{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6KXW73APP4DHWBD7L5BFPH4746","short_pith_number":"pith:6KXW73AP","canonical_record":{"source":{"id":"1811.03887","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-09T12:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"b60d9e55cb6c81b30185e2a8fb1fc7d310cb326905c4c9627a8dfc1666feec07","abstract_canon_sha256":"3459208c80e622657a9d49a9f6c4c9a277e4add63282a7ecccae0951ff4f7b26"},"schema_version":"1.0"},"canonical_sha256":"f2af6fec0f7f067b047f5f42579f9fe78981a39e9b3884ff1e1d4a15c6cd2894","source":{"kind":"arxiv","id":"1811.03887","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03887","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03887v3","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03887","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"6KXW73APP4DH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KXW73APP4DHWBD7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KXW73AP","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6KXW73APP4DHWBD7L5BFPH4746","target":"record","payload":{"canonical_record":{"source":{"id":"1811.03887","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-09T12:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"b60d9e55cb6c81b30185e2a8fb1fc7d310cb326905c4c9627a8dfc1666feec07","abstract_canon_sha256":"3459208c80e622657a9d49a9f6c4c9a277e4add63282a7ecccae0951ff4f7b26"},"schema_version":"1.0"},"canonical_sha256":"f2af6fec0f7f067b047f5f42579f9fe78981a39e9b3884ff1e1d4a15c6cd2894","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:06.426974Z","signature_b64":"XY78TMcZyFN5ZOVmkVS1/AEGzEpf5HEx5iHhIYExtaGWSzrum00W/6NNN3eFG1CbYRl1O88mkspj1QrKkTe5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2af6fec0f7f067b047f5f42579f9fe78981a39e9b3884ff1e1d4a15c6cd2894","last_reissued_at":"2026-05-17T23:48:06.426605Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:06.426605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.03887","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FYjrVaGnoJ0uKKrmav9yqWZtdH2Ffb//PrNqBEASJWm1VJN1OWf+jX+3bQwuOvb4njtLguLSANEbd7bvsDsHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:57:06.235412Z"},"content_sha256":"cb8e0d9e2e1213550b983dc37bcf583339138caf17e71043accee91c89453a9e","schema_version":"1.0","event_id":"sha256:cb8e0d9e2e1213550b983dc37bcf583339138caf17e71043accee91c89453a9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6KXW73APP4DHWBD7L5BFPH4746","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hecke eigenform and double Eisenstein series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Koji Tasaka","submitted_at":"2018-11-09T12:53:44Z","abstract_excerpt":"Cusp forms for the full modular group can be written as linear combination of double Eisenstein series introduced by Gangl, Kaneko and Zagier. We give an explicit formula for decomposing a Hecke eigenform into double Eisenstein series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03887","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2ZzY4zZGtp5OQTt8TXDecc8PwFtHteDRw+9HneI6Tl6em5W7gTD88rymmu++/LnwYY7ltfwH3M12hlMH0ORDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:57:06.235770Z"},"content_sha256":"ac6a0d620ee2ec54d71cb86142d60e94cbff53d550d0ac4e0f90da96891e8c22","schema_version":"1.0","event_id":"sha256:ac6a0d620ee2ec54d71cb86142d60e94cbff53d550d0ac4e0f90da96891e8c22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KXW73APP4DHWBD7L5BFPH4746/bundle.json","state_url":"https://pith.science/pith/6KXW73APP4DHWBD7L5BFPH4746/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KXW73APP4DHWBD7L5BFPH4746/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":"2026-06-10T19:57:06Z","links":{"resolver":"https://pith.science/pith/6KXW73APP4DHWBD7L5BFPH4746","bundle":"https://pith.science/pith/6KXW73APP4DHWBD7L5BFPH4746/bundle.json","state":"https://pith.science/pith/6KXW73APP4DHWBD7L5BFPH4746/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KXW73APP4DHWBD7L5BFPH4746/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6KXW73APP4DHWBD7L5BFPH4746","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":"3459208c80e622657a9d49a9f6c4c9a277e4add63282a7ecccae0951ff4f7b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-09T12:53:44Z","title_canon_sha256":"b60d9e55cb6c81b30185e2a8fb1fc7d310cb326905c4c9627a8dfc1666feec07"},"schema_version":"1.0","source":{"id":"1811.03887","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03887","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03887v3","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03887","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"6KXW73APP4DH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6KXW73APP4DHWBD7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6KXW73AP","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:ac6a0d620ee2ec54d71cb86142d60e94cbff53d550d0ac4e0f90da96891e8c22","target":"graph","created_at":"2026-05-17T23:48:06Z","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"},"paper":{"abstract_excerpt":"Cusp forms for the full modular group can be written as linear combination of double Eisenstein series introduced by Gangl, Kaneko and Zagier. We give an explicit formula for decomposing a Hecke eigenform into double Eisenstein series.","authors_text":"Koji Tasaka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-09T12:53:44Z","title":"Hecke eigenform and double Eisenstein series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03887","kind":"arxiv","version":3},"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:cb8e0d9e2e1213550b983dc37bcf583339138caf17e71043accee91c89453a9e","target":"record","created_at":"2026-05-17T23:48:06Z","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":"3459208c80e622657a9d49a9f6c4c9a277e4add63282a7ecccae0951ff4f7b26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-11-09T12:53:44Z","title_canon_sha256":"b60d9e55cb6c81b30185e2a8fb1fc7d310cb326905c4c9627a8dfc1666feec07"},"schema_version":"1.0","source":{"id":"1811.03887","kind":"arxiv","version":3}},"canonical_sha256":"f2af6fec0f7f067b047f5f42579f9fe78981a39e9b3884ff1e1d4a15c6cd2894","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2af6fec0f7f067b047f5f42579f9fe78981a39e9b3884ff1e1d4a15c6cd2894","first_computed_at":"2026-05-17T23:48:06.426605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.426605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XY78TMcZyFN5ZOVmkVS1/AEGzEpf5HEx5iHhIYExtaGWSzrum00W/6NNN3eFG1CbYRl1O88mkspj1QrKkTe5AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.426974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03887","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb8e0d9e2e1213550b983dc37bcf583339138caf17e71043accee91c89453a9e","sha256:ac6a0d620ee2ec54d71cb86142d60e94cbff53d550d0ac4e0f90da96891e8c22"],"state_sha256":"a846a237799aedfd3f7ae51f06285ca4eb0289759f959220984dcc71d1e048ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pLyXvRRVzPkQpe9aX6od7CNAK8g0+PyYK9EG56kH1dWMzCAeZIwCxV8XEit1mAo+NwjNUEbkOL1vazfnsYyfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:57:06.237759Z","bundle_sha256":"3c62e83d658dc1a910827c6de3fe3ecec2851cfbb730c3cef197f5ff12c98131"}}