{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6WP7DCQC5XYSWH7IZ5VXEJYJSP","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":"0b23a19c78ebcbbfb981bbba89fcabd0ce01fd90890cfd2296b79530f60ab832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-20T21:05:28Z","title_canon_sha256":"55ddf2eb98818e16e8d7c84d1f107572e98cc8e75d62ea5dccf899b2d9b50f64"},"schema_version":"1.0","source":{"id":"1909.09717","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.09717","created_at":"2026-07-05T01:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1909.09717v2","created_at":"2026-07-05T01:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.09717","created_at":"2026-07-05T01:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"6WP7DCQC5XYS","created_at":"2026-07-05T01:08:24Z"},{"alias_kind":"pith_short_16","alias_value":"6WP7DCQC5XYSWH7I","created_at":"2026-07-05T01:08:24Z"},{"alias_kind":"pith_short_8","alias_value":"6WP7DCQC","created_at":"2026-07-05T01:08:24Z"}],"graph_snapshots":[{"event_id":"sha256:f7b37adc25a0195f50bcd5823e7cc02dc9270fe8350ed36c3177e357dc2d60cb","target":"graph","created_at":"2026-07-05T01:08:24Z","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/1909.09717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes give an informal and leisurely introduction to $\\mathrm{G}_2$ geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structure in $7$ dimensions that is the pointwise model for $\\mathrm{G}_2$ geometry, using the octonions. The basics of $\\mathrm{G}_2$-structures are introduced, from a Riemannian geometric point of view, including a discussion of the torsion and its relation to curvature for a general $\\mathrm{G}_2$-structure, as well as the connection to Riemannian holonomy. The history and properties of torsion-free $\\mathrm{G}_2$ manifo","authors_text":"Spiro Karigiannis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-20T21:05:28Z","title":"Introduction to $\\mathrm{G}_2$ geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.09717","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":"sha256:006363e715abc656f1bb467139b36698af7d86df9e52257f2b7749245b18410f","target":"record","created_at":"2026-07-05T01:08:24Z","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":"0b23a19c78ebcbbfb981bbba89fcabd0ce01fd90890cfd2296b79530f60ab832","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-09-20T21:05:28Z","title_canon_sha256":"55ddf2eb98818e16e8d7c84d1f107572e98cc8e75d62ea5dccf899b2d9b50f64"},"schema_version":"1.0","source":{"id":"1909.09717","kind":"arxiv","version":2}},"canonical_sha256":"f59ff18a02edf12b1fe8cf6b72270993c3d16241eff8cc899c26062c5f8d648e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f59ff18a02edf12b1fe8cf6b72270993c3d16241eff8cc899c26062c5f8d648e","first_computed_at":"2026-07-05T01:08:24.862604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:08:24.862604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7I3LmoTxoMGmzOaDXc8ZVMrzAhN1Kmp5Hs/WJLq54Y80wEJU5UijKfijPu75kTEkt8Shay19CwMuTJjJ+d/Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:08:24.862995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.09717","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:006363e715abc656f1bb467139b36698af7d86df9e52257f2b7749245b18410f","sha256:f7b37adc25a0195f50bcd5823e7cc02dc9270fe8350ed36c3177e357dc2d60cb"],"state_sha256":"91604551d483fb0957757e3e44531312c4ca743e21408edd8b807d32ffeeaac7"}