{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EKCLI2JJBEMF2YYZYTFQY7Z6TO","short_pith_number":"pith:EKCLI2JJ","canonical_record":{"source":{"id":"2607.27702","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-30T05:38:51Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"efa9852ea23fc09bd122b34e32e56e97828dd68644c02d35d8704b750f47e1ac","abstract_canon_sha256":"4c5928d9a66aea3b74ea5b3d643eabaa9a7b07d4a39e0c330b6e714d5336efbd"},"schema_version":"1.0"},"canonical_sha256":"2284b4692909185d6319c4cb0c7f3e9b91def013f176c6b4c43d7460e2183ffd","source":{"kind":"arxiv","id":"2607.27702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27702","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27702v1","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27702","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"EKCLI2JJBEMF","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"EKCLI2JJBEMF2YYZ","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"EKCLI2JJ","created_at":"2026-07-31T01:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EKCLI2JJBEMF2YYZYTFQY7Z6TO","target":"record","payload":{"canonical_record":{"source":{"id":"2607.27702","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-30T05:38:51Z","cross_cats_sorted":["math.CO","math.QA"],"title_canon_sha256":"efa9852ea23fc09bd122b34e32e56e97828dd68644c02d35d8704b750f47e1ac","abstract_canon_sha256":"4c5928d9a66aea3b74ea5b3d643eabaa9a7b07d4a39e0c330b6e714d5336efbd"},"schema_version":"1.0"},"canonical_sha256":"2284b4692909185d6319c4cb0c7f3e9b91def013f176c6b4c43d7460e2183ffd","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2284b4692909185d6319c4cb0c7f3e9b91def013f176c6b4c43d7460e2183ffd","last_reissued_at":"2026-07-31T01:29:55.435473Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:29:55.435473Z"},"source_kind":"arxiv","source_id":"2607.27702","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":"2026-07-31T01:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d+Dwt3jvVmL8HBhURR0zWAKi0tzPSOV53926gYu4AC8xihnp1lZoUyt2kBa/QphN4lYPuoIe9CGV2wluFOUCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:43:08.274666Z"},"content_sha256":"05245406ab0417bf75b6100e5d02cfdcf966046b11c503b317a227ac13167b4b","schema_version":"1.0","event_id":"sha256:05245406ab0417bf75b6100e5d02cfdcf966046b11c503b317a227ac13167b4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EKCLI2JJBEMF2YYZYTFQY7Z6TO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schur Eisenstein series and Schur MacMahon series","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.NT","authors_text":"Henrik Bachmann, Jinbo Yu","submitted_at":"2026-07-30T05:38:51Z","abstract_excerpt":"We introduce and study two partition-indexed families of quasimodular forms obtained from Schur functions: Schur Eisenstein series and Schur MacMahon series. An explicit transition between them can be interpreted as a convolution in a Fa\\`a di Bruno Hopf algebra of symmetric functions. We discuss the classical sl2-action and prove that Schur Eisenstein series for partitions with parts of size at most 3 give a basis for quasimodular forms. Further, we conjecture that the Schur MacMahon series span all quasimodular forms with integral coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27702","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/2607.27702/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":"2026-07-31T01:29:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SiHlH0cp0UJNuuJTiImOT8PeFojUDBgnu9+nPWgPwoGzLnYdqZaUZ8V40GFDOS2QRc5qeDX4s9kHbgnWUe7/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T11:43:08.275258Z"},"content_sha256":"788e03ba1460a6db760ad0eabcb6dafb4552b708761274c17af3008a68761079","schema_version":"1.0","event_id":"sha256:788e03ba1460a6db760ad0eabcb6dafb4552b708761274c17af3008a68761079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/bundle.json","state_url":"https://pith.science/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/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":"2026-08-11T11:43:08Z","links":{"resolver":"https://pith.science/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO","bundle":"https://pith.science/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/bundle.json","state":"https://pith.science/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKCLI2JJBEMF2YYZYTFQY7Z6TO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EKCLI2JJBEMF2YYZYTFQY7Z6TO","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":"4c5928d9a66aea3b74ea5b3d643eabaa9a7b07d4a39e0c330b6e714d5336efbd","cross_cats_sorted":["math.CO","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-30T05:38:51Z","title_canon_sha256":"efa9852ea23fc09bd122b34e32e56e97828dd68644c02d35d8704b750f47e1ac"},"schema_version":"1.0","source":{"id":"2607.27702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27702","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27702v1","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27702","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_12","alias_value":"EKCLI2JJBEMF","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"EKCLI2JJBEMF2YYZ","created_at":"2026-07-31T01:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"EKCLI2JJ","created_at":"2026-07-31T01:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:788e03ba1460a6db760ad0eabcb6dafb4552b708761274c17af3008a68761079","target":"graph","created_at":"2026-07-31T01:29:55Z","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/2607.27702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce and study two partition-indexed families of quasimodular forms obtained from Schur functions: Schur Eisenstein series and Schur MacMahon series. An explicit transition between them can be interpreted as a convolution in a Fa\\`a di Bruno Hopf algebra of symmetric functions. We discuss the classical sl2-action and prove that Schur Eisenstein series for partitions with parts of size at most 3 give a basis for quasimodular forms. Further, we conjecture that the Schur MacMahon series span all quasimodular forms with integral coefficients.","authors_text":"Henrik Bachmann, Jinbo Yu","cross_cats":["math.CO","math.QA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-30T05:38:51Z","title":"Schur Eisenstein series and Schur MacMahon series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27702","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":"sha256:05245406ab0417bf75b6100e5d02cfdcf966046b11c503b317a227ac13167b4b","target":"record","created_at":"2026-07-31T01:29:55Z","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":"4c5928d9a66aea3b74ea5b3d643eabaa9a7b07d4a39e0c330b6e714d5336efbd","cross_cats_sorted":["math.CO","math.QA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2026-07-30T05:38:51Z","title_canon_sha256":"efa9852ea23fc09bd122b34e32e56e97828dd68644c02d35d8704b750f47e1ac"},"schema_version":"1.0","source":{"id":"2607.27702","kind":"arxiv","version":1}},"canonical_sha256":"2284b4692909185d6319c4cb0c7f3e9b91def013f176c6b4c43d7460e2183ffd","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2284b4692909185d6319c4cb0c7f3e9b91def013f176c6b4c43d7460e2183ffd","first_computed_at":"2026-07-31T01:29:55.435473Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:29:55.435473Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05245406ab0417bf75b6100e5d02cfdcf966046b11c503b317a227ac13167b4b","sha256:788e03ba1460a6db760ad0eabcb6dafb4552b708761274c17af3008a68761079"],"state_sha256":"5eed7a32683981b62106df2f87f7013e51910b2d5c18393247874cfeb615ba30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WvM97C1z9l1+POer/mUtI6tDUapuQm2jrB76os3QlhWTsXscVtOsW2Ptu8uvt5NOyxGb5j2usRobfp20h7CWDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T11:43:08.281144Z","bundle_sha256":"7938cdf39e13417dc31f090ba35b279b8e58cc364850fe7d7494180957cfcdfc"}}