{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VGBS6OVMYLI7LQLJE4WMXTUBFN","short_pith_number":"pith:VGBS6OVM","canonical_record":{"source":{"id":"1703.05133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-15T13:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"b9cc783772dbfbbf8b7d820a0724bd7f1aeba5d8fed4c99219233798dff12337","abstract_canon_sha256":"aa03398ba0a16964e03e57f585e6d1cba643eb700201bcf6d6b3fc11b03c8425"},"schema_version":"1.0"},"canonical_sha256":"a9832f3aacc2d1f5c169272ccbce812b5fac77eb067aebfc78b906559ba6e034","source":{"kind":"arxiv","id":"1703.05133","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05133","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05133v2","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05133","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"VGBS6OVMYLI7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VGBS6OVMYLI7LQLJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VGBS6OVM","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VGBS6OVMYLI7LQLJE4WMXTUBFN","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05133","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-15T13:05:10Z","cross_cats_sorted":[],"title_canon_sha256":"b9cc783772dbfbbf8b7d820a0724bd7f1aeba5d8fed4c99219233798dff12337","abstract_canon_sha256":"aa03398ba0a16964e03e57f585e6d1cba643eb700201bcf6d6b3fc11b03c8425"},"schema_version":"1.0"},"canonical_sha256":"a9832f3aacc2d1f5c169272ccbce812b5fac77eb067aebfc78b906559ba6e034","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:01.559986Z","signature_b64":"gL2qJThh3VGOcGBYjIEqWpGKDHJrM+U9CNcr977Dn1vR72/dX6n3yskz/E8HNX6YE3YGdBNogtzGVJ4vm/8aBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9832f3aacc2d1f5c169272ccbce812b5fac77eb067aebfc78b906559ba6e034","last_reissued_at":"2026-05-17T23:53:01.559398Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:01.559398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05133","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uxva27UKyLeySaMEVm4NvVVIMNc0ApKyRNxzJqwpiBJv2GCzvSxn3w/4ekiDVNG/TDVDR5Eqqv0x0wtRgsoNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:27:45.469352Z"},"content_sha256":"155d021085f4e89a2f547e94966844ffb0a61d1f56d7f1eecb661770317564ca","schema_version":"1.0","event_id":"sha256:155d021085f4e89a2f547e94966844ffb0a61d1f56d7f1eecb661770317564ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VGBS6OVMYLI7LQLJE4WMXTUBFN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fr\\\"olicher-Nijenhuis cohomology on $G_2$- and ${\\rm Spin}(7)$-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H\\^ong V\\^an L\\^e, Kotaro Kawai, Lorenz Schwachh\\\"ofer","submitted_at":"2017-03-15T13:05:10Z","abstract_excerpt":"In this paper we show that a parallel differential form $\\Psi$ of even degree on a Riemannian manifold allows to define a natural differential both on $\\Omega^\\ast(M)$ and $\\Omega^\\ast(M, TM)$, defined via the Fr\\\"olicher-Nijenhuis bracket. For instance, on a K\\\"ahler manifold, these operators are the complex differential and the Dolbeault differential, respectively. We investigate this construction when taking the differential w.r.t. the canonical parallel $4$-form on a $G_2$- and ${\\rm Spin}(7)$-manifold, respectively. We calculate the cohomology groups of $\\Omega^\\ast(M)$ and give a partial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05133","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V/0Y83YoPtOnmT7KX+9X+tbgLF0IpJ4/js+cV2CLk/M5+iAcFP4RbXgdeNdXybR8EaCOf5GcYbJ6uUxDeJY/DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:27:45.469706Z"},"content_sha256":"e9390430d05dcbf412e212d74426c8bb8a5931bd17aa4ddcc563f46abf9ea0f8","schema_version":"1.0","event_id":"sha256:e9390430d05dcbf412e212d74426c8bb8a5931bd17aa4ddcc563f46abf9ea0f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/bundle.json","state_url":"https://pith.science/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/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":"2026-06-25T18:27:45Z","links":{"resolver":"https://pith.science/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN","bundle":"https://pith.science/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/bundle.json","state":"https://pith.science/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VGBS6OVMYLI7LQLJE4WMXTUBFN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VGBS6OVMYLI7LQLJE4WMXTUBFN","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":"aa03398ba0a16964e03e57f585e6d1cba643eb700201bcf6d6b3fc11b03c8425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-15T13:05:10Z","title_canon_sha256":"b9cc783772dbfbbf8b7d820a0724bd7f1aeba5d8fed4c99219233798dff12337"},"schema_version":"1.0","source":{"id":"1703.05133","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05133","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05133v2","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05133","created_at":"2026-05-17T23:53:01Z"},{"alias_kind":"pith_short_12","alias_value":"VGBS6OVMYLI7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VGBS6OVMYLI7LQLJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VGBS6OVM","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:e9390430d05dcbf412e212d74426c8bb8a5931bd17aa4ddcc563f46abf9ea0f8","target":"graph","created_at":"2026-05-17T23:53:01Z","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"},"paper":{"abstract_excerpt":"In this paper we show that a parallel differential form $\\Psi$ of even degree on a Riemannian manifold allows to define a natural differential both on $\\Omega^\\ast(M)$ and $\\Omega^\\ast(M, TM)$, defined via the Fr\\\"olicher-Nijenhuis bracket. For instance, on a K\\\"ahler manifold, these operators are the complex differential and the Dolbeault differential, respectively. We investigate this construction when taking the differential w.r.t. the canonical parallel $4$-form on a $G_2$- and ${\\rm Spin}(7)$-manifold, respectively. We calculate the cohomology groups of $\\Omega^\\ast(M)$ and give a partial","authors_text":"H\\^ong V\\^an L\\^e, Kotaro Kawai, Lorenz Schwachh\\\"ofer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-15T13:05:10Z","title":"Fr\\\"olicher-Nijenhuis cohomology on $G_2$- and ${\\rm Spin}(7)$-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05133","kind":"arxiv","version":2},"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":"sha256:155d021085f4e89a2f547e94966844ffb0a61d1f56d7f1eecb661770317564ca","target":"record","created_at":"2026-05-17T23:53:01Z","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":"aa03398ba0a16964e03e57f585e6d1cba643eb700201bcf6d6b3fc11b03c8425","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-15T13:05:10Z","title_canon_sha256":"b9cc783772dbfbbf8b7d820a0724bd7f1aeba5d8fed4c99219233798dff12337"},"schema_version":"1.0","source":{"id":"1703.05133","kind":"arxiv","version":2}},"canonical_sha256":"a9832f3aacc2d1f5c169272ccbce812b5fac77eb067aebfc78b906559ba6e034","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9832f3aacc2d1f5c169272ccbce812b5fac77eb067aebfc78b906559ba6e034","first_computed_at":"2026-05-17T23:53:01.559398Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:01.559398Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gL2qJThh3VGOcGBYjIEqWpGKDHJrM+U9CNcr977Dn1vR72/dX6n3yskz/E8HNX6YE3YGdBNogtzGVJ4vm/8aBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:01.559986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05133","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:155d021085f4e89a2f547e94966844ffb0a61d1f56d7f1eecb661770317564ca","sha256:e9390430d05dcbf412e212d74426c8bb8a5931bd17aa4ddcc563f46abf9ea0f8"],"state_sha256":"f71638ca0a6ddc78ca946fc6e41f682a4fa5b8c7d357ee61f745f3d77e65e7a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CPB1uAwcd6IdAGUpEo/S7GQdL4E9RHlfspavtK0npDep4rMJbMHrDhE+XffVfXvDwLsaHpLjYOKswgKc0fuFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:27:45.471735Z","bundle_sha256":"5a6bb628829be72ee42538a272870a57d781c5eaccea4e3643c7a9b398b30652"}}