{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:STFILUMB72WZPOGXY2NSQYNT7M","short_pith_number":"pith:STFILUMB","canonical_record":{"source":{"id":"1802.04976","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T07:41:04Z","cross_cats_sorted":[],"title_canon_sha256":"8c30fad048a3aa738f6b4be7c9adc9179a3398b404c8f171b23e4e133187668a","abstract_canon_sha256":"5a5acd4c2ce41d590f17bffe552005feebecdd29d7476c56caf6451903f6cbe2"},"schema_version":"1.0"},"canonical_sha256":"94ca85d181fead97b8d7c69b2861b3fb0e1139b64569c526314189f5b0fa8816","source":{"kind":"arxiv","id":"1802.04976","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04976","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04976v3","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04976","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"STFILUMB72WZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"STFILUMB72WZPOGX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"STFILUMB","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:STFILUMB72WZPOGXY2NSQYNT7M","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04976","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T07:41:04Z","cross_cats_sorted":[],"title_canon_sha256":"8c30fad048a3aa738f6b4be7c9adc9179a3398b404c8f171b23e4e133187668a","abstract_canon_sha256":"5a5acd4c2ce41d590f17bffe552005feebecdd29d7476c56caf6451903f6cbe2"},"schema_version":"1.0"},"canonical_sha256":"94ca85d181fead97b8d7c69b2861b3fb0e1139b64569c526314189f5b0fa8816","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:21.548296Z","signature_b64":"S2IfSUIdi0Z6p2GtZ6WOOYn63u40lhHDRvHJmRADcecpvzWL3eUWcgXagqFB9WCfd1Vtr16SVcTwHHnbmjUIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94ca85d181fead97b8d7c69b2861b3fb0e1139b64569c526314189f5b0fa8816","last_reissued_at":"2026-05-18T00:13:21.547678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:21.547678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04976","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":"2026-05-18T00:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"14tmZQsqg9XjZivkOL05hj3+OcWLs5mmIVAHgpEfY7EGdr1FnsURLwo+qGoBzbL68sCY19CjGC9B+NkrlL9/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:48:21.014642Z"},"content_sha256":"f0194f74aefe76b872a8ef8a8e24d5a8768708a1031f6c130694dc6ac6454f4a","schema_version":"1.0","event_id":"sha256:f0194f74aefe76b872a8ef8a8e24d5a8768708a1031f6c130694dc6ac6454f4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:STFILUMB72WZPOGXY2NSQYNT7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ian Kiming, Nadim Rustom","submitted_at":"2018-02-14T07:41:04Z","abstract_excerpt":"We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve defined over ${\\mathbb Q}$. We produce the lift by showing that the coefficients of the initial, weak eigenform (almost all) occur as traces of Frobenii in the Galois representation on the 4-torsion of the elliptic curve. The example is remarkable as the initial form is known not to be liftable to any characteristic 0 eigenform of level 1. We use th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04976","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":"2026-05-18T00:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BRDfHqvBGkmdv/PKljFaqzVULNq/u7ZK2bbFXrh+ISt+RHI6mSNqIx6jWOtyghGBcClAADaoYwotvXsW6ZCTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:48:21.015273Z"},"content_sha256":"c29fc97eb677d2600d220156218feaa074c54a182ddc91a8b9157ce0bd627c85","schema_version":"1.0","event_id":"sha256:c29fc97eb677d2600d220156218feaa074c54a182ddc91a8b9157ce0bd627c85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/STFILUMB72WZPOGXY2NSQYNT7M/bundle.json","state_url":"https://pith.science/pith/STFILUMB72WZPOGXY2NSQYNT7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/STFILUMB72WZPOGXY2NSQYNT7M/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":"2026-06-02T07:48:21Z","links":{"resolver":"https://pith.science/pith/STFILUMB72WZPOGXY2NSQYNT7M","bundle":"https://pith.science/pith/STFILUMB72WZPOGXY2NSQYNT7M/bundle.json","state":"https://pith.science/pith/STFILUMB72WZPOGXY2NSQYNT7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/STFILUMB72WZPOGXY2NSQYNT7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:STFILUMB72WZPOGXY2NSQYNT7M","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":"5a5acd4c2ce41d590f17bffe552005feebecdd29d7476c56caf6451903f6cbe2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T07:41:04Z","title_canon_sha256":"8c30fad048a3aa738f6b4be7c9adc9179a3398b404c8f171b23e4e133187668a"},"schema_version":"1.0","source":{"id":"1802.04976","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04976","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04976v3","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04976","created_at":"2026-05-18T00:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"STFILUMB72WZ","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"STFILUMB72WZPOGX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"STFILUMB","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:c29fc97eb677d2600d220156218feaa074c54a182ddc91a8b9157ce0bd627c85","target":"graph","created_at":"2026-05-18T00:13:21Z","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":"We work out a non-trivial example of lifting a so-called weak eigenform to a true, characteristic 0 eigenform. The weak eigenform is closely related to Ramanujan's tau function whereas the characteristic 0 eigenform is attached to an elliptic curve defined over ${\\mathbb Q}$. We produce the lift by showing that the coefficients of the initial, weak eigenform (almost all) occur as traces of Frobenii in the Galois representation on the 4-torsion of the elliptic curve. The example is remarkable as the initial form is known not to be liftable to any characteristic 0 eigenform of level 1. We use th","authors_text":"Ian Kiming, Nadim Rustom","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T07:41:04Z","title":"Dihedral Group, 4-Torsion on an Elliptic Curve, and a Peculiar Eigenform Modulo 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04976","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:f0194f74aefe76b872a8ef8a8e24d5a8768708a1031f6c130694dc6ac6454f4a","target":"record","created_at":"2026-05-18T00:13:21Z","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":"5a5acd4c2ce41d590f17bffe552005feebecdd29d7476c56caf6451903f6cbe2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-02-14T07:41:04Z","title_canon_sha256":"8c30fad048a3aa738f6b4be7c9adc9179a3398b404c8f171b23e4e133187668a"},"schema_version":"1.0","source":{"id":"1802.04976","kind":"arxiv","version":3}},"canonical_sha256":"94ca85d181fead97b8d7c69b2861b3fb0e1139b64569c526314189f5b0fa8816","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94ca85d181fead97b8d7c69b2861b3fb0e1139b64569c526314189f5b0fa8816","first_computed_at":"2026-05-18T00:13:21.547678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:21.547678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S2IfSUIdi0Z6p2GtZ6WOOYn63u40lhHDRvHJmRADcecpvzWL3eUWcgXagqFB9WCfd1Vtr16SVcTwHHnbmjUIDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:21.548296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04976","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0194f74aefe76b872a8ef8a8e24d5a8768708a1031f6c130694dc6ac6454f4a","sha256:c29fc97eb677d2600d220156218feaa074c54a182ddc91a8b9157ce0bd627c85"],"state_sha256":"d3424f7731e2acebc87565acd890489d61f42eae6118eab873933ab4fdf4278d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIHeHK20ZeMkdP/nKeZeNIvYedAQF6b0Mg7HfDDcNXAJCGWRe3qEeyk6kGck0QvDeWIpTYexQ0IYUcHSD1/mCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:48:21.018523Z","bundle_sha256":"8c0258b9b73275a8c9918df84ce3eba679e8ca9b4c05eda67e47f40e0f66900a"}}