{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:YC5CBJSJLMCOKYOOLEKUJ36AO7","short_pith_number":"pith:YC5CBJSJ","canonical_record":{"source":{"id":"2209.02716","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-06T18:00:02Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"25db394ed76ee101fc1e6ebc6e652d3b432088e90cf1749dede2c9d040c5c961","abstract_canon_sha256":"3085c7282d9bf90f7b8d704ea1c5b411567932e3d8599b256e801ca808e93ee6"},"schema_version":"1.0"},"canonical_sha256":"c0ba20a6495b04e561ce591544efc077c653ff2d028067346e5ea26b72a3ad59","source":{"kind":"arxiv","id":"2209.02716","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02716","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02716v3","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02716","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_12","alias_value":"YC5CBJSJLMCO","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_16","alias_value":"YC5CBJSJLMCOKYOO","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_8","alias_value":"YC5CBJSJ","created_at":"2026-07-05T06:34:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:YC5CBJSJLMCOKYOOLEKUJ36AO7","target":"record","payload":{"canonical_record":{"source":{"id":"2209.02716","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-06T18:00:02Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"25db394ed76ee101fc1e6ebc6e652d3b432088e90cf1749dede2c9d040c5c961","abstract_canon_sha256":"3085c7282d9bf90f7b8d704ea1c5b411567932e3d8599b256e801ca808e93ee6"},"schema_version":"1.0"},"canonical_sha256":"c0ba20a6495b04e561ce591544efc077c653ff2d028067346e5ea26b72a3ad59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:34:19.242303Z","signature_b64":"B5XlzDvjHljptra96HCA5RTPqpGxdvn+xSFF8XgDhfKQz4EfrQFwLjFJYBjJcoyuGsNFZeu1SIOXIPvYrYD0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0ba20a6495b04e561ce591544efc077c653ff2d028067346e5ea26b72a3ad59","last_reissued_at":"2026-07-05T06:34:19.241826Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:34:19.241826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.02716","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:34:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2OMKfNpknCix6jzGR4DLp2Xn33Nc0L7WsvU01aZXA0U+geMnombCdndLpnbvOG02tMFrMZUKTU89iytyp6leCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:10:52.077530Z"},"content_sha256":"72db4bb917ef59303a75a89cfa554b4c3af50cf4db222d6aabd295f853d77949","schema_version":"1.0","event_id":"sha256:72db4bb917ef59303a75a89cfa554b4c3af50cf4db222d6aabd295f853d77949"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:YC5CBJSJLMCOKYOOLEKUJ36AO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative hamiltonian formalism for noncommutative gravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Leonardo Castellani","submitted_at":"2022-09-06T18:00:02Z","abstract_excerpt":"We present a covariant canonical formalism for noncommutative gravity, and in general for noncommutative geometric theories defined via a twisted $\\star$-wedge product between forms. Noether theorems are generalized to the noncommutative setting, and gauge generators are constructed in a twisted phase space with $\\star$-deformed Poisson bracket. This formalism is applied to noncommutative $d=4$ vierbein gravity, and allows to find the canonical generators of the tangent space $\\star$-gauge group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02716","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/2209.02716/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":"2026-07-05T06:34:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6iLcqxljbTE+lZQJDbSJs6FqkJMrVlx//TQS7ZmRkr4iRefDwNyvRCjrWiE657uiB5+TiZrCwqjyODg8QHQxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:10:52.078278Z"},"content_sha256":"e03aed2f2c64d5bf1addcb58bca1dcc1aab01b88b46d9bc17c1c732ec75e8097","schema_version":"1.0","event_id":"sha256:e03aed2f2c64d5bf1addcb58bca1dcc1aab01b88b46d9bc17c1c732ec75e8097"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/bundle.json","state_url":"https://pith.science/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/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":"2026-08-04T04:10:52Z","links":{"resolver":"https://pith.science/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7","bundle":"https://pith.science/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/bundle.json","state":"https://pith.science/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YC5CBJSJLMCOKYOOLEKUJ36AO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YC5CBJSJLMCOKYOOLEKUJ36AO7","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":"3085c7282d9bf90f7b8d704ea1c5b411567932e3d8599b256e801ca808e93ee6","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-06T18:00:02Z","title_canon_sha256":"25db394ed76ee101fc1e6ebc6e652d3b432088e90cf1749dede2c9d040c5c961"},"schema_version":"1.0","source":{"id":"2209.02716","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.02716","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"arxiv_version","alias_value":"2209.02716v3","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.02716","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_12","alias_value":"YC5CBJSJLMCO","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_16","alias_value":"YC5CBJSJLMCOKYOO","created_at":"2026-07-05T06:34:19Z"},{"alias_kind":"pith_short_8","alias_value":"YC5CBJSJ","created_at":"2026-07-05T06:34:19Z"}],"graph_snapshots":[{"event_id":"sha256:e03aed2f2c64d5bf1addcb58bca1dcc1aab01b88b46d9bc17c1c732ec75e8097","target":"graph","created_at":"2026-07-05T06:34:19Z","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/2209.02716/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a covariant canonical formalism for noncommutative gravity, and in general for noncommutative geometric theories defined via a twisted $\\star$-wedge product between forms. Noether theorems are generalized to the noncommutative setting, and gauge generators are constructed in a twisted phase space with $\\star$-deformed Poisson bracket. This formalism is applied to noncommutative $d=4$ vierbein gravity, and allows to find the canonical generators of the tangent space $\\star$-gauge group.","authors_text":"Leonardo Castellani","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-06T18:00:02Z","title":"Noncommutative hamiltonian formalism for noncommutative gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.02716","kind":"arxiv","version":3},"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":"sha256:72db4bb917ef59303a75a89cfa554b4c3af50cf4db222d6aabd295f853d77949","target":"record","created_at":"2026-07-05T06:34:19Z","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":"3085c7282d9bf90f7b8d704ea1c5b411567932e3d8599b256e801ca808e93ee6","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-09-06T18:00:02Z","title_canon_sha256":"25db394ed76ee101fc1e6ebc6e652d3b432088e90cf1749dede2c9d040c5c961"},"schema_version":"1.0","source":{"id":"2209.02716","kind":"arxiv","version":3}},"canonical_sha256":"c0ba20a6495b04e561ce591544efc077c653ff2d028067346e5ea26b72a3ad59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0ba20a6495b04e561ce591544efc077c653ff2d028067346e5ea26b72a3ad59","first_computed_at":"2026-07-05T06:34:19.241826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:34:19.241826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B5XlzDvjHljptra96HCA5RTPqpGxdvn+xSFF8XgDhfKQz4EfrQFwLjFJYBjJcoyuGsNFZeu1SIOXIPvYrYD0Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:34:19.242303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.02716","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72db4bb917ef59303a75a89cfa554b4c3af50cf4db222d6aabd295f853d77949","sha256:e03aed2f2c64d5bf1addcb58bca1dcc1aab01b88b46d9bc17c1c732ec75e8097"],"state_sha256":"0d3a5bf5962ca2cff0a5069863e45d575ffad1c659190feb52cf3bfe90f00684"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F1CfVkuq0tmuHtQDcmAg2rye3ti3jduBARq0JX0oDFBsyX8XyQE7fFVUxbfDHzZ70nWX8hFUU/M1Nk17nuB+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:10:52.085781Z","bundle_sha256":"097527a55f384d9e27e36298475d78f63bff549ebc172eb46e90d464c9e572e6"}}