{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:A736VMJC55RXQAYFFR6EEX667D","short_pith_number":"pith:A736VMJC","schema_version":"1.0","canonical_sha256":"07f7eab122ef637803052c7c425fdef8fd544af8b4c2cbf856d1b506c09340d4","source":{"kind":"arxiv","id":"1905.06805","version":2},"attestation_state":"computed","paper":{"title":"A duality of fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Wen-Du Li, Wu-Sheng Dai","submitted_at":"2019-05-08T20:12:02Z","abstract_excerpt":"It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different fields may have different numbers of dual fields, e.g., the free field and the $\\phi^{4}$-field are self-dual, the $\\phi^{n}$-field has one dual field, a field with an $n$-term polynomial potential has $n+1$ dual fields, and a field with a nonpolynomial potential may have infinite number of dual fields. All fields which are dual to each other form a duality f"},"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":"1905.06805","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2019-05-08T20:12:02Z","cross_cats_sorted":[],"title_canon_sha256":"30b4d97ccbb5730c4462567f8860f92e838de812222e6303ef6f01a151c51859","abstract_canon_sha256":"412322d32a6cd8b43bda059af1116943f85e677b51dd04469ed6b5fc4b087cf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:51.457533Z","signature_b64":"2P5fdK7CZlhLsu3kqZbFyGKIeyExQhseW7ANSNDWsAVGhKTSh3DoKf8FyICb3oClqqfvF5aoxKqE6ldO9u6eDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"07f7eab122ef637803052c7c425fdef8fd544af8b4c2cbf856d1b506c09340d4","last_reissued_at":"2026-05-17T23:45:51.456960Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:51.456960Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A duality of fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Wen-Du Li, Wu-Sheng Dai","submitted_at":"2019-05-08T20:12:02Z","abstract_excerpt":"It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different fields may have different numbers of dual fields, e.g., the free field and the $\\phi^{4}$-field are self-dual, the $\\phi^{n}$-field has one dual field, a field with an $n$-term polynomial potential has $n+1$ dual fields, and a field with a nonpolynomial potential may have infinite number of dual fields. All fields which are dual to each other form a duality f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06805","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.06805","created_at":"2026-05-17T23:45:51.457059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.06805v2","created_at":"2026-05-17T23:45:51.457059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06805","created_at":"2026-05-17T23:45:51.457059+00:00"},{"alias_kind":"pith_short_12","alias_value":"A736VMJC55RX","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"A736VMJC55RXQAYF","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"A736VMJC","created_at":"2026-05-18T12:33:12.712433+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1909.01089","citing_title":"A duality in classical and quantum mechanics: General results","ref_index":21,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D","json":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D.json","graph_json":"https://pith.science/api/pith-number/A736VMJC55RXQAYFFR6EEX667D/graph.json","events_json":"https://pith.science/api/pith-number/A736VMJC55RXQAYFFR6EEX667D/events.json","paper":"https://pith.science/paper/A736VMJC"},"agent_actions":{"view_html":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D","download_json":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D.json","view_paper":"https://pith.science/paper/A736VMJC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.06805&json=true","fetch_graph":"https://pith.science/api/pith-number/A736VMJC55RXQAYFFR6EEX667D/graph.json","fetch_events":"https://pith.science/api/pith-number/A736VMJC55RXQAYFFR6EEX667D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D/action/storage_attestation","attest_author":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D/action/author_attestation","sign_citation":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D/action/citation_signature","submit_replication":"https://pith.science/pith/A736VMJC55RXQAYFFR6EEX667D/action/replication_record"}},"created_at":"2026-05-17T23:45:51.457059+00:00","updated_at":"2026-05-17T23:45:51.457059+00:00"}