{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:Y5H7VGELV45Z3D2MHFDYK3RNQH","short_pith_number":"pith:Y5H7VGEL","canonical_record":{"source":{"id":"0909.1975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-10T15:28:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1add64876670d9ddc56f9cbaf75d0744a2618c6e575705009bda4a3f38f40b04","abstract_canon_sha256":"fd59d59b9731fe55a1f815551629d1b3ad391c983246b58c1ca8bb0beab18dcf"},"schema_version":"1.0"},"canonical_sha256":"c74ffa988baf3b9d8f4c3947856e2d81cff93762b3b82fbd22e949cd8a9baf40","source":{"kind":"arxiv","id":"0909.1975","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1975","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1975v2","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1975","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"Y5H7VGELV45Z","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Y5H7VGELV45Z3D2M","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Y5H7VGEL","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:Y5H7VGELV45Z3D2MHFDYK3RNQH","target":"record","payload":{"canonical_record":{"source":{"id":"0909.1975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-10T15:28:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1add64876670d9ddc56f9cbaf75d0744a2618c6e575705009bda4a3f38f40b04","abstract_canon_sha256":"fd59d59b9731fe55a1f815551629d1b3ad391c983246b58c1ca8bb0beab18dcf"},"schema_version":"1.0"},"canonical_sha256":"c74ffa988baf3b9d8f4c3947856e2d81cff93762b3b82fbd22e949cd8a9baf40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:54.607733Z","signature_b64":"lZoVR3sb5DZbg8UZ9L0Kl7RAEwtNFtfUTeYkOFTHK13t/kfxLjkFEOaTRFU8aCkNxz60HwfJM5e1tTEkWB/UDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c74ffa988baf3b9d8f4c3947856e2d81cff93762b3b82fbd22e949cd8a9baf40","last_reissued_at":"2026-05-18T04:32:54.607157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:54.607157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.1975","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XMpA6PrnbpsRxdFwqdCxQjXBIhcKDbui9V3hPsplJMH9F6FF5fmDMWH/tGAaeiaROseh17uHyC3UnkYgG+jgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:48.277749Z"},"content_sha256":"8a9eec8b6f639322d07d10fddc9f7bafd9061a5590c11200465a4f4dde0b4342","schema_version":"1.0","event_id":"sha256:8a9eec8b6f639322d07d10fddc9f7bafd9061a5590c11200465a4f4dde0b4342"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:Y5H7VGELV45Z3D2MHFDYK3RNQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classifying superpotentials: three summands case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Andrew Dancer, Mckenzie Wang","submitted_at":"2009-09-10T15:28:27Z","abstract_excerpt":"We give an overview of our earlier classification results in [DW4] and [DW6] for superpotentials of scalar curvature type of the cohomogeneity one Ricci-flat equations. We then give an account of the classification in the case where the isotropy representation of the principal orbit consists of exactly three distinct irreducible real summands--the leftover case from [DW6]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1975","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":"2026-05-18T04:32:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SP8wB4+jaEzDWzUIMzB7hOtfuDUQOzVzl/fc4StgEliYmseQGCAUjRGGuoKWaMBZpWmHvpk0nYGdWZPw8imdCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:34:48.278107Z"},"content_sha256":"65bd6db0a22aaac14afff87c1f21d589934720de5310044918deeb98424d787f","schema_version":"1.0","event_id":"sha256:65bd6db0a22aaac14afff87c1f21d589934720de5310044918deeb98424d787f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/bundle.json","state_url":"https://pith.science/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/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":"2026-05-28T13:34:48Z","links":{"resolver":"https://pith.science/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH","bundle":"https://pith.science/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/bundle.json","state":"https://pith.science/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5H7VGELV45Z3D2MHFDYK3RNQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Y5H7VGELV45Z3D2MHFDYK3RNQH","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":"fd59d59b9731fe55a1f815551629d1b3ad391c983246b58c1ca8bb0beab18dcf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-10T15:28:27Z","title_canon_sha256":"1add64876670d9ddc56f9cbaf75d0744a2618c6e575705009bda4a3f38f40b04"},"schema_version":"1.0","source":{"id":"0909.1975","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.1975","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"arxiv_version","alias_value":"0909.1975v2","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.1975","created_at":"2026-05-18T04:32:54Z"},{"alias_kind":"pith_short_12","alias_value":"Y5H7VGELV45Z","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Y5H7VGELV45Z3D2M","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Y5H7VGEL","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:65bd6db0a22aaac14afff87c1f21d589934720de5310044918deeb98424d787f","target":"graph","created_at":"2026-05-18T04:32:54Z","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 an overview of our earlier classification results in [DW4] and [DW6] for superpotentials of scalar curvature type of the cohomogeneity one Ricci-flat equations. We then give an account of the classification in the case where the isotropy representation of the principal orbit consists of exactly three distinct irreducible real summands--the leftover case from [DW6].","authors_text":"Andrew Dancer, Mckenzie Wang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-10T15:28:27Z","title":"Classifying superpotentials: three summands case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1975","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":"sha256:8a9eec8b6f639322d07d10fddc9f7bafd9061a5590c11200465a4f4dde0b4342","target":"record","created_at":"2026-05-18T04:32:54Z","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":"fd59d59b9731fe55a1f815551629d1b3ad391c983246b58c1ca8bb0beab18dcf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-09-10T15:28:27Z","title_canon_sha256":"1add64876670d9ddc56f9cbaf75d0744a2618c6e575705009bda4a3f38f40b04"},"schema_version":"1.0","source":{"id":"0909.1975","kind":"arxiv","version":2}},"canonical_sha256":"c74ffa988baf3b9d8f4c3947856e2d81cff93762b3b82fbd22e949cd8a9baf40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c74ffa988baf3b9d8f4c3947856e2d81cff93762b3b82fbd22e949cd8a9baf40","first_computed_at":"2026-05-18T04:32:54.607157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:54.607157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lZoVR3sb5DZbg8UZ9L0Kl7RAEwtNFtfUTeYkOFTHK13t/kfxLjkFEOaTRFU8aCkNxz60HwfJM5e1tTEkWB/UDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:54.607733Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.1975","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a9eec8b6f639322d07d10fddc9f7bafd9061a5590c11200465a4f4dde0b4342","sha256:65bd6db0a22aaac14afff87c1f21d589934720de5310044918deeb98424d787f"],"state_sha256":"e07b469900ce9125843faf6fedc16be849a85bc06aa0a59d8955ca42b1f4ba66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVbqn3wZ6TzDLrv5Fs8ZJZ63/eU/IAjKPbD3QEGAV3I6A1JtDXNlhF8yN4TP2UApoO0lK8wnn4eJViLTyFfcAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:34:48.280203Z","bundle_sha256":"f75f86d8ec9643f71452fb82098a015826b3b7b5ba884535f037fcd127af9463"}}