{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GZAWX44A6VD2H24MW2EJJQ4RHC","short_pith_number":"pith:GZAWX44A","canonical_record":{"source":{"id":"1407.6838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T10:10:56Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"712919ad1152bbaaa4aabbf01eed46ad63811fae6abed10287b12772b467819e","abstract_canon_sha256":"3122678bda50f82b6afb8143712c0bf75f73b0c390fd7c9d58133445ec3bfd90"},"schema_version":"1.0"},"canonical_sha256":"36416bf380f547a3eb8cb68894c3913888c833bdac80b47a5b3c3d18080de1ec","source":{"kind":"arxiv","id":"1407.6838","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6838","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6838v3","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6838","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"GZAWX44A6VD2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZAWX44A6VD2H24M","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZAWX44A","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GZAWX44A6VD2H24MW2EJJQ4RHC","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6838","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T10:10:56Z","cross_cats_sorted":["math.AC","math.CV"],"title_canon_sha256":"712919ad1152bbaaa4aabbf01eed46ad63811fae6abed10287b12772b467819e","abstract_canon_sha256":"3122678bda50f82b6afb8143712c0bf75f73b0c390fd7c9d58133445ec3bfd90"},"schema_version":"1.0"},"canonical_sha256":"36416bf380f547a3eb8cb68894c3913888c833bdac80b47a5b3c3d18080de1ec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:32.683426Z","signature_b64":"2p/IuKYmUhFEElHWW/TyoK1GseY15TVeJredNw8pE8UKqJMoc4vy+NJ9CrMjdwvcLfWAfVuTF/hIUbhrjAQJDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36416bf380f547a3eb8cb68894c3913888c833bdac80b47a5b3c3d18080de1ec","last_reissued_at":"2026-05-18T01:21:32.682861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:32.682861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6838","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C81KRcPARJNkaOxXWnoxxARGcyai1SB2g3mszJHtaiLNmfTqnM5+D/nrNOIf1NSOacCpuKdfGsVmOOu7kk9bBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:19:32.440134Z"},"content_sha256":"fc3963216df6493e5e1e03e04aee8fff8058c7148959592c1c26f411da22ec3a","schema_version":"1.0","event_id":"sha256:fc3963216df6493e5e1e03e04aee8fff8058c7148959592c1c26f411da22ec3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GZAWX44A6VD2H24MW2EJJQ4RHC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Associated Forms and Hypersurface Singularities: The Binary Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV"],"primary_cat":"math.AG","authors_text":"Alexander Isaev, Jarod Alper","submitted_at":"2014-07-25T10:10:56Z","abstract_excerpt":"In the recent articles by Alper, Eastwood and Isaev, it was conjectured that all rational $GL_n({\\mathbb C})$-invariant functions of forms of degree $d\\ge 3$ on ${\\mathbb C}^n$ can be extracted, in a canonical way, from those of forms of degree $n(d-2)$ by means of assigning every form with nonvanishing discriminant the so-called associated form. While this surprising statement is interesting from the point of view of classical invariant theory, its original motivation was the reconstruction problem for isolated hypersurface singularities, which is the problem of finding a constructive proof o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6838","kind":"arxiv","version":3},"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":"2026-05-18T01:21:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0b5Gc5kjJxC8UO8alblpydSaqJYmshgr0LYpMb8idIbL3qXFDsFdumtI4zuCdCop10JZtCdRBadAvP4Bn+rBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:19:32.440493Z"},"content_sha256":"05dfd5a3c8bf986c4ec28de60c5b0bebbbe156e3ea4e3a167ceff761dd84fc1b","schema_version":"1.0","event_id":"sha256:05dfd5a3c8bf986c4ec28de60c5b0bebbbe156e3ea4e3a167ceff761dd84fc1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/bundle.json","state_url":"https://pith.science/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/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":"2026-06-23T18:19:32Z","links":{"resolver":"https://pith.science/pith/GZAWX44A6VD2H24MW2EJJQ4RHC","bundle":"https://pith.science/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/bundle.json","state":"https://pith.science/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZAWX44A6VD2H24MW2EJJQ4RHC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GZAWX44A6VD2H24MW2EJJQ4RHC","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":"3122678bda50f82b6afb8143712c0bf75f73b0c390fd7c9d58133445ec3bfd90","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T10:10:56Z","title_canon_sha256":"712919ad1152bbaaa4aabbf01eed46ad63811fae6abed10287b12772b467819e"},"schema_version":"1.0","source":{"id":"1407.6838","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6838","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6838v3","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6838","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"GZAWX44A6VD2","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GZAWX44A6VD2H24M","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GZAWX44A","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:05dfd5a3c8bf986c4ec28de60c5b0bebbbe156e3ea4e3a167ceff761dd84fc1b","target":"graph","created_at":"2026-05-18T01:21:32Z","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":"In the recent articles by Alper, Eastwood and Isaev, it was conjectured that all rational $GL_n({\\mathbb C})$-invariant functions of forms of degree $d\\ge 3$ on ${\\mathbb C}^n$ can be extracted, in a canonical way, from those of forms of degree $n(d-2)$ by means of assigning every form with nonvanishing discriminant the so-called associated form. While this surprising statement is interesting from the point of view of classical invariant theory, its original motivation was the reconstruction problem for isolated hypersurface singularities, which is the problem of finding a constructive proof o","authors_text":"Alexander Isaev, Jarod Alper","cross_cats":["math.AC","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T10:10:56Z","title":"Associated Forms and Hypersurface Singularities: The Binary Case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6838","kind":"arxiv","version":3},"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:fc3963216df6493e5e1e03e04aee8fff8058c7148959592c1c26f411da22ec3a","target":"record","created_at":"2026-05-18T01:21:32Z","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":"3122678bda50f82b6afb8143712c0bf75f73b0c390fd7c9d58133445ec3bfd90","cross_cats_sorted":["math.AC","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-25T10:10:56Z","title_canon_sha256":"712919ad1152bbaaa4aabbf01eed46ad63811fae6abed10287b12772b467819e"},"schema_version":"1.0","source":{"id":"1407.6838","kind":"arxiv","version":3}},"canonical_sha256":"36416bf380f547a3eb8cb68894c3913888c833bdac80b47a5b3c3d18080de1ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36416bf380f547a3eb8cb68894c3913888c833bdac80b47a5b3c3d18080de1ec","first_computed_at":"2026-05-18T01:21:32.682861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:32.682861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2p/IuKYmUhFEElHWW/TyoK1GseY15TVeJredNw8pE8UKqJMoc4vy+NJ9CrMjdwvcLfWAfVuTF/hIUbhrjAQJDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:32.683426Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6838","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc3963216df6493e5e1e03e04aee8fff8058c7148959592c1c26f411da22ec3a","sha256:05dfd5a3c8bf986c4ec28de60c5b0bebbbe156e3ea4e3a167ceff761dd84fc1b"],"state_sha256":"7421b1d6534276c10d7d38443a9e37904851294bf201a7f37986a2d40c635279"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIPGoV6xPn1F0dzElm8Mqn1KhORgB+8c78JGd9sxwDX8AEvsHy+Qef6z+GQkPIiGSoMJ1KLN6cXFhcZEHpkNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:19:32.442559Z","bundle_sha256":"4bc30c4e2c8012ac80160acbde35e26406cc5fc6c282f5687a86d8bea1be374f"}}