{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:EJJRRKCW4BUJWJD77XMRPOIVZI","short_pith_number":"pith:EJJRRKCW","canonical_record":{"source":{"id":"1203.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-25T22:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"739f2f80f44ca0d0f7b1e834b0cbc883e80ad5ee39b723a630ab1248f6c84379","abstract_canon_sha256":"3c6d792a39210231ae1ea24f0d723cd0676288c8ba9cb34ef04d84f2ac590f37"},"schema_version":"1.0"},"canonical_sha256":"225318a856e0689b247ffdd917b915ca1a67966add37fd9ba173185d57556d27","source":{"kind":"arxiv","id":"1203.5549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5549","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5549v1","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5549","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"EJJRRKCW4BUJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EJJRRKCW4BUJWJD7","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EJJRRKCW","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:EJJRRKCW4BUJWJD77XMRPOIVZI","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-25T22:09:26Z","cross_cats_sorted":[],"title_canon_sha256":"739f2f80f44ca0d0f7b1e834b0cbc883e80ad5ee39b723a630ab1248f6c84379","abstract_canon_sha256":"3c6d792a39210231ae1ea24f0d723cd0676288c8ba9cb34ef04d84f2ac590f37"},"schema_version":"1.0"},"canonical_sha256":"225318a856e0689b247ffdd917b915ca1a67966add37fd9ba173185d57556d27","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:14.829968Z","signature_b64":"vudc1zWjvJM6KnBlcQ1vCeKQcbc/Wc4EpoO3zvCbGHqr9P1hLhHYquAVIjZkKsyttMX+FUzWpYzw0kT30hM2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"225318a856e0689b247ffdd917b915ca1a67966add37fd9ba173185d57556d27","last_reissued_at":"2026-05-18T03:59:14.829144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:14.829144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5549","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":"2026-05-18T03:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FBaiurh+ZYxU4UHUf17qJA6JJQANilKVPStgiTz4Ja1gjkU0pnwLCNob3bQ4Xu2WX2WUi+sK1HL3cuaW+1wRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:05:51.509901Z"},"content_sha256":"298cbe2375c7b325689b31ab8558c8c839ae81790134d10f756dfe96a3f4f258","schema_version":"1.0","event_id":"sha256:298cbe2375c7b325689b31ab8558c8c839ae81790134d10f756dfe96a3f4f258"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:EJJRRKCW4BUJWJD77XMRPOIVZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"A. V. Isaev, N. G. Kruzhilin","submitted_at":"2012-03-25T22:09:26Z","abstract_excerpt":"By the Mather-Yau theorem, a complex hypersurface germ $V$ with isolated singularity is completely determined by its moduli algebra $A(V)$. The proof of the theorem does not provide an explicit procedure for recovering $V$ from $A(V)$, and finding such a procedure is a long-standing open problem. In this paper, we present an explicit way for reconstructing $V$ from $A(V)$ up to biholomorphic equivalence under the assumption that the singularity of $V$ is homogeneous, in which case $A(V)$ coincides with the Milnor algebra of $V$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5549","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":"2026-05-18T03:59:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AtfGlG03QN5ye4/GidJmodvgpOh7jXcvUvCmod1iMDWaMc3QbCWqAw0UoUOd34V2ZHRhGeHFwYxFzTHMiDmIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:05:51.510237Z"},"content_sha256":"3cb9a818d9242ea02287427b62db69ab9f2c018976a4941cca39d5f3177fdaf1","schema_version":"1.0","event_id":"sha256:3cb9a818d9242ea02287427b62db69ab9f2c018976a4941cca39d5f3177fdaf1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/bundle.json","state_url":"https://pith.science/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/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":"2026-06-24T21:05:51Z","links":{"resolver":"https://pith.science/pith/EJJRRKCW4BUJWJD77XMRPOIVZI","bundle":"https://pith.science/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/bundle.json","state":"https://pith.science/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJJRRKCW4BUJWJD77XMRPOIVZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EJJRRKCW4BUJWJD77XMRPOIVZI","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":"3c6d792a39210231ae1ea24f0d723cd0676288c8ba9cb34ef04d84f2ac590f37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-25T22:09:26Z","title_canon_sha256":"739f2f80f44ca0d0f7b1e834b0cbc883e80ad5ee39b723a630ab1248f6c84379"},"schema_version":"1.0","source":{"id":"1203.5549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5549","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5549v1","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5549","created_at":"2026-05-18T03:59:14Z"},{"alias_kind":"pith_short_12","alias_value":"EJJRRKCW4BUJ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EJJRRKCW4BUJWJD7","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EJJRRKCW","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:3cb9a818d9242ea02287427b62db69ab9f2c018976a4941cca39d5f3177fdaf1","target":"graph","created_at":"2026-05-18T03:59:14Z","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":"By the Mather-Yau theorem, a complex hypersurface germ $V$ with isolated singularity is completely determined by its moduli algebra $A(V)$. The proof of the theorem does not provide an explicit procedure for recovering $V$ from $A(V)$, and finding such a procedure is a long-standing open problem. In this paper, we present an explicit way for reconstructing $V$ from $A(V)$ up to biholomorphic equivalence under the assumption that the singularity of $V$ is homogeneous, in which case $A(V)$ coincides with the Milnor algebra of $V$.","authors_text":"A. V. Isaev, N. G. Kruzhilin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-25T22:09:26Z","title":"Explicit reconstruction of homogeneous isolated hypersurface singularities from their Milnor algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5549","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":"sha256:298cbe2375c7b325689b31ab8558c8c839ae81790134d10f756dfe96a3f4f258","target":"record","created_at":"2026-05-18T03:59:14Z","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":"3c6d792a39210231ae1ea24f0d723cd0676288c8ba9cb34ef04d84f2ac590f37","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-25T22:09:26Z","title_canon_sha256":"739f2f80f44ca0d0f7b1e834b0cbc883e80ad5ee39b723a630ab1248f6c84379"},"schema_version":"1.0","source":{"id":"1203.5549","kind":"arxiv","version":1}},"canonical_sha256":"225318a856e0689b247ffdd917b915ca1a67966add37fd9ba173185d57556d27","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"225318a856e0689b247ffdd917b915ca1a67966add37fd9ba173185d57556d27","first_computed_at":"2026-05-18T03:59:14.829144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:14.829144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vudc1zWjvJM6KnBlcQ1vCeKQcbc/Wc4EpoO3zvCbGHqr9P1hLhHYquAVIjZkKsyttMX+FUzWpYzw0kT30hM2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:14.829968Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:298cbe2375c7b325689b31ab8558c8c839ae81790134d10f756dfe96a3f4f258","sha256:3cb9a818d9242ea02287427b62db69ab9f2c018976a4941cca39d5f3177fdaf1"],"state_sha256":"d7deb34d056f112b84b79db71d9a7ea1ffe7d5fd347d33f1be7f8388ed3d4988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5QNH/wz3E8lbVTj27lN2LwSYmJfPXiPSOm/bdrcoGLTBXALwQF2DT8nt3boSNjRIcrfzrrvfefxr0JflVzhpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:05:51.512101Z","bundle_sha256":"6c81ccb635ea0a1f287b0babd177ff959a932478f23a36ee60081fdee244dedd"}}