{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:NGYLKIU2NAKBMQYATEOYR5OGRL","short_pith_number":"pith:NGYLKIU2","schema_version":"1.0","canonical_sha256":"69b0b5229a6814164300991d88f5c68ac1d639a73ca3c6f6e4d45249fc855f8d","source":{"kind":"arxiv","id":"2406.17194","version":3},"attestation_state":"computed","paper":{"title":"Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Christian Ferko, Cian Luke Martin","submitted_at":"2024-06-25T00:43:02Z","abstract_excerpt":"We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\\mu \\nu}$ replaced by a unit-determinant metric $h_{\\mu \\nu} ( F )$ which is a function of the field strength $F_{\\mu \\nu}$, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric $h_{\\mu \\nu} ( F )$ produces identical equations of motion when it is coupled to the Maxwell theory via two 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":"2406.17194","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2024-06-25T00:43:02Z","cross_cats_sorted":["cond-mat.str-el","hep-ph","math-ph","math.MP"],"title_canon_sha256":"d9e3ac35952a3c5057ff5a7657aa06ce6fa4263ce5a25af008c06865939c5d61","abstract_canon_sha256":"6a89bfc7b2c51bf63b57b1af46c00ccb5f9b97a147c54e626b451f937f086ff2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:43.490357Z","signature_b64":"9YoE5MM+9ZrkqwEwQSrilPjh/XT3wWqpNIZZD1YQhGd/AuSVYAg+dhbs0ghOkkkx++BgWaQW4q1rTOG+7RzQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b0b5229a6814164300991d88f5c68ac1d639a73ca3c6f6e4d45249fc855f8d","last_reissued_at":"2026-06-23T03:13:43.489911Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:43.489911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Field-Dependent Metrics and Higher-Form Symmetries in Duality-Invariant Theories of Non-Linear Electrodynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","hep-ph","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Christian Ferko, Cian Luke Martin","submitted_at":"2024-06-25T00:43:02Z","abstract_excerpt":"We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\\mu \\nu}$ replaced by a unit-determinant metric $h_{\\mu \\nu} ( F )$ which is a function of the field strength $F_{\\mu \\nu}$, if and only if the theory enjoys electric-magnetic duality invariance. Among duality-invariant models, the Modified Maxwell (ModMax) theory is special because the associated metric $h_{\\mu \\nu} ( F )$ produces identical equations of motion when it is coupled to the Maxwell theory via two d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.17194","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/2406.17194/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":"2406.17194","created_at":"2026-06-23T03:13:43.489971+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.17194v3","created_at":"2026-06-23T03:13:43.489971+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.17194","created_at":"2026-06-23T03:13:43.489971+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGYLKIU2NAKB","created_at":"2026-06-23T03:13:43.489971+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGYLKIU2NAKBMQYA","created_at":"2026-06-23T03:13:43.489971+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGYLKIU2","created_at":"2026-06-23T03:13:43.489971+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.05081","citing_title":"Soliton Surfaces and the Geometry of Integrable Deformations of the $\\mathbb{CP}^{N-1}$ Model","ref_index":74,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL","json":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL.json","graph_json":"https://pith.science/api/pith-number/NGYLKIU2NAKBMQYATEOYR5OGRL/graph.json","events_json":"https://pith.science/api/pith-number/NGYLKIU2NAKBMQYATEOYR5OGRL/events.json","paper":"https://pith.science/paper/NGYLKIU2"},"agent_actions":{"view_html":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL","download_json":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL.json","view_paper":"https://pith.science/paper/NGYLKIU2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.17194&json=true","fetch_graph":"https://pith.science/api/pith-number/NGYLKIU2NAKBMQYATEOYR5OGRL/graph.json","fetch_events":"https://pith.science/api/pith-number/NGYLKIU2NAKBMQYATEOYR5OGRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL/action/storage_attestation","attest_author":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL/action/author_attestation","sign_citation":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL/action/citation_signature","submit_replication":"https://pith.science/pith/NGYLKIU2NAKBMQYATEOYR5OGRL/action/replication_record"}},"created_at":"2026-06-23T03:13:43.489971+00:00","updated_at":"2026-06-23T03:13:43.489971+00:00"}