{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KRONFUXUVUJK27Z3GQZ65RTYE5","short_pith_number":"pith:KRONFUXU","canonical_record":{"source":{"id":"2607.25173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T00:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"6852d9044010b84a74872d99c3bafefed483343c896d9965fe0d26822fbabc93","abstract_canon_sha256":"e805753e26bc2a303c682eae180311c4ec97b22155c645d10416387390423ac1"},"schema_version":"1.0"},"canonical_sha256":"545cd2d2f4ad12ad7f3b3433eec67827719bc07020d6dc0b30df5cc3958d8cb8","source":{"kind":"arxiv","id":"2607.25173","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25173","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25173v1","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25173","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"KRONFUXUVUJK","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_16","alias_value":"KRONFUXUVUJK27Z3","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_8","alias_value":"KRONFUXU","created_at":"2026-07-29T00:25:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KRONFUXUVUJK27Z3GQZ65RTYE5","target":"record","payload":{"canonical_record":{"source":{"id":"2607.25173","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T00:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"6852d9044010b84a74872d99c3bafefed483343c896d9965fe0d26822fbabc93","abstract_canon_sha256":"e805753e26bc2a303c682eae180311c4ec97b22155c645d10416387390423ac1"},"schema_version":"1.0"},"canonical_sha256":"545cd2d2f4ad12ad7f3b3433eec67827719bc07020d6dc0b30df5cc3958d8cb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-29T00:25:06.760794Z","signature_b64":"uuYMgqDGgtJs4MC5IRhkasnH9KnaEOnePp7dg6tJ/Md7m7i/lzX2zsk5dRRBe1121glV0AIOe1NmenYs908DAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"545cd2d2f4ad12ad7f3b3433eec67827719bc07020d6dc0b30df5cc3958d8cb8","last_reissued_at":"2026-07-29T00:25:06.759947Z","signature_status":"signed_v1","first_computed_at":"2026-07-29T00:25:06.759947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.25173","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":"2026-07-29T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdSC+0mj8//2aSPExE8jGiZQtURtvSjq0MHvDXBHtVIw+54Y0vvarUIxy5xxJNGD3CACpmTLcwO67KCfyqYICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:57:58.676575Z"},"content_sha256":"7423a9880cca19c35e900cd95cc57083b6eb57645de806fcc7bac614acb88c8e","schema_version":"1.0","event_id":"sha256:7423a9880cca19c35e900cd95cc57083b6eb57645de806fcc7bac614acb88c8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KRONFUXUVUJK27Z3GQZ65RTYE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Explicit Hypergeometric Modularity Method III","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Brian Grove, Esme Rosen, Fang-Ting Tu, Ling Long","submitted_at":"2026-07-28T00:54:30Z","abstract_excerpt":"We refine the Explicit Hypergeometric Modularity Method (EHMM) and develop a variant that applies to a broader class of hypergeometric data. As an application, we establish the modularity of hypergeometric Galois representations arising from length-$4$ data that are not necessarily defined over $\\mathbb{Q}$. We also use this method to give explicit constructions of nine modular forms associated with hypergeometric rigid Calabi-Yau threefolds conjectured to be modular by Rodriguez-Villegas. The modularity of these threefolds was first proved by Long-Tu-Yui-Zudilin using a different approach bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25173","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/2607.25173/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":"2026-07-29T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tp8mTz/SenwqGQiVxMZ3XLPQKwLuagHpYY/4p+kIqeTvDJX4410XzisxCj806cq2QzmeJujHmyKla3rIY/UwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:57:58.677348Z"},"content_sha256":"993a17c09e0ae7f9ef2bed4a25d2f8cbba1914c69d93065f91cb91b8f54ac712","schema_version":"1.0","event_id":"sha256:993a17c09e0ae7f9ef2bed4a25d2f8cbba1914c69d93065f91cb91b8f54ac712"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/bundle.json","state_url":"https://pith.science/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/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":"2026-08-13T01:57:58Z","links":{"resolver":"https://pith.science/pith/KRONFUXUVUJK27Z3GQZ65RTYE5","bundle":"https://pith.science/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/bundle.json","state":"https://pith.science/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KRONFUXUVUJK27Z3GQZ65RTYE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KRONFUXUVUJK27Z3GQZ65RTYE5","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":"e805753e26bc2a303c682eae180311c4ec97b22155c645d10416387390423ac1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T00:54:30Z","title_canon_sha256":"6852d9044010b84a74872d99c3bafefed483343c896d9965fe0d26822fbabc93"},"schema_version":"1.0","source":{"id":"2607.25173","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25173","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25173v1","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25173","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"KRONFUXUVUJK","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_16","alias_value":"KRONFUXUVUJK27Z3","created_at":"2026-07-29T00:25:06Z"},{"alias_kind":"pith_short_8","alias_value":"KRONFUXU","created_at":"2026-07-29T00:25:06Z"}],"graph_snapshots":[{"event_id":"sha256:993a17c09e0ae7f9ef2bed4a25d2f8cbba1914c69d93065f91cb91b8f54ac712","target":"graph","created_at":"2026-07-29T00:25:06Z","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/2607.25173/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We refine the Explicit Hypergeometric Modularity Method (EHMM) and develop a variant that applies to a broader class of hypergeometric data. As an application, we establish the modularity of hypergeometric Galois representations arising from length-$4$ data that are not necessarily defined over $\\mathbb{Q}$. We also use this method to give explicit constructions of nine modular forms associated with hypergeometric rigid Calabi-Yau threefolds conjectured to be modular by Rodriguez-Villegas. The modularity of these threefolds was first proved by Long-Tu-Yui-Zudilin using a different approach bas","authors_text":"Brian Grove, Esme Rosen, Fang-Ting Tu, Ling Long","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T00:54:30Z","title":"The Explicit Hypergeometric Modularity Method III"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25173","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":"sha256:7423a9880cca19c35e900cd95cc57083b6eb57645de806fcc7bac614acb88c8e","target":"record","created_at":"2026-07-29T00:25:06Z","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":"e805753e26bc2a303c682eae180311c4ec97b22155c645d10416387390423ac1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-28T00:54:30Z","title_canon_sha256":"6852d9044010b84a74872d99c3bafefed483343c896d9965fe0d26822fbabc93"},"schema_version":"1.0","source":{"id":"2607.25173","kind":"arxiv","version":1}},"canonical_sha256":"545cd2d2f4ad12ad7f3b3433eec67827719bc07020d6dc0b30df5cc3958d8cb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"545cd2d2f4ad12ad7f3b3433eec67827719bc07020d6dc0b30df5cc3958d8cb8","first_computed_at":"2026-07-29T00:25:06.759947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:25:06.759947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uuYMgqDGgtJs4MC5IRhkasnH9KnaEOnePp7dg6tJ/Md7m7i/lzX2zsk5dRRBe1121glV0AIOe1NmenYs908DAw==","signature_status":"signed_v1","signed_at":"2026-07-29T00:25:06.760794Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25173","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7423a9880cca19c35e900cd95cc57083b6eb57645de806fcc7bac614acb88c8e","sha256:993a17c09e0ae7f9ef2bed4a25d2f8cbba1914c69d93065f91cb91b8f54ac712"],"state_sha256":"c6ac14ccab3a07a4a3fab8f4ec707158fd27e1a4ed5c7630c3a60a9d3b9e0de8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4ps/CTEqBqUbbUJsGAAM11dlGu5xSFFirrRSwEVEYz6GVQHozFPcAkgznHUrwj9w5RmGf6pOur4g6Zuw5DgCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:57:58.684305Z","bundle_sha256":"669be45b3e632f3421095ed3098502e6a52373aabd76de2422ad39a0476bac7f"}}