{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:KIKFN3MCROAPNEB2RSCL7EF3BD","short_pith_number":"pith:KIKFN3MC","canonical_record":{"source":{"id":"math-ph/0503054","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-03-22T17:53:27Z","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"title_canon_sha256":"bd7bf43f961700e03bedf4fc874ba64e19f3777bcc578506cce96053bc192481","abstract_canon_sha256":"f01d10d29b070e5d906c1872e8262640e4a5fcfd82a3641188d7649cc3ba1376"},"schema_version":"1.0"},"canonical_sha256":"521456ed828b80f6903a8c84bf90bb08f8522e04bb5dbae4822768eb47eedf50","source":{"kind":"arxiv","id":"math-ph/0503054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0503054","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0503054v1","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0503054","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"KIKFN3MCROAP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"KIKFN3MCROAPNEB2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"KIKFN3MC","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:KIKFN3MCROAPNEB2RSCL7EF3BD","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0503054","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2005-03-22T17:53:27Z","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"title_canon_sha256":"bd7bf43f961700e03bedf4fc874ba64e19f3777bcc578506cce96053bc192481","abstract_canon_sha256":"f01d10d29b070e5d906c1872e8262640e4a5fcfd82a3641188d7649cc3ba1376"},"schema_version":"1.0"},"canonical_sha256":"521456ed828b80f6903a8c84bf90bb08f8522e04bb5dbae4822768eb47eedf50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:36.508043Z","signature_b64":"1wc1/3SXIq2q9lnzRdzKUWS8yXuwXVhsKeyLdVbqDbvaVyBBig0cyoPN9whTENDUa1cA6gO9oDYtiimzJIAqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"521456ed828b80f6903a8c84bf90bb08f8522e04bb5dbae4822768eb47eedf50","last_reissued_at":"2026-05-18T04:24:36.507596Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:36.507596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0503054","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":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LPBtCfkdm1rIIaU740c68WrriF3bmXoLdD3h6UIUob/HbOMo7wZUzBfZExcrqM9R7GYrjZcxyEBOkt9dvgCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:58:13.342533Z"},"content_sha256":"d55c403e8c539f53f87106f700b1e06e6b4a825fc3afbf7ec7c66e9e57a38c14","schema_version":"1.0","event_id":"sha256:d55c403e8c539f53f87106f700b1e06e6b4a825fc3afbf7ec7c66e9e57a38c14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:KIKFN3MCROAPNEB2RSCL7EF3BD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple parametrization for G2","license":"","headline":"","cross_cats":["hep-lat","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Sergio L. Cacciatori","submitted_at":"2005-03-22T17:53:27Z","abstract_excerpt":"We give a simple parametrization of the $G_2$ group, which is consistent with the structure of $G_2$ as a SU(3) fibration. We also explicitly compute the (bi)invariant measure, which turns out to have a simple expression."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0503054","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":"2026-05-18T04:24:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUJoNAjfRZ3XbGFSAjo/+t2kNkFxx52IN3+CrPSL998v9RPDdbneIpYPFosDa/tZKQ+rBZG7Stmr+25rAH27CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T12:58:13.342926Z"},"content_sha256":"1bf4fcca0fdbd1e1b246066ff92a2c709574a9a858fc0b8202bcacc5161bd46e","schema_version":"1.0","event_id":"sha256:1bf4fcca0fdbd1e1b246066ff92a2c709574a9a858fc0b8202bcacc5161bd46e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/bundle.json","state_url":"https://pith.science/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/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":"2026-06-08T12:58:13Z","links":{"resolver":"https://pith.science/pith/KIKFN3MCROAPNEB2RSCL7EF3BD","bundle":"https://pith.science/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/bundle.json","state":"https://pith.science/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KIKFN3MCROAPNEB2RSCL7EF3BD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:KIKFN3MCROAPNEB2RSCL7EF3BD","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":"f01d10d29b070e5d906c1872e8262640e4a5fcfd82a3641188d7649cc3ba1376","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-03-22T17:53:27Z","title_canon_sha256":"bd7bf43f961700e03bedf4fc874ba64e19f3777bcc578506cce96053bc192481"},"schema_version":"1.0","source":{"id":"math-ph/0503054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0503054","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0503054v1","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0503054","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"KIKFN3MCROAP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"KIKFN3MCROAPNEB2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"KIKFN3MC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:1bf4fcca0fdbd1e1b246066ff92a2c709574a9a858fc0b8202bcacc5161bd46e","target":"graph","created_at":"2026-05-18T04:24:36Z","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":"We give a simple parametrization of the $G_2$ group, which is consistent with the structure of $G_2$ as a SU(3) fibration. We also explicitly compute the (bi)invariant measure, which turns out to have a simple expression.","authors_text":"Sergio L. Cacciatori","cross_cats":["hep-lat","hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2005-03-22T17:53:27Z","title":"A simple parametrization for G2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0503054","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:d55c403e8c539f53f87106f700b1e06e6b4a825fc3afbf7ec7c66e9e57a38c14","target":"record","created_at":"2026-05-18T04:24:36Z","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":"f01d10d29b070e5d906c1872e8262640e4a5fcfd82a3641188d7649cc3ba1376","cross_cats_sorted":["hep-lat","hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2005-03-22T17:53:27Z","title_canon_sha256":"bd7bf43f961700e03bedf4fc874ba64e19f3777bcc578506cce96053bc192481"},"schema_version":"1.0","source":{"id":"math-ph/0503054","kind":"arxiv","version":1}},"canonical_sha256":"521456ed828b80f6903a8c84bf90bb08f8522e04bb5dbae4822768eb47eedf50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"521456ed828b80f6903a8c84bf90bb08f8522e04bb5dbae4822768eb47eedf50","first_computed_at":"2026-05-18T04:24:36.507596Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:36.507596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1wc1/3SXIq2q9lnzRdzKUWS8yXuwXVhsKeyLdVbqDbvaVyBBig0cyoPN9whTENDUa1cA6gO9oDYtiimzJIAqCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:36.508043Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0503054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d55c403e8c539f53f87106f700b1e06e6b4a825fc3afbf7ec7c66e9e57a38c14","sha256:1bf4fcca0fdbd1e1b246066ff92a2c709574a9a858fc0b8202bcacc5161bd46e"],"state_sha256":"9b1a3bd40ff3518b10712133dc8d442b45aee8cd5c9f6fa59d681f860ae085d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JvIsD7dnXcvPgttmdTbM38Dp4L1TEFL4o+9UeyltR/w/8xai+A7zoEm7ic7Atv322w4ppxc2kA9lc3q2v4snAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T12:58:13.345124Z","bundle_sha256":"5f55ea28cd7842a36385ba6dd1000b5e6ab18aa6da44fcb457b9e4e07697752a"}}