{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GGXJPRP4DI4ZZFVP2IL44AMBW2","short_pith_number":"pith:GGXJPRP4","canonical_record":{"source":{"id":"1703.00438","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T18:42:01Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"12925bb8d71ea9d829458928617755ddf46f49b4db96e1cfba20a993de4e39b8","abstract_canon_sha256":"81dc2774a5698c1863670cb2800a816eb675204b3a58df48961f792c8684fba9"},"schema_version":"1.0"},"canonical_sha256":"31ae97c5fc1a399c96afd217ce0181b6bc5e69874771e42f549e2f791478d158","source":{"kind":"arxiv","id":"1703.00438","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00438","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00438v5","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00438","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"GGXJPRP4DI4Z","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GGXJPRP4DI4ZZFVP","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GGXJPRP4","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GGXJPRP4DI4ZZFVP2IL44AMBW2","target":"record","payload":{"canonical_record":{"source":{"id":"1703.00438","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T18:42:01Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"12925bb8d71ea9d829458928617755ddf46f49b4db96e1cfba20a993de4e39b8","abstract_canon_sha256":"81dc2774a5698c1863670cb2800a816eb675204b3a58df48961f792c8684fba9"},"schema_version":"1.0"},"canonical_sha256":"31ae97c5fc1a399c96afd217ce0181b6bc5e69874771e42f549e2f791478d158","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:39.935836Z","signature_b64":"GEfNKs6Iruq8d133Zs61/YUUExHf+3q52qAc6SE2I1ToEicjfJBzn83JVWcujBAMFYTIjIJeaE3pI7lvOm7ZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ae97c5fc1a399c96afd217ce0181b6bc5e69874771e42f549e2f791478d158","last_reissued_at":"2026-05-18T00:20:39.935225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:39.935225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.00438","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ME/3yefe1KbpvgLDkM5O9j13usqJNDzNmzWbyDP9vc6J8eVTQDSYeG5Ez3sRKalDrkhxN/G5nFPQg6ypEMk0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:07:02.529107Z"},"content_sha256":"f7c8ec0eaefd55bffe269c9a21e117222ba7f26b41efe03d0134b62eadbe8f39","schema_version":"1.0","event_id":"sha256:f7c8ec0eaefd55bffe269c9a21e117222ba7f26b41efe03d0134b62eadbe8f39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GGXJPRP4DI4ZZFVP2IL44AMBW2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability of associated forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Alexander Isaev, Maksym Fedorchuk","submitted_at":"2017-03-01T18:42:01Z","abstract_excerpt":"We show that the associated form, or equivalently a Macaulay inverse system, of an Artinian complete intersection of type $(d,\\dots, d)$ is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00438","kind":"arxiv","version":5},"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":"2026-05-18T00:20:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QqA0zcFNJp3uybjEwVjCDvpHl37WSON8j8bgwu34Lo5kIhrb8hNyJ/aZet93U/hLk24iCJZMrUvAuyhqfdPiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:07:02.529467Z"},"content_sha256":"fd1a5674d6283b4d06f8356b394931d027566a79f18a0f742ff2e539205d6102","schema_version":"1.0","event_id":"sha256:fd1a5674d6283b4d06f8356b394931d027566a79f18a0f742ff2e539205d6102"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/bundle.json","state_url":"https://pith.science/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/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":"2026-06-04T20:07:02Z","links":{"resolver":"https://pith.science/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2","bundle":"https://pith.science/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/bundle.json","state":"https://pith.science/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGXJPRP4DI4ZZFVP2IL44AMBW2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GGXJPRP4DI4ZZFVP2IL44AMBW2","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":"81dc2774a5698c1863670cb2800a816eb675204b3a58df48961f792c8684fba9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T18:42:01Z","title_canon_sha256":"12925bb8d71ea9d829458928617755ddf46f49b4db96e1cfba20a993de4e39b8"},"schema_version":"1.0","source":{"id":"1703.00438","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.00438","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"arxiv_version","alias_value":"1703.00438v5","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00438","created_at":"2026-05-18T00:20:39Z"},{"alias_kind":"pith_short_12","alias_value":"GGXJPRP4DI4Z","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GGXJPRP4DI4ZZFVP","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GGXJPRP4","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:fd1a5674d6283b4d06f8356b394931d027566a79f18a0f742ff2e539205d6102","target":"graph","created_at":"2026-05-18T00:20:39Z","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 show that the associated form, or equivalently a Macaulay inverse system, of an Artinian complete intersection of type $(d,\\dots, d)$ is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities.","authors_text":"Alexander Isaev, Maksym Fedorchuk","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T18:42:01Z","title":"Stability of associated forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00438","kind":"arxiv","version":5},"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:f7c8ec0eaefd55bffe269c9a21e117222ba7f26b41efe03d0134b62eadbe8f39","target":"record","created_at":"2026-05-18T00:20:39Z","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":"81dc2774a5698c1863670cb2800a816eb675204b3a58df48961f792c8684fba9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-01T18:42:01Z","title_canon_sha256":"12925bb8d71ea9d829458928617755ddf46f49b4db96e1cfba20a993de4e39b8"},"schema_version":"1.0","source":{"id":"1703.00438","kind":"arxiv","version":5}},"canonical_sha256":"31ae97c5fc1a399c96afd217ce0181b6bc5e69874771e42f549e2f791478d158","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31ae97c5fc1a399c96afd217ce0181b6bc5e69874771e42f549e2f791478d158","first_computed_at":"2026-05-18T00:20:39.935225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:20:39.935225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GEfNKs6Iruq8d133Zs61/YUUExHf+3q52qAc6SE2I1ToEicjfJBzn83JVWcujBAMFYTIjIJeaE3pI7lvOm7ZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:20:39.935836Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.00438","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7c8ec0eaefd55bffe269c9a21e117222ba7f26b41efe03d0134b62eadbe8f39","sha256:fd1a5674d6283b4d06f8356b394931d027566a79f18a0f742ff2e539205d6102"],"state_sha256":"eaa256dd29359c23e2f7943556bc9b19a0a3421758ab7adc9a47c845fd00d055"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gy0bWhBMABhDbPl1kWqYYs/MUyoHd9v13lNPViOSN+aMrkrK4NS6soezr8cgcioAhdsUpXiUY36hTsAGKBLUDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:07:02.531484Z","bundle_sha256":"6b27ee4ad5f5ecc59460bce8e0c4f978e74f7c23cd9ca67b9389bfdc0b3f8949"}}