{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YYBDZDX75U4XRR3DSOQHLODKN4","short_pith_number":"pith:YYBDZDX7","canonical_record":{"source":{"id":"1210.5318","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T05:37:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5786593a4b010d76e4b85cd6db97a2b6faf1012a0c13860ce4440dffad1e2cc3","abstract_canon_sha256":"2cb4c56538f007406de79dc3a8fcdd5521703d7fd6706c656b850ea4d4ecb7c8"},"schema_version":"1.0"},"canonical_sha256":"c6023c8effed3978c76393a075b86a6f258f75aa0582c29d34bb47a85230c7ca","source":{"kind":"arxiv","id":"1210.5318","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5318","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5318v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5318","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"YYBDZDX75U4X","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYBDZDX75U4XRR3D","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYBDZDX7","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YYBDZDX75U4XRR3DSOQHLODKN4","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5318","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T05:37:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"5786593a4b010d76e4b85cd6db97a2b6faf1012a0c13860ce4440dffad1e2cc3","abstract_canon_sha256":"2cb4c56538f007406de79dc3a8fcdd5521703d7fd6706c656b850ea4d4ecb7c8"},"schema_version":"1.0"},"canonical_sha256":"c6023c8effed3978c76393a075b86a6f258f75aa0582c29d34bb47a85230c7ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:45.559324Z","signature_b64":"WHpe616D9DcgZ3aT0o4mWVKf6tJdLTc4bs5YQrFG1Akz52IhuHQAsEHaII5HgcZpz1Dk4BtnhE6kEwSpCRc1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6023c8effed3978c76393a075b86a6f258f75aa0582c29d34bb47a85230c7ca","last_reissued_at":"2026-05-18T03:42:45.558877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:45.558877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5318","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E6KQFaoEIpoA+E8eoUtStdAADtt5d5Ep5XqLSS+PIrNevP9eGJ/Wdv9imt0ZJ94H1zwsjjiEScGgaNGNpfs4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:27:02.031165Z"},"content_sha256":"6f9d96da227a3c62f3df8de77222b2c9bc99f5f02c4bf51c1a3b43cbef2fa333","schema_version":"1.0","event_id":"sha256:6f9d96da227a3c62f3df8de77222b2c9bc99f5f02c4bf51c1a3b43cbef2fa333"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YYBDZDX75U4XRR3DSOQHLODKN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sylvester versus Gundelfinger","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Andries E. Brouwer, Mihaela Popoviciu","submitted_at":"2012-10-19T05:37:11Z","abstract_excerpt":"Let $V_n$ be the ${\\rm SL}_2$-module of binary forms of degree $n$ and let $V = V_1 \\oplus V_3 \\oplus V_4$. We show that the minimum number of generators of the algebra $R = \\mathbb{C}[V]^{{\\rm SL}_2}$ of polynomial functions on $V$ invariant under the action of ${\\rm SL}_2$ equals 63. This settles a 143-year old question."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5318","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4P++/fvUrqKm6XGljbfZwczyLs0SZ9WcqwaZtQVfCNOQe1nTfor6AG0+Jco5zDIJsoz0qvRt3soO9upkexG7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:27:02.031521Z"},"content_sha256":"35c5e2eeea500047001da572758a143e0ba9a5ea3581fe183fe258ba232b96f9","schema_version":"1.0","event_id":"sha256:35c5e2eeea500047001da572758a143e0ba9a5ea3581fe183fe258ba232b96f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YYBDZDX75U4XRR3DSOQHLODKN4/bundle.json","state_url":"https://pith.science/pith/YYBDZDX75U4XRR3DSOQHLODKN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YYBDZDX75U4XRR3DSOQHLODKN4/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":"2026-06-01T16:27:02Z","links":{"resolver":"https://pith.science/pith/YYBDZDX75U4XRR3DSOQHLODKN4","bundle":"https://pith.science/pith/YYBDZDX75U4XRR3DSOQHLODKN4/bundle.json","state":"https://pith.science/pith/YYBDZDX75U4XRR3DSOQHLODKN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YYBDZDX75U4XRR3DSOQHLODKN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YYBDZDX75U4XRR3DSOQHLODKN4","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":"2cb4c56538f007406de79dc3a8fcdd5521703d7fd6706c656b850ea4d4ecb7c8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T05:37:11Z","title_canon_sha256":"5786593a4b010d76e4b85cd6db97a2b6faf1012a0c13860ce4440dffad1e2cc3"},"schema_version":"1.0","source":{"id":"1210.5318","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5318","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5318v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5318","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"YYBDZDX75U4X","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"YYBDZDX75U4XRR3D","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"YYBDZDX7","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:35c5e2eeea500047001da572758a143e0ba9a5ea3581fe183fe258ba232b96f9","target":"graph","created_at":"2026-05-18T03:42:45Z","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":"Let $V_n$ be the ${\\rm SL}_2$-module of binary forms of degree $n$ and let $V = V_1 \\oplus V_3 \\oplus V_4$. We show that the minimum number of generators of the algebra $R = \\mathbb{C}[V]^{{\\rm SL}_2}$ of polynomial functions on $V$ invariant under the action of ${\\rm SL}_2$ equals 63. This settles a 143-year old question.","authors_text":"Andries E. Brouwer, Mihaela Popoviciu","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T05:37:11Z","title":"Sylvester versus Gundelfinger"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5318","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":"sha256:6f9d96da227a3c62f3df8de77222b2c9bc99f5f02c4bf51c1a3b43cbef2fa333","target":"record","created_at":"2026-05-18T03:42:45Z","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":"2cb4c56538f007406de79dc3a8fcdd5521703d7fd6706c656b850ea4d4ecb7c8","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T05:37:11Z","title_canon_sha256":"5786593a4b010d76e4b85cd6db97a2b6faf1012a0c13860ce4440dffad1e2cc3"},"schema_version":"1.0","source":{"id":"1210.5318","kind":"arxiv","version":1}},"canonical_sha256":"c6023c8effed3978c76393a075b86a6f258f75aa0582c29d34bb47a85230c7ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6023c8effed3978c76393a075b86a6f258f75aa0582c29d34bb47a85230c7ca","first_computed_at":"2026-05-18T03:42:45.558877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:45.558877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WHpe616D9DcgZ3aT0o4mWVKf6tJdLTc4bs5YQrFG1Akz52IhuHQAsEHaII5HgcZpz1Dk4BtnhE6kEwSpCRc1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:45.559324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5318","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f9d96da227a3c62f3df8de77222b2c9bc99f5f02c4bf51c1a3b43cbef2fa333","sha256:35c5e2eeea500047001da572758a143e0ba9a5ea3581fe183fe258ba232b96f9"],"state_sha256":"b10565312fb0d0c1f9071d6cb8a05d89ee7ca7eced26a09e5cd8c1b7abc4bba4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8y/NWwJwEcW4pekl4DIrKKnw0DqJ444V0+HMH6ptkhjALseXHRTqxJD+4QeRS5iIfBLWkP68aRwBe6t8ysq7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:27:02.033370Z","bundle_sha256":"b4b42fda5efaa1230f5202efc4607bf0b70b5806b8abec5ceb130d7ae1817387"}}