{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:CNFFY7NMRL7QLVSRIZNDZEERL3","short_pith_number":"pith:CNFFY7NM","canonical_record":{"source":{"id":"alg-geom/9305006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:42:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dae59eccf06c060c6da9df58ed04d5a752ad3d6414a3e69ba1239daccc56056b","abstract_canon_sha256":"4f28ca8dfba1d4dad94a072c2f64dfed607603b71ec7e9e062e1f12c9040db2b"},"schema_version":"1.0"},"canonical_sha256":"134a5c7dac8aff05d651465a3c90915ede49a5491e6dd5e76e1edca68ab4eb26","source":{"kind":"arxiv","id":"alg-geom/9305006","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9305006","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9305006v1","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9305006","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"CNFFY7NMRL7Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CNFFY7NMRL7QLVSR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CNFFY7NM","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:CNFFY7NMRL7QLVSRIZNDZEERL3","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9305006","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:42:51Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dae59eccf06c060c6da9df58ed04d5a752ad3d6414a3e69ba1239daccc56056b","abstract_canon_sha256":"4f28ca8dfba1d4dad94a072c2f64dfed607603b71ec7e9e062e1f12c9040db2b"},"schema_version":"1.0"},"canonical_sha256":"134a5c7dac8aff05d651465a3c90915ede49a5491e6dd5e76e1edca68ab4eb26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:21.822396Z","signature_b64":"0NK8WNfuVeD3mUgKi52PtwCA7OjhpGODuK6u7hv+YHULlsJdiyr9xRBL/6xTq0nHPfzAmf0tvpo7kzFxaSavAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"134a5c7dac8aff05d651465a3c90915ede49a5491e6dd5e76e1edca68ab4eb26","last_reissued_at":"2026-05-18T01:09:21.822026Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:21.822026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9305006","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":"2026-05-18T01:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sbLx2Vua9BXWEtwdqfLoCdKNmDZMfMS8BP53579jodM/1UmjNw4+vVwrj4pHI8+hX4t0oAe6plcQsgkGudHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:31:52.973250Z"},"content_sha256":"d7e59f04fac4fd91f7be566984a883d014f0f67549263f8ec806e6650f272a37","schema_version":"1.0","event_id":"sha256:d7e59f04fac4fd91f7be566984a883d014f0f67549263f8ec806e6650f272a37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:CNFFY7NMRL7QLVSRIZNDZEERL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Noether exponent and Jacobi formula","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Arkadiusz P{\\l}oski","submitted_at":"1993-05-19T07:42:51Z","abstract_excerpt":"For any polynomial mapping $F=(F_1,\\dots ,F_n)$ of $\\Cal C^n$ with a finite number of zeros we define the Noether exponent $\\nu(F)$. We prove the Jacobi formula for all polynomials of degree strictly less than $\\sum_{i=1}^n (\\deg F_i-1)-\\nu(F)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9305006","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":"2026-05-18T01:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ukzV3sl6/8KaVdVN9STeDfzf5PsSLYfdjTJlzXysUXFf5ice6gSbYl2wbDiitBMkVibti4EY8eyDvDqLCKGGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:31:52.973677Z"},"content_sha256":"c7c832a292ca2727fbc89eab6c2877cb63590fcdcbc3d67ba320d171d97448b9","schema_version":"1.0","event_id":"sha256:c7c832a292ca2727fbc89eab6c2877cb63590fcdcbc3d67ba320d171d97448b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/bundle.json","state_url":"https://pith.science/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/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":"2026-06-25T10:31:52Z","links":{"resolver":"https://pith.science/pith/CNFFY7NMRL7QLVSRIZNDZEERL3","bundle":"https://pith.science/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/bundle.json","state":"https://pith.science/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CNFFY7NMRL7QLVSRIZNDZEERL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:CNFFY7NMRL7QLVSRIZNDZEERL3","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":"4f28ca8dfba1d4dad94a072c2f64dfed607603b71ec7e9e062e1f12c9040db2b","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:42:51Z","title_canon_sha256":"dae59eccf06c060c6da9df58ed04d5a752ad3d6414a3e69ba1239daccc56056b"},"schema_version":"1.0","source":{"id":"alg-geom/9305006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9305006","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9305006v1","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9305006","created_at":"2026-05-18T01:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"CNFFY7NMRL7Q","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CNFFY7NMRL7QLVSR","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CNFFY7NM","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:c7c832a292ca2727fbc89eab6c2877cb63590fcdcbc3d67ba320d171d97448b9","target":"graph","created_at":"2026-05-18T01:09:21Z","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":"For any polynomial mapping $F=(F_1,\\dots ,F_n)$ of $\\Cal C^n$ with a finite number of zeros we define the Noether exponent $\\nu(F)$. We prove the Jacobi formula for all polynomials of degree strictly less than $\\sum_{i=1}^n (\\deg F_i-1)-\\nu(F)$.","authors_text":"Arkadiusz P{\\l}oski","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:42:51Z","title":"The Noether exponent and Jacobi formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9305006","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:d7e59f04fac4fd91f7be566984a883d014f0f67549263f8ec806e6650f272a37","target":"record","created_at":"2026-05-18T01:09:21Z","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":"4f28ca8dfba1d4dad94a072c2f64dfed607603b71ec7e9e062e1f12c9040db2b","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1993-05-19T07:42:51Z","title_canon_sha256":"dae59eccf06c060c6da9df58ed04d5a752ad3d6414a3e69ba1239daccc56056b"},"schema_version":"1.0","source":{"id":"alg-geom/9305006","kind":"arxiv","version":1}},"canonical_sha256":"134a5c7dac8aff05d651465a3c90915ede49a5491e6dd5e76e1edca68ab4eb26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"134a5c7dac8aff05d651465a3c90915ede49a5491e6dd5e76e1edca68ab4eb26","first_computed_at":"2026-05-18T01:09:21.822026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:21.822026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0NK8WNfuVeD3mUgKi52PtwCA7OjhpGODuK6u7hv+YHULlsJdiyr9xRBL/6xTq0nHPfzAmf0tvpo7kzFxaSavAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:21.822396Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9305006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7e59f04fac4fd91f7be566984a883d014f0f67549263f8ec806e6650f272a37","sha256:c7c832a292ca2727fbc89eab6c2877cb63590fcdcbc3d67ba320d171d97448b9"],"state_sha256":"b400b435701e853acaf963f97852dd55835f1d1e6aa2026a6fa1e84843683935"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Wphvmd+o9bgRVNo/FPj4DglumJExZE2BU39x6d6gY8AoIx+NbEjFxzudMYKO0LUlyMDukUcqe0qqBdPuflrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:31:52.975700Z","bundle_sha256":"765486dd2d35cf8a5c1f23b4eb38bccc1fcd13e521a43b01610c824f83704311"}}