248414df763cf039fb0915bd71401de"}}