{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VEE7MQ2UXNJCRVD2WNVXKDWS6M","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":"cfce850539b19f8ff30c4239c6dc19323149f27b4ceda8d10d0801b2735b328f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-10T16:37:19Z","title_canon_sha256":"f4c0e7245bf0235a39554d07644f278ec45076e123793004a781533c03b11f7e"},"schema_version":"1.0","source":{"id":"1912.04804","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.04804","created_at":"2026-07-05T01:12:30Z"},{"alias_kind":"arxiv_version","alias_value":"1912.04804v3","created_at":"2026-07-05T01:12:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.04804","created_at":"2026-07-05T01:12:30Z"},{"alias_kind":"pith_short_12","alias_value":"VEE7MQ2UXNJC","created_at":"2026-07-05T01:12:30Z"},{"alias_kind":"pith_short_16","alias_value":"VEE7MQ2UXNJCRVD2","created_at":"2026-07-05T01:12:30Z"},{"alias_kind":"pith_short_8","alias_value":"VEE7MQ2U","created_at":"2026-07-05T01:12:30Z"}],"graph_snapshots":[{"event_id":"sha256:a24fc4f7ae5e8c51406dac30d5b7f9f40d8b2c1f571bfd7782d0bed7be0a56f1","target":"graph","created_at":"2026-07-05T01:12:30Z","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/1912.04804/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Costa et al. [Phys. Rev. Lett. 123, 151601 (2019)] recently gave a general solution to the anomaly equations for $n$ charges in a $U(1)$ gauge theory. `Primitive' solutions of chiral fermion charges were parameterised and it was shown how operations performed upon them (concatenation with other primitive solutions and with vector-like solutions) yield the general solution. We show that the ingenious methods used there have a simple geometric interpretation, corresponding to elementary constructions in number theory. Viewing them in this context allows the fully general solution to be written d","authors_text":"B. C. Allanach, Ben Gripaios, Joseph Tooby-Smith","cross_cats":["hep-ph","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-10T16:37:19Z","title":"Geometric General Solution to the $U(1)$ Anomaly Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.04804","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":"sha256:4ec9ec17115aa92ced4a2aa2f8f1dcb3393916a5acb600ad61a06bac447e6878","target":"record","created_at":"2026-07-05T01:12:30Z","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":"cfce850539b19f8ff30c4239c6dc19323149f27b4ceda8d10d0801b2735b328f","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-10T16:37:19Z","title_canon_sha256":"f4c0e7245bf0235a39554d07644f278ec45076e123793004a781533c03b11f7e"},"schema_version":"1.0","source":{"id":"1912.04804","kind":"arxiv","version":3}},"canonical_sha256":"a909f64354bb5228d47ab36b750ed2f30372271265b7e6f5d3d02513d345b202","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a909f64354bb5228d47ab36b750ed2f30372271265b7e6f5d3d02513d345b202","first_computed_at":"2026-07-05T01:12:30.293342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:12:30.293342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZdNHmJjm+hV0tiD4wX/a+lVNSAFYHz+Zmn0TCkWgZLluPnUIZcAcUajwF504AgW5IiY1LiIhPw1khDJ6x6UDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:12:30.293807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.04804","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ec9ec17115aa92ced4a2aa2f8f1dcb3393916a5acb600ad61a06bac447e6878","sha256:a24fc4f7ae5e8c51406dac30d5b7f9f40d8b2c1f571bfd7782d0bed7be0a56f1"],"state_sha256":"d0d179f7da37fc7ba0a3a336f2e97ceca54040aebf353492c1556da5812b3316"}