{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:7FFOXDCO7AU2U25MGCZCI6ALDU","short_pith_number":"pith:7FFOXDCO","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"},"canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","source":{"kind":"arxiv","id":"2305.06034","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.06034","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2305.06034v1","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.06034","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"7FFOXDCO7AU2","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"7FFOXDCO7AU2U25M","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"7FFOXDCO","created_at":"2026-07-05T06:08:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:7FFOXDCO7AU2U25MGCZCI6ALDU","target":"record","payload":{"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"},"canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","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"},"source_kind":"arxiv","source_id":"2305.06034","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KD7XuAn8dGvMH1WCviccXrarTtws/c4QTDTHOyG5MJZeZ+q9eHJ/3ZscMtnwuHz0qjLPGd8+LQrs6MGuI6lDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:05:04.315139Z"},"content_sha256":"ca0d7e867ca52d9a7333016ef7b0db45dfadab30eaad056b80afd7863ccfae59","schema_version":"1.0","event_id":"sha256:ca0d7e867ca52d9a7333016ef7b0db45dfadab30eaad056b80afd7863ccfae59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:7FFOXDCO7AU2U25MGCZCI6ALDU","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:08:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R/be8gqUiCrlmS/7RyFRPvTSQMUIrmJoDouAwtyht8/5QW2khwLL6DVWEd3ViAFITQdRheU7esr8T7MZvUOACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:05:04.315637Z"},"content_sha256":"de471146776b753c4100c69b4424399cf9540657ddcf42e0dde82e7db191550a","schema_version":"1.0","event_id":"sha256:de471146776b753c4100c69b4424399cf9540657ddcf42e0dde82e7db191550a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/bundle.json","state_url":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-04T04:05:04Z","links":{"resolver":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU","bundle":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/bundle.json","state":"https://pith.science/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FFOXDCO7AU2U25MGCZCI6ALDU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7FFOXDCO7AU2U25MGCZCI6ALDU","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":"97caf646b9a1e624728243f0059b7c57699f66d0d4899e2b31a8b533fc2dd664","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-05-10T10:35:15Z","title_canon_sha256":"12456507c06e71a963bb783be82d4c9c919e33969302a0064a750fdcb4373003"},"schema_version":"1.0","source":{"id":"2305.06034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.06034","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"arxiv_version","alias_value":"2305.06034v1","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.06034","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_12","alias_value":"7FFOXDCO7AU2","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_16","alias_value":"7FFOXDCO7AU2U25M","created_at":"2026-07-05T06:08:58Z"},{"alias_kind":"pith_short_8","alias_value":"7FFOXDCO","created_at":"2026-07-05T06:08:58Z"}],"graph_snapshots":[{"event_id":"sha256:de471146776b753c4100c69b4424399cf9540657ddcf42e0dde82e7db191550a","target":"graph","created_at":"2026-07-05T06:08:58Z","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/2305.06034/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Leonardo Castellani, Pietro Antonio Grassi","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-05-10T10:35:15Z","title":"Hodge Duality and Supergravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.06034","kind":"arxiv","version":1},"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:ca0d7e867ca52d9a7333016ef7b0db45dfadab30eaad056b80afd7863ccfae59","target":"record","created_at":"2026-07-05T06:08:58Z","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":"97caf646b9a1e624728243f0059b7c57699f66d0d4899e2b31a8b533fc2dd664","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2023-05-10T10:35:15Z","title_canon_sha256":"12456507c06e71a963bb783be82d4c9c919e33969302a0064a750fdcb4373003"},"schema_version":"1.0","source":{"id":"2305.06034","kind":"arxiv","version":1}},"canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f94aeb8c4ef829aa6bac30b224780b1d13d942a9240c0c6d616c77b56284ea35","first_computed_at":"2026-07-05T06:08:58.909721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:08:58.909721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpih/Ey8kSy0LB9n7iioGbAjH1I20J6e6c4IfnUcx0FxhEmMnWaQWjipcCebkEn+BRar9JBD195jb8KLZxsPDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:08:58.910130Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.06034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca0d7e867ca52d9a7333016ef7b0db45dfadab30eaad056b80afd7863ccfae59","sha256:de471146776b753c4100c69b4424399cf9540657ddcf42e0dde82e7db191550a"],"state_sha256":"575bc6abe1f7bd82011be7470f21d470c5307ab285151d2dae6bd6777bd746c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SL5S1zxVKkUsLKOrVjEAalYzcpJYb5U0roe891AR50yQ8+6X+Qiw5XXWBpWcttCaX4ukLpY5wsVhhBqCSpwZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:05:04.320875Z","bundle_sha256":"0bf4f68bc8b79c44b265836fb28547d62c27c2e2252d67d609a09f949e074185"}}