{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LSTQF222DT2EBGC7ZEIAQN3WS7","short_pith_number":"pith:LSTQF222","canonical_record":{"source":{"id":"2403.16661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-25T11:54:35Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"27b874e5fce67ddfca812e3f6844d4777a4bda6612f7f00487606bd2d528a575","abstract_canon_sha256":"a41a240bd0a1097acf564a838247e0369f324fed4019b942b5a5938d83d42fdc"},"schema_version":"1.0"},"canonical_sha256":"5ca702eb5a1cf440985fc91008377697df9c2dd926f367285f6ab6e5309e4005","source":{"kind":"arxiv","id":"2403.16661","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.16661","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2403.16661v2","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.16661","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"LSTQF222DT2E","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"LSTQF222DT2EBGC7","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"LSTQF222","created_at":"2026-05-18T12:33:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LSTQF222DT2EBGC7ZEIAQN3WS7","target":"record","payload":{"canonical_record":{"source":{"id":"2403.16661","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-25T11:54:35Z","cross_cats_sorted":["gr-qc","hep-th"],"title_canon_sha256":"27b874e5fce67ddfca812e3f6844d4777a4bda6612f7f00487606bd2d528a575","abstract_canon_sha256":"a41a240bd0a1097acf564a838247e0369f324fed4019b942b5a5938d83d42fdc"},"schema_version":"1.0"},"canonical_sha256":"5ca702eb5a1cf440985fc91008377697df9c2dd926f367285f6ab6e5309e4005","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:46.971678Z","signature_b64":"f5iEtpobQF+J3EI9aqH95HmduVqJlZm9FLIDo+WRAEWEqku60mg3MYQqMZMFWawBiVUeP6fDfENGUVk3CVZHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ca702eb5a1cf440985fc91008377697df9c2dd926f367285f6ab6e5309e4005","last_reissued_at":"2026-05-18T03:09:46.970760Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:46.970760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.16661","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":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BtmcyFCzHcgxfjVnZceAiEQacA26vebZmB4+KTri4iWdYm5sYAUhzSlOEo1XcMZ/hV7Z6olPkhmj1VG0WdooCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:20.772566Z"},"content_sha256":"b4486dd86b8d82c865ef29a6404533a4cec917a876362e8f0512afc454d70b2c","schema_version":"1.0","event_id":"sha256:b4486dd86b8d82c865ef29a6404533a4cec917a876362e8f0512afc454d70b2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LSTQF222DT2EBGC7ZEIAQN3WS7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of Cayley Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-th"],"primary_cat":"math.DG","authors_text":"Kirill Krasnov","submitted_at":"2024-03-25T11:54:35Z","abstract_excerpt":"The most natural first-order PDEs to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. In this work, we investigate the natural second-order conditions. We start at the linearised level, and construct the most general diffeomorphism-invariant second order in derivatives Lagrangian that is quadratic in the perturbations of the Cayley form, finding a two-parameter family. We then describe a non-linear completion of the linear story. We parametrise the intrinsic torsion of a Spin(7)-structure by a 3-form, and show that this 3-form is completely determined by th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16661","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":"2026-05-18T03:09:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f4QVs1guRjj+eUau9wp2xUa9yjc/UWmmmPpVFaAKJUiC5zh9x69GjCkWDq1WTF44of0GL2ncBEKEEWni0V1kBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:40:20.773238Z"},"content_sha256":"9209a1936dfe91a1d8e7d8ef8e59703690583bd75bafa2afa6c2dcea3e06dd28","schema_version":"1.0","event_id":"sha256:9209a1936dfe91a1d8e7d8ef8e59703690583bd75bafa2afa6c2dcea3e06dd28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/bundle.json","state_url":"https://pith.science/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/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":"2026-05-28T16:40:20Z","links":{"resolver":"https://pith.science/pith/LSTQF222DT2EBGC7ZEIAQN3WS7","bundle":"https://pith.science/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/bundle.json","state":"https://pith.science/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSTQF222DT2EBGC7ZEIAQN3WS7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LSTQF222DT2EBGC7ZEIAQN3WS7","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":"a41a240bd0a1097acf564a838247e0369f324fed4019b942b5a5938d83d42fdc","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-25T11:54:35Z","title_canon_sha256":"27b874e5fce67ddfca812e3f6844d4777a4bda6612f7f00487606bd2d528a575"},"schema_version":"1.0","source":{"id":"2403.16661","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.16661","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"2403.16661v2","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.16661","created_at":"2026-05-18T03:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"LSTQF222DT2E","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"LSTQF222DT2EBGC7","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"LSTQF222","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:9209a1936dfe91a1d8e7d8ef8e59703690583bd75bafa2afa6c2dcea3e06dd28","target":"graph","created_at":"2026-05-18T03:09:46Z","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":"The most natural first-order PDEs to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. In this work, we investigate the natural second-order conditions. We start at the linearised level, and construct the most general diffeomorphism-invariant second order in derivatives Lagrangian that is quadratic in the perturbations of the Cayley form, finding a two-parameter family. We then describe a non-linear completion of the linear story. We parametrise the intrinsic torsion of a Spin(7)-structure by a 3-form, and show that this 3-form is completely determined by th","authors_text":"Kirill Krasnov","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-25T11:54:35Z","title":"Dynamics of Cayley Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.16661","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:b4486dd86b8d82c865ef29a6404533a4cec917a876362e8f0512afc454d70b2c","target":"record","created_at":"2026-05-18T03:09:46Z","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":"a41a240bd0a1097acf564a838247e0369f324fed4019b942b5a5938d83d42fdc","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-25T11:54:35Z","title_canon_sha256":"27b874e5fce67ddfca812e3f6844d4777a4bda6612f7f00487606bd2d528a575"},"schema_version":"1.0","source":{"id":"2403.16661","kind":"arxiv","version":2}},"canonical_sha256":"5ca702eb5a1cf440985fc91008377697df9c2dd926f367285f6ab6e5309e4005","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ca702eb5a1cf440985fc91008377697df9c2dd926f367285f6ab6e5309e4005","first_computed_at":"2026-05-18T03:09:46.970760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:46.970760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5iEtpobQF+J3EI9aqH95HmduVqJlZm9FLIDo+WRAEWEqku60mg3MYQqMZMFWawBiVUeP6fDfENGUVk3CVZHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:46.971678Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.16661","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4486dd86b8d82c865ef29a6404533a4cec917a876362e8f0512afc454d70b2c","sha256:9209a1936dfe91a1d8e7d8ef8e59703690583bd75bafa2afa6c2dcea3e06dd28"],"state_sha256":"833335b49840b4eaf8f07fab22d776d96f6bdb5b722ddb47722ac0aee727c283"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qm4O4lLV8iC4zJYDAyi6az6AKYWcNZfjQrNTVPcZlRXx3dBr9h+t/OQmSdkrDSw71LdS+EZk5VA+V+/k5nzPCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:40:20.776920Z","bundle_sha256":"35f7fd0c47eb531cb20f643bfe64a0ddeb33e77fd5caf8fd9b25c6cc9b88c3b3"}}