{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YLRHR7WYUTMWW7MXWHCKAWOPLX","short_pith_number":"pith:YLRHR7WY","canonical_record":{"source":{"id":"0911.1079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-05T17:22:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8ba558f4b49a4b5e0bcfe99e6f2d83c6f991884c0b131ff8c5d41d6fae709e28","abstract_canon_sha256":"f21eca585ed527ed9a2ee138c0c378d33798f14a05c5939d653201da8f2edd78"},"schema_version":"1.0"},"canonical_sha256":"c2e278fed8a4d96b7d97b1c4a059cf5de6f6b2ef9bcdba43cd7138b1043de19e","source":{"kind":"arxiv","id":"0911.1079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1079","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1079v1","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1079","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"YLRHR7WYUTMW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YLRHR7WYUTMWW7MX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YLRHR7WY","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YLRHR7WYUTMWW7MXWHCKAWOPLX","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-05T17:22:37Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"8ba558f4b49a4b5e0bcfe99e6f2d83c6f991884c0b131ff8c5d41d6fae709e28","abstract_canon_sha256":"f21eca585ed527ed9a2ee138c0c378d33798f14a05c5939d653201da8f2edd78"},"schema_version":"1.0"},"canonical_sha256":"c2e278fed8a4d96b7d97b1c4a059cf5de6f6b2ef9bcdba43cd7138b1043de19e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:59.184530Z","signature_b64":"/Qpqz/yhqH5MWOqW5NphYKvQt10z7mLZ1Nsbnxu6aoherXhVEQpbjKuxPoXUgtgqDknQkeXsV70UFDNA/WiNAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2e278fed8a4d96b7d97b1c4a059cf5de6f6b2ef9bcdba43cd7138b1043de19e","last_reissued_at":"2026-05-18T02:10:59.183881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:59.183881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1079","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":"2026-05-18T02:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKMZz++Y1+yIdS173fEWlARtM4MJKOfyZp+bGFeWWajZkmM4mX9hu0LfMZyh+PpBqz6wRwX3NRm8JMZW3L3OAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:09:34.126361Z"},"content_sha256":"4266fd429630f4ca401e46de98ef488968b30b4c393886bdb0fc5dcc54d6c507","schema_version":"1.0","event_id":"sha256:4266fd429630f4ca401e46de98ef488968b30b4c393886bdb0fc5dcc54d6c507"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YLRHR7WYUTMWW7MXWHCKAWOPLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The canonical 8-form on manifolds with holonomy group Spin(9)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"I. Mykytyuk, M. Castrillon Lopez, P. M. Gadea","submitted_at":"2009-11-05T17:22:37Z","abstract_excerpt":"An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1079","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":""},"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":"2026-05-18T02:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cSifdn5rBF2zXP+A3YvSbLF8X3ymiUCab50z0mip7zb9KT2s3dsI3Ry8uM5EGII70Vwo37ZCCosTBACbG4goDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:09:34.127010Z"},"content_sha256":"da44c33c4cfd6088231b78c2b2a7a2207d936a3a00b63690f8563c641b1969df","schema_version":"1.0","event_id":"sha256:da44c33c4cfd6088231b78c2b2a7a2207d936a3a00b63690f8563c641b1969df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/bundle.json","state_url":"https://pith.science/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/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":"2026-06-07T21:09:34Z","links":{"resolver":"https://pith.science/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX","bundle":"https://pith.science/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/bundle.json","state":"https://pith.science/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLRHR7WYUTMWW7MXWHCKAWOPLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YLRHR7WYUTMWW7MXWHCKAWOPLX","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":"f21eca585ed527ed9a2ee138c0c378d33798f14a05c5939d653201da8f2edd78","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-05T17:22:37Z","title_canon_sha256":"8ba558f4b49a4b5e0bcfe99e6f2d83c6f991884c0b131ff8c5d41d6fae709e28"},"schema_version":"1.0","source":{"id":"0911.1079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1079","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1079v1","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1079","created_at":"2026-05-18T02:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"YLRHR7WYUTMW","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YLRHR7WYUTMWW7MX","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YLRHR7WY","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:da44c33c4cfd6088231b78c2b2a7a2207d936a3a00b63690f8563c641b1969df","target":"graph","created_at":"2026-05-18T02:10:59Z","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":"An explicit expression of the canonical 8-form on a Riemannian manifold with a Spin(9)-structure, in terms of the nine local symmetric involutions involved, is given. The list of explicit expressions of all the canonical forms related to Berger's list of holonomy groups is thus completed. Moreover, some results on Spin(9)-structures as G-structures defined by a tensor and on the curvature tensor of the Cayley planes, are obtained.","authors_text":"I. Mykytyuk, M. Castrillon Lopez, P. M. Gadea","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-05T17:22:37Z","title":"The canonical 8-form on manifolds with holonomy group Spin(9)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1079","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":"sha256:4266fd429630f4ca401e46de98ef488968b30b4c393886bdb0fc5dcc54d6c507","target":"record","created_at":"2026-05-18T02:10:59Z","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":"f21eca585ed527ed9a2ee138c0c378d33798f14a05c5939d653201da8f2edd78","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-05T17:22:37Z","title_canon_sha256":"8ba558f4b49a4b5e0bcfe99e6f2d83c6f991884c0b131ff8c5d41d6fae709e28"},"schema_version":"1.0","source":{"id":"0911.1079","kind":"arxiv","version":1}},"canonical_sha256":"c2e278fed8a4d96b7d97b1c4a059cf5de6f6b2ef9bcdba43cd7138b1043de19e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2e278fed8a4d96b7d97b1c4a059cf5de6f6b2ef9bcdba43cd7138b1043de19e","first_computed_at":"2026-05-18T02:10:59.183881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:59.183881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Qpqz/yhqH5MWOqW5NphYKvQt10z7mLZ1Nsbnxu6aoherXhVEQpbjKuxPoXUgtgqDknQkeXsV70UFDNA/WiNAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:59.184530Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4266fd429630f4ca401e46de98ef488968b30b4c393886bdb0fc5dcc54d6c507","sha256:da44c33c4cfd6088231b78c2b2a7a2207d936a3a00b63690f8563c641b1969df"],"state_sha256":"73dc157b03b873a48ba885549ed836e2b4bc5a4aa971ad3ae771de242afe5bc8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXXQ0fuJUShrmUDF3GGcS7UZNovk7AY+SJYnZ5ozJy1WP9IsP+ualOMl1KiD/akzuLcF5W7xnQraFCHrMBAuCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:09:34.130848Z","bundle_sha256":"34f68e43b3f8c662efc3c5b5082eb0e7a4a9c80d1eb9508d316385dcd43c8c0f"}}