{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VEE7MQ2UXNJCRVD2WNVXKDWS6M","short_pith_number":"pith:VEE7MQ2U","schema_version":"1.0","canonical_sha256":"a909f64354bb5228d47ab36b750ed2f30372271265b7e6f5d3d02513d345b202","source":{"kind":"arxiv","id":"1912.04804","version":3},"attestation_state":"computed","paper":{"title":"Geometric General Solution to the $U(1)$ Anomaly Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"B. C. Allanach, Ben Gripaios, Joseph Tooby-Smith","submitted_at":"2019-12-10T16:37:19Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1912.04804","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-10T16:37:19Z","cross_cats_sorted":["hep-ph","math-ph","math.MP"],"title_canon_sha256":"f4c0e7245bf0235a39554d07644f278ec45076e123793004a781533c03b11f7e","abstract_canon_sha256":"cfce850539b19f8ff30c4239c6dc19323149f27b4ceda8d10d0801b2735b328f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:12:30.293807Z","signature_b64":"8ZdNHmJjm+hV0tiD4wX/a+lVNSAFYHz+Zmn0TCkWgZLluPnUIZcAcUajwF504AgW5IiY1LiIhPw1khDJ6x6UDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a909f64354bb5228d47ab36b750ed2f30372271265b7e6f5d3d02513d345b202","last_reissued_at":"2026-07-05T01:12:30.293342Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:12:30.293342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric General Solution to the $U(1)$ Anomaly Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"B. C. Allanach, Ben Gripaios, Joseph Tooby-Smith","submitted_at":"2019-12-10T16:37:19Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.04804","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.04804/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1912.04804","created_at":"2026-07-05T01:12:30.293398+00:00"},{"alias_kind":"arxiv_version","alias_value":"1912.04804v3","created_at":"2026-07-05T01:12:30.293398+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.04804","created_at":"2026-07-05T01:12:30.293398+00:00"},{"alias_kind":"pith_short_12","alias_value":"VEE7MQ2UXNJC","created_at":"2026-07-05T01:12:30.293398+00:00"},{"alias_kind":"pith_short_16","alias_value":"VEE7MQ2UXNJCRVD2","created_at":"2026-07-05T01:12:30.293398+00:00"},{"alias_kind":"pith_short_8","alias_value":"VEE7MQ2U","created_at":"2026-07-05T01:12:30.293398+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.09860","citing_title":"More varieties of 4-d gauge theories: product representations","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M","json":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M.json","graph_json":"https://pith.science/api/pith-number/VEE7MQ2UXNJCRVD2WNVXKDWS6M/graph.json","events_json":"https://pith.science/api/pith-number/VEE7MQ2UXNJCRVD2WNVXKDWS6M/events.json","paper":"https://pith.science/paper/VEE7MQ2U"},"agent_actions":{"view_html":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M","download_json":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M.json","view_paper":"https://pith.science/paper/VEE7MQ2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1912.04804&json=true","fetch_graph":"https://pith.science/api/pith-number/VEE7MQ2UXNJCRVD2WNVXKDWS6M/graph.json","fetch_events":"https://pith.science/api/pith-number/VEE7MQ2UXNJCRVD2WNVXKDWS6M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M/action/storage_attestation","attest_author":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M/action/author_attestation","sign_citation":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M/action/citation_signature","submit_replication":"https://pith.science/pith/VEE7MQ2UXNJCRVD2WNVXKDWS6M/action/replication_record"}},"created_at":"2026-07-05T01:12:30.293398+00:00","updated_at":"2026-07-05T01:12:30.293398+00:00"}