{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:M4LBLJ6MZCMAZFHALWLTDVRLSE","short_pith_number":"pith:M4LBLJ6M","canonical_record":{"source":{"id":"0807.4104","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-07-25T14:16:55Z","cross_cats_sorted":[],"title_canon_sha256":"b0480b4820861448e6c27af9a2ac0e1f3cda314df0ead5599b0e5a5d01b8f06d","abstract_canon_sha256":"1cb86388b4c63f05a94031f933bfd948115ea320f7cfd3c6bd28af02835a1794"},"schema_version":"1.0"},"canonical_sha256":"671615a7ccc8980c94e05d9731d62b9104799092db2262d08182f9ecbda7a22b","source":{"kind":"arxiv","id":"0807.4104","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4104","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4104v4","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4104","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"M4LBLJ6MZCMA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"M4LBLJ6MZCMAZFHA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"M4LBLJ6M","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:M4LBLJ6MZCMAZFHALWLTDVRLSE","target":"record","payload":{"canonical_record":{"source":{"id":"0807.4104","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-07-25T14:16:55Z","cross_cats_sorted":[],"title_canon_sha256":"b0480b4820861448e6c27af9a2ac0e1f3cda314df0ead5599b0e5a5d01b8f06d","abstract_canon_sha256":"1cb86388b4c63f05a94031f933bfd948115ea320f7cfd3c6bd28af02835a1794"},"schema_version":"1.0"},"canonical_sha256":"671615a7ccc8980c94e05d9731d62b9104799092db2262d08182f9ecbda7a22b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:07.347059Z","signature_b64":"AtxGlJqVl3f/UxUS7fx9Z/BYxJcNd9oyATJ5rNIv0WY3zpTQ0FIFlSgra/RBLXQVqRMlai1iENrLsdC7YzzEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"671615a7ccc8980c94e05d9731d62b9104799092db2262d08182f9ecbda7a22b","last_reissued_at":"2026-05-18T02:44:07.346526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:07.346526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.4104","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FCmBayxavK8e+G78ZF18CfGAOmtM+38PHWJoB6ITGmrdap/5JQLKxB9Gkwc6GA4/C+ys6MIu8wa5FR4qSCZcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:01:56.135656Z"},"content_sha256":"bb0384f75449d104ef484149f867ca61eaf59d6f8ca2c8fa2c411dd581688dfd","schema_version":"1.0","event_id":"sha256:bb0384f75449d104ef484149f867ca61eaf59d6f8ca2c8fa2c411dd581688dfd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:M4LBLJ6MZCMAZFHALWLTDVRLSE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a remark by Y. Namikawa","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michele Rossi","submitted_at":"2008-07-25T14:16:55Z","abstract_excerpt":"The aim of the present paper is on the one hand to produce examples supporting the conclusion of Y. Namikawa in Remark 2.8 of \\cite{N} and improving considerations of Example 1.11 of the same paper. On the other hand, it is intended to give a geometric interpretation of the rigidity properties of some trees of exceptional rational curves, as observed by Namikawa, which can be obtained by factorizing small resolutions through nodal threefolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4104","kind":"arxiv","version":4},"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":"2026-05-18T02:44:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xxu2K1jBfoqgHI7g+TQqQLV5JL0dV6bu/bTL/Puq5hoNnPVacrZlA7gf1kyjjWw75jpjCE0g0qgPfk70wkRLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:01:56.136335Z"},"content_sha256":"e646cd4bf69a82de8c32a0557ddbc6ebafe04e1386c5ee6a0a2d7b1bc63f193f","schema_version":"1.0","event_id":"sha256:e646cd4bf69a82de8c32a0557ddbc6ebafe04e1386c5ee6a0a2d7b1bc63f193f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/bundle.json","state_url":"https://pith.science/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/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":"2026-05-26T00:01:56Z","links":{"resolver":"https://pith.science/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE","bundle":"https://pith.science/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/bundle.json","state":"https://pith.science/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4LBLJ6MZCMAZFHALWLTDVRLSE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:M4LBLJ6MZCMAZFHALWLTDVRLSE","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":"1cb86388b4c63f05a94031f933bfd948115ea320f7cfd3c6bd28af02835a1794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-07-25T14:16:55Z","title_canon_sha256":"b0480b4820861448e6c27af9a2ac0e1f3cda314df0ead5599b0e5a5d01b8f06d"},"schema_version":"1.0","source":{"id":"0807.4104","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.4104","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"arxiv_version","alias_value":"0807.4104v4","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4104","created_at":"2026-05-18T02:44:07Z"},{"alias_kind":"pith_short_12","alias_value":"M4LBLJ6MZCMA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"M4LBLJ6MZCMAZFHA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"M4LBLJ6M","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e646cd4bf69a82de8c32a0557ddbc6ebafe04e1386c5ee6a0a2d7b1bc63f193f","target":"graph","created_at":"2026-05-18T02:44:07Z","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":"The aim of the present paper is on the one hand to produce examples supporting the conclusion of Y. Namikawa in Remark 2.8 of \\cite{N} and improving considerations of Example 1.11 of the same paper. On the other hand, it is intended to give a geometric interpretation of the rigidity properties of some trees of exceptional rational curves, as observed by Namikawa, which can be obtained by factorizing small resolutions through nodal threefolds.","authors_text":"Michele Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-07-25T14:16:55Z","title":"On a remark by Y. Namikawa"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4104","kind":"arxiv","version":4},"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:bb0384f75449d104ef484149f867ca61eaf59d6f8ca2c8fa2c411dd581688dfd","target":"record","created_at":"2026-05-18T02:44:07Z","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":"1cb86388b4c63f05a94031f933bfd948115ea320f7cfd3c6bd28af02835a1794","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-07-25T14:16:55Z","title_canon_sha256":"b0480b4820861448e6c27af9a2ac0e1f3cda314df0ead5599b0e5a5d01b8f06d"},"schema_version":"1.0","source":{"id":"0807.4104","kind":"arxiv","version":4}},"canonical_sha256":"671615a7ccc8980c94e05d9731d62b9104799092db2262d08182f9ecbda7a22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"671615a7ccc8980c94e05d9731d62b9104799092db2262d08182f9ecbda7a22b","first_computed_at":"2026-05-18T02:44:07.346526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:07.346526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AtxGlJqVl3f/UxUS7fx9Z/BYxJcNd9oyATJ5rNIv0WY3zpTQ0FIFlSgra/RBLXQVqRMlai1iENrLsdC7YzzEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:07.347059Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.4104","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb0384f75449d104ef484149f867ca61eaf59d6f8ca2c8fa2c411dd581688dfd","sha256:e646cd4bf69a82de8c32a0557ddbc6ebafe04e1386c5ee6a0a2d7b1bc63f193f"],"state_sha256":"224a13a040cf289ab5ed1229ac6db54f18160167f7ea7d828e9c3c35f88ed04a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZbdjSKZGkOb1N4+SptfZJ/vrTRAG4AeqAqM7VkKzgSccBIm0yQaB4U26tlIUmoXw2HBp8qy+L8XMKhb649vDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:01:56.140000Z","bundle_sha256":"a8efd9daeecfdc2198cfd4f578a435702b27dfa0654d76a9f0f7537683603f07"}}