{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4S7XGTY6JBH3F6SUDYFSNCD33C","short_pith_number":"pith:4S7XGTY6","canonical_record":{"source":{"id":"1109.6777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-30T10:01:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"15b010a489756781ec2fdb5898431b841c707806f8beaa31235eded3ce609879","abstract_canon_sha256":"40622be13d6a9c0fc0433fdf0f4641d09fc6fd8e7c6a0a1d65a93ba862dc78cf"},"schema_version":"1.0"},"canonical_sha256":"e4bf734f1e484fb2fa541e0b26887bd8bdbd8255e5eb24b44ad00897089d2148","source":{"kind":"arxiv","id":"1109.6777","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6777","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6777v2","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6777","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"4S7XGTY6JBH3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4S7XGTY6JBH3F6SU","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4S7XGTY6","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4S7XGTY6JBH3F6SUDYFSNCD33C","target":"record","payload":{"canonical_record":{"source":{"id":"1109.6777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-30T10:01:39Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"15b010a489756781ec2fdb5898431b841c707806f8beaa31235eded3ce609879","abstract_canon_sha256":"40622be13d6a9c0fc0433fdf0f4641d09fc6fd8e7c6a0a1d65a93ba862dc78cf"},"schema_version":"1.0"},"canonical_sha256":"e4bf734f1e484fb2fa541e0b26887bd8bdbd8255e5eb24b44ad00897089d2148","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:36.786547Z","signature_b64":"UZWgqHCZJ9uUYZXpBTy5Q2OQTqyI0g6uGguldHjvq/QpzAtBcWIXieTphsu15yiZyt8fX9iAMrCM/x2YULnbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4bf734f1e484fb2fa541e0b26887bd8bdbd8255e5eb24b44ad00897089d2148","last_reissued_at":"2026-05-18T00:32:36.785855Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:36.785855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.6777","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":"2026-05-18T00:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mamKxcaHzz7ZRloTBdfUTBPOlM+25jhR0GZ/e5g1sS3HfaOAimCu8oPNCcphGZniC6x4H/tps4RW5wze6LjSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:22:29.242438Z"},"content_sha256":"6457f75873014cecf26072e9266624caf109ecd183e3180f88809e09887c662d","schema_version":"1.0","event_id":"sha256:6457f75873014cecf26072e9266624caf109ecd183e3180f88809e09887c662d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4S7XGTY6JBH3F6SUDYFSNCD33C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spherical systems of the wonderful reductive subgroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Guido Pezzini, Paolo Bravi","submitted_at":"2011-09-30T10:01:39Z","abstract_excerpt":"We provide the spherical systems of the wonderful reductive subgroups of any reductive group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6777","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":"2026-05-18T00:32:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y9AFtAwAIl7Vb218xuoncl5bkrAAMGTk3KJkyXk2IL3GCoMbhTw+jW8UbDPNK6GcLHFiNMNFr0cUtTF2FuVOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:22:29.243153Z"},"content_sha256":"f6a352046255343fb13db089501bc4bc0cc0d08364276e10b53f489bc0032731","schema_version":"1.0","event_id":"sha256:f6a352046255343fb13db089501bc4bc0cc0d08364276e10b53f489bc0032731"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/bundle.json","state_url":"https://pith.science/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/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":"2026-06-10T06:22:29Z","links":{"resolver":"https://pith.science/pith/4S7XGTY6JBH3F6SUDYFSNCD33C","bundle":"https://pith.science/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/bundle.json","state":"https://pith.science/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4S7XGTY6JBH3F6SUDYFSNCD33C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4S7XGTY6JBH3F6SUDYFSNCD33C","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":"40622be13d6a9c0fc0433fdf0f4641d09fc6fd8e7c6a0a1d65a93ba862dc78cf","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-30T10:01:39Z","title_canon_sha256":"15b010a489756781ec2fdb5898431b841c707806f8beaa31235eded3ce609879"},"schema_version":"1.0","source":{"id":"1109.6777","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6777","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6777v2","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6777","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"4S7XGTY6JBH3","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4S7XGTY6JBH3F6SU","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4S7XGTY6","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:f6a352046255343fb13db089501bc4bc0cc0d08364276e10b53f489bc0032731","target":"graph","created_at":"2026-05-18T00:32:36Z","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 provide the spherical systems of the wonderful reductive subgroups of any reductive group.","authors_text":"Guido Pezzini, Paolo Bravi","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-30T10:01:39Z","title":"The spherical systems of the wonderful reductive subgroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6777","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":"sha256:6457f75873014cecf26072e9266624caf109ecd183e3180f88809e09887c662d","target":"record","created_at":"2026-05-18T00:32:36Z","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":"40622be13d6a9c0fc0433fdf0f4641d09fc6fd8e7c6a0a1d65a93ba862dc78cf","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-09-30T10:01:39Z","title_canon_sha256":"15b010a489756781ec2fdb5898431b841c707806f8beaa31235eded3ce609879"},"schema_version":"1.0","source":{"id":"1109.6777","kind":"arxiv","version":2}},"canonical_sha256":"e4bf734f1e484fb2fa541e0b26887bd8bdbd8255e5eb24b44ad00897089d2148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4bf734f1e484fb2fa541e0b26887bd8bdbd8255e5eb24b44ad00897089d2148","first_computed_at":"2026-05-18T00:32:36.785855Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:36.785855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UZWgqHCZJ9uUYZXpBTy5Q2OQTqyI0g6uGguldHjvq/QpzAtBcWIXieTphsu15yiZyt8fX9iAMrCM/x2YULnbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:36.786547Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6777","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6457f75873014cecf26072e9266624caf109ecd183e3180f88809e09887c662d","sha256:f6a352046255343fb13db089501bc4bc0cc0d08364276e10b53f489bc0032731"],"state_sha256":"bad0205c996ca7b71b433806c71d0dc3622dfb12187606e604564ba0e32814e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"awUIpdY3i/P2ORdUm9ryN2nKqa12cFZpvOgNRJyayqLqmHoZtKRS1C6X9vv5QxbaM2LvA6NG0zH/Q1c51ol1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T06:22:29.247488Z","bundle_sha256":"6eb94c475c287ef6c9f179795225a0806e96e8e6bcc00e052463dddfac272d93"}}