{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZKMVRVJJMZX7V6FESHGERXYGQL","short_pith_number":"pith:ZKMVRVJJ","canonical_record":{"source":{"id":"2505.13984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-20T06:33:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e0767ef25fe2801ff5250f53be95d06aa15f3ca16021c9a5b7057c07f93404a4","abstract_canon_sha256":"fa8898cddefbf07a3222885510d7b4dcd07d4f20910723baf6f98a5ff4233350"},"schema_version":"1.0"},"canonical_sha256":"ca9958d529666ffaf8a491cc48df0682c5c47d5aac04a241fdc07506c7a6eb7f","source":{"kind":"arxiv","id":"2505.13984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13984","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13984v1","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13984","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZKMVRVJJMZX7","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZKMVRVJJMZX7V6FE","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZKMVRVJJ","created_at":"2026-07-05T11:05:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZKMVRVJJMZX7V6FESHGERXYGQL","target":"record","payload":{"canonical_record":{"source":{"id":"2505.13984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-20T06:33:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e0767ef25fe2801ff5250f53be95d06aa15f3ca16021c9a5b7057c07f93404a4","abstract_canon_sha256":"fa8898cddefbf07a3222885510d7b4dcd07d4f20910723baf6f98a5ff4233350"},"schema_version":"1.0"},"canonical_sha256":"ca9958d529666ffaf8a491cc48df0682c5c47d5aac04a241fdc07506c7a6eb7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:54.287638Z","signature_b64":"yM0DS7jISxYbjDWo40lCSCFvNdBkGwijQMg8xIginYjBoKzSc/qQN9oqgz0m6RL84VHF09HiWjfnPzyjo0+LDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca9958d529666ffaf8a491cc48df0682c5c47d5aac04a241fdc07506c7a6eb7f","last_reissued_at":"2026-07-05T11:05:54.287152Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:54.287152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.13984","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":"2026-07-05T11:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93/R3sVP2/Q29+xRkhNY5DO9TOGZ5qfVYLUGyHY3xMy1X3yhMYhPmA9Up+kptu9Kni2wLjE9iPsX96dLIY3ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:06:41.946279Z"},"content_sha256":"185c3052912d9bbcf6ce6742ffe3ded750ff6ebaf4a539991fc1e07834019cfa","schema_version":"1.0","event_id":"sha256:185c3052912d9bbcf6ce6742ffe3ded750ff6ebaf4a539991fc1e07834019cfa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZKMVRVJJMZX7V6FESHGERXYGQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of noncommutative Levi-Civita connections in derivation based calculi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Joakim Arnlind, Victor Hildebrandsson","submitted_at":"2025-05-20T06:33:01Z","abstract_excerpt":"We study the existence of Levi-Civita connections, i.e torsion free connections compatible with a hermitian form, in the setting of derivation based noncommutative differential calculi over $\\ast$-algebras. We prove a necessary and sufficient condition for the existence of Levi-Civita connections in terms of the image of an operator derived from the hermitian form. Moreover, we identify a necessary symmetry condition on the hermitian form that extends the classical notion of metric symmetry in Riemannian geometry. The theory is illustrated with explicit computations for free modules of rank th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13984","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/2505.13984/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":"2026-07-05T11:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W35Hn6ZXq9JeDj8qYUKxoYU173tLW5HUUiiDzQAvu7qFL1l8GbdpJD6oNdsqZMvP22hSUIw7m1RKIowTH5LpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T16:06:41.946804Z"},"content_sha256":"254b1b050950ca3b981e12e5cc5e819c87f0c04435cc3f559cbc8682d5dc118e","schema_version":"1.0","event_id":"sha256:254b1b050950ca3b981e12e5cc5e819c87f0c04435cc3f559cbc8682d5dc118e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/bundle.json","state_url":"https://pith.science/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/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":"2026-08-12T16:06:41Z","links":{"resolver":"https://pith.science/pith/ZKMVRVJJMZX7V6FESHGERXYGQL","bundle":"https://pith.science/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/bundle.json","state":"https://pith.science/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZKMVRVJJMZX7V6FESHGERXYGQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZKMVRVJJMZX7V6FESHGERXYGQL","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":"fa8898cddefbf07a3222885510d7b4dcd07d4f20910723baf6f98a5ff4233350","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-20T06:33:01Z","title_canon_sha256":"e0767ef25fe2801ff5250f53be95d06aa15f3ca16021c9a5b7057c07f93404a4"},"schema_version":"1.0","source":{"id":"2505.13984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.13984","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"2505.13984v1","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13984","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZKMVRVJJMZX7","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZKMVRVJJMZX7V6FE","created_at":"2026-07-05T11:05:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZKMVRVJJ","created_at":"2026-07-05T11:05:54Z"}],"graph_snapshots":[{"event_id":"sha256:254b1b050950ca3b981e12e5cc5e819c87f0c04435cc3f559cbc8682d5dc118e","target":"graph","created_at":"2026-07-05T11:05:54Z","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/2505.13984/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the existence of Levi-Civita connections, i.e torsion free connections compatible with a hermitian form, in the setting of derivation based noncommutative differential calculi over $\\ast$-algebras. We prove a necessary and sufficient condition for the existence of Levi-Civita connections in terms of the image of an operator derived from the hermitian form. Moreover, we identify a necessary symmetry condition on the hermitian form that extends the classical notion of metric symmetry in Riemannian geometry. The theory is illustrated with explicit computations for free modules of rank th","authors_text":"Joakim Arnlind, Victor Hildebrandsson","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-20T06:33:01Z","title":"On the existence of noncommutative Levi-Civita connections in derivation based calculi"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13984","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":"sha256:185c3052912d9bbcf6ce6742ffe3ded750ff6ebaf4a539991fc1e07834019cfa","target":"record","created_at":"2026-07-05T11:05:54Z","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":"fa8898cddefbf07a3222885510d7b4dcd07d4f20910723baf6f98a5ff4233350","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2025-05-20T06:33:01Z","title_canon_sha256":"e0767ef25fe2801ff5250f53be95d06aa15f3ca16021c9a5b7057c07f93404a4"},"schema_version":"1.0","source":{"id":"2505.13984","kind":"arxiv","version":1}},"canonical_sha256":"ca9958d529666ffaf8a491cc48df0682c5c47d5aac04a241fdc07506c7a6eb7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca9958d529666ffaf8a491cc48df0682c5c47d5aac04a241fdc07506c7a6eb7f","first_computed_at":"2026-07-05T11:05:54.287152Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:54.287152Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yM0DS7jISxYbjDWo40lCSCFvNdBkGwijQMg8xIginYjBoKzSc/qQN9oqgz0m6RL84VHF09HiWjfnPzyjo0+LDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:54.287638Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.13984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:185c3052912d9bbcf6ce6742ffe3ded750ff6ebaf4a539991fc1e07834019cfa","sha256:254b1b050950ca3b981e12e5cc5e819c87f0c04435cc3f559cbc8682d5dc118e"],"state_sha256":"5278899732c0c3a7b3324d570b08c792bef3094a319f1b3fae6d861773014fc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XOSu+Ho+CFF/6dhoTznn+gY3FhQk/u0oT+eHlsH9tEalVHVUWFjew1U7pkkgjlw1JFYOaO548KRdaTGoSEkdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T16:06:41.957381Z","bundle_sha256":"fcdc4130643f1531731dda7135ff1b246cf2189058bdb47e4acc4000e525df5b"}}