{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:7FFOXDCO7AU2U25MGCZCI6ALDU","short_pith_number":"pith:7FFOXDCO","schema_version":"1.0","canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","source":{"kind":"arxiv","id":"2305.06034","version":1},"attestation_state":"computed","paper":{"title":"Hodge Duality and Supergravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Leonardo Castellani, Pietro Antonio Grassi","submitted_at":"2023-05-10T10:35:15Z","abstract_excerpt":"The Hodge dual operator, recently introduced for supermanifolds, is used to reformulate super Yang-Mills and supergravity in $D=4$. We first recall the definition of the Hodge dual operator for flat and curved supermanifolds. Then we show how to recover the usual super-Yang-Mills equations of motion for $N=1,2$ supersymmetry, and the obstacles (as seen from Hodge dual point of view) in the case $N \\geq 3$. We reconsider several ingredients of supergeometry, relevant for a superspace formulation of supergravity, in terms of the Hodge dual operator. Finally we discuss how $D=4$ and $N=1$ supergr"},"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":"2305.06034","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-05-10T10:35:15Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"12456507c06e71a963bb783be82d4c9c919e33969302a0064a750fdcb4373003","abstract_canon_sha256":"97caf646b9a1e624728243f0059b7c57699f66d0d4899e2b31a8b533fc2dd664"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:08:58.910130Z","signature_b64":"wpih/Ey8kSy0LB9n7iioGbAjH1I20J6e6c4IfnUcx0FxhEmMnWaQWjipcCebkEn+BRar9JBD195jb8KLZxsPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","last_reissued_at":"2026-07-05T06:08:58.909721Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:08:58.909721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hodge Duality and Supergravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Leonardo Castellani, Pietro Antonio Grassi","submitted_at":"2023-05-10T10:35:15Z","abstract_excerpt":"The Hodge dual operator, recently introduced for supermanifolds, is used to reformulate super Yang-Mills and supergravity in $D=4$. We first recall the definition of the Hodge dual operator for flat and curved supermanifolds. Then we show how to recover the usual super-Yang-Mills equations of motion for $N=1,2$ supersymmetry, and the obstacles (as seen from Hodge dual point of view) in the case $N \\geq 3$. We reconsider several ingredients of supergeometry, relevant for a superspace formulation of supergravity, in terms of the Hodge dual operator. Finally we discuss how $D=4$ and $N=1$ supergr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06034","kind":"arxiv","version":1},"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/2305.06034/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":"2305.06034","created_at":"2026-07-05T06:08:58.909777+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.06034v1","created_at":"2026-07-05T06:08:58.909777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.06034","created_at":"2026-07-05T06:08:58.909777+00:00"},{"alias_kind":"pith_short_12","alias_value":"7FFOXDCO7AU2","created_at":"2026-07-05T06:08:58.909777+00:00"},{"alias_kind":"pith_short_16","alias_value":"7FFOXDCO7AU2U25M","created_at":"2026-07-05T06:08:58.909777+00:00"},{"alias_kind":"pith_short_8","alias_value":"7FFOXDCO","created_at":"2026-07-05T06:08:58.909777+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.15424","citing_title":"SymTFT in Superspace","ref_index":45,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU","json":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU.json","graph_json":"https://pith.science/api/pith-number/7FFOXDCO7AU2U25MGCZCI6ALDU/graph.json","events_json":"https://pith.science/api/pith-number/7FFOXDCO7AU2U25MGCZCI6ALDU/events.json","paper":"https://pith.science/paper/7FFOXDCO"},"agent_actions":{"view_html":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU","download_json":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU.json","view_paper":"https://pith.science/paper/7FFOXDCO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.06034&json=true","fetch_graph":"https://pith.science/api/pith-number/7FFOXDCO7AU2U25MGCZCI6ALDU/graph.json","fetch_events":"https://pith.science/api/pith-number/7FFOXDCO7AU2U25MGCZCI6ALDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/action/storage_attestation","attest_author":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/action/author_attestation","sign_citation":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/action/citation_signature","submit_replication":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/action/replication_record"}},"created_at":"2026-07-05T06:08:58.909777+00:00","updated_at":"2026-07-05T06:08:58.909777+00:00"}