{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:46L7P5Y55FGXD32YDKH2KP5GC3","short_pith_number":"pith:46L7P5Y5","canonical_record":{"source":{"id":"1306.4838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-20T11:59:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6c344f9c8bba9cb4098e9a7d68c81813ebbda62bdc537e809aee94942e5a08b9","abstract_canon_sha256":"a53aa1664b0d5bcad0d40820e9d521e7aef0d7903856af360ee6a4b66ad81c67"},"schema_version":"1.0"},"canonical_sha256":"e797f7f71de94d71ef581a8fa53fa616e2e9fe8aaa4b06cdd49d4ba0f0bf0e7d","source":{"kind":"arxiv","id":"1306.4838","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4838","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4838v2","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4838","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"46L7P5Y55FGX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46L7P5Y55FGXD32Y","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46L7P5Y5","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:46L7P5Y55FGXD32YDKH2KP5GC3","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4838","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-20T11:59:29Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6c344f9c8bba9cb4098e9a7d68c81813ebbda62bdc537e809aee94942e5a08b9","abstract_canon_sha256":"a53aa1664b0d5bcad0d40820e9d521e7aef0d7903856af360ee6a4b66ad81c67"},"schema_version":"1.0"},"canonical_sha256":"e797f7f71de94d71ef581a8fa53fa616e2e9fe8aaa4b06cdd49d4ba0f0bf0e7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:07.648478Z","signature_b64":"G1k91Tl0cKtbMZO+fdzl4CVQQzLKK6yFmCRYs0V0fICW/u8KtqrbFaEnAV/4arjlXGT9cd8OYKnGQ3rLai3ZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e797f7f71de94d71ef581a8fa53fa616e2e9fe8aaa4b06cdd49d4ba0f0bf0e7d","last_reissued_at":"2026-05-18T01:16:07.647791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:07.647791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4838","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":"2026-05-18T01:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AqzdDXdppTMTj/1rvYZU4d0KMQWsY2eaK8wACea+JHJ+Mb2C85caod9vOo2UOQsatUowN6he3Bg4YC7LyUvtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:17:32.040928Z"},"content_sha256":"bf3531e186b847feea068332258339420304423699df9e891061e8e43b1aff0b","schema_version":"1.0","event_id":"sha256:bf3531e186b847feea068332258339420304423699df9e891061e8e43b1aff0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:46L7P5Y55FGXD32YDKH2KP5GC3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Laurent Evain (LAREMA), Michael Bulois","submitted_at":"2013-06-20T11:59:29Z","abstract_excerpt":"It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting variety of parabolic subalgebras of $M\\_n(\\K)$ and to the punctual nested Hilbert scheme. By this method, we obtain a lower bound on the dimension of these moduli spaces. We characterize the numerical conditions under which they are irreducible. In some reducible cases, we describe the irreducible components and their dimension."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4838","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":"2026-05-18T01:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"He5uXLIELyxUBDL6vj3LgPfYaoQvPB1HJZQlxozl1Y46s/FxmCabK6CGvF+Nhz63DZcDFt0/NDsAZ7g06lMhBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:17:32.041279Z"},"content_sha256":"3d182ae69fdbbdc170a9e5bb47dba4b243d5b259451c1c1eb11f17b83f8d6259","schema_version":"1.0","event_id":"sha256:3d182ae69fdbbdc170a9e5bb47dba4b243d5b259451c1c1eb11f17b83f8d6259"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/46L7P5Y55FGXD32YDKH2KP5GC3/bundle.json","state_url":"https://pith.science/pith/46L7P5Y55FGXD32YDKH2KP5GC3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/46L7P5Y55FGXD32YDKH2KP5GC3/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":"2026-06-02T04:17:32Z","links":{"resolver":"https://pith.science/pith/46L7P5Y55FGXD32YDKH2KP5GC3","bundle":"https://pith.science/pith/46L7P5Y55FGXD32YDKH2KP5GC3/bundle.json","state":"https://pith.science/pith/46L7P5Y55FGXD32YDKH2KP5GC3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/46L7P5Y55FGXD32YDKH2KP5GC3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:46L7P5Y55FGXD32YDKH2KP5GC3","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":"a53aa1664b0d5bcad0d40820e9d521e7aef0d7903856af360ee6a4b66ad81c67","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-20T11:59:29Z","title_canon_sha256":"6c344f9c8bba9cb4098e9a7d68c81813ebbda62bdc537e809aee94942e5a08b9"},"schema_version":"1.0","source":{"id":"1306.4838","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4838","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4838v2","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4838","created_at":"2026-05-18T01:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"46L7P5Y55FGX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"46L7P5Y55FGXD32Y","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"46L7P5Y5","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:3d182ae69fdbbdc170a9e5bb47dba4b243d5b259451c1c1eb11f17b83f8d6259","target":"graph","created_at":"2026-05-18T01:16:07Z","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":"It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting variety of parabolic subalgebras of $M\\_n(\\K)$ and to the punctual nested Hilbert scheme. By this method, we obtain a lower bound on the dimension of these moduli spaces. We characterize the numerical conditions under which they are irreducible. In some reducible cases, we describe the irreducible components and their dimension.","authors_text":"Laurent Evain (LAREMA), Michael Bulois","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-20T11:59:29Z","title":"Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4838","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:bf3531e186b847feea068332258339420304423699df9e891061e8e43b1aff0b","target":"record","created_at":"2026-05-18T01:16:07Z","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":"a53aa1664b0d5bcad0d40820e9d521e7aef0d7903856af360ee6a4b66ad81c67","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-06-20T11:59:29Z","title_canon_sha256":"6c344f9c8bba9cb4098e9a7d68c81813ebbda62bdc537e809aee94942e5a08b9"},"schema_version":"1.0","source":{"id":"1306.4838","kind":"arxiv","version":2}},"canonical_sha256":"e797f7f71de94d71ef581a8fa53fa616e2e9fe8aaa4b06cdd49d4ba0f0bf0e7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e797f7f71de94d71ef581a8fa53fa616e2e9fe8aaa4b06cdd49d4ba0f0bf0e7d","first_computed_at":"2026-05-18T01:16:07.647791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:07.647791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G1k91Tl0cKtbMZO+fdzl4CVQQzLKK6yFmCRYs0V0fICW/u8KtqrbFaEnAV/4arjlXGT9cd8OYKnGQ3rLai3ZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:07.648478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4838","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf3531e186b847feea068332258339420304423699df9e891061e8e43b1aff0b","sha256:3d182ae69fdbbdc170a9e5bb47dba4b243d5b259451c1c1eb11f17b83f8d6259"],"state_sha256":"6df0314c43ffafacf8b89a0c1d5083ca5c9c2dc7ce5f2ee877e793aa78273e2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7HtEfF/8TCY89OVgc8lW0ki9X7DN4RLDq6NeI49k83k+bgSjlos++QybXZXwc42mrFV4NCs7GohKjeQlJ/JADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:17:32.043434Z","bundle_sha256":"6f968e03ee2bfa99a54bd506a2f4f36a232a0f2bbead6a40859659513988417e"}}