{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GTOLJZ4SHZB44GCOC6NII6OFRS","short_pith_number":"pith:GTOLJZ4S","canonical_record":{"source":{"id":"1607.04860","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-17T12:33:16Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3d232150e24d7474b80e786096e1ec746a946c33acc79be088c9b5dc11fe59b2","abstract_canon_sha256":"3033e85f512048af72da20b9050f93b8e62c899d38d4a68a76cfe1c25100a2f3"},"schema_version":"1.0"},"canonical_sha256":"34dcb4e7923e43ce184e179a8479c58c81783eeda2f0e30f9adddbe8f083be45","source":{"kind":"arxiv","id":"1607.04860","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04860","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04860v4","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04860","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"GTOLJZ4SHZB4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GTOLJZ4SHZB44GCO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GTOLJZ4S","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GTOLJZ4SHZB44GCOC6NII6OFRS","target":"record","payload":{"canonical_record":{"source":{"id":"1607.04860","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-17T12:33:16Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3d232150e24d7474b80e786096e1ec746a946c33acc79be088c9b5dc11fe59b2","abstract_canon_sha256":"3033e85f512048af72da20b9050f93b8e62c899d38d4a68a76cfe1c25100a2f3"},"schema_version":"1.0"},"canonical_sha256":"34dcb4e7923e43ce184e179a8479c58c81783eeda2f0e30f9adddbe8f083be45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:57.910050Z","signature_b64":"kU3jpqJVz78LaJF0pVV1yIqCpQjm/dYO6lXK66CTbqfSjMjyK1aA4HTFKB3FbKDYlDytwRPCzaa+o81tttnRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34dcb4e7923e43ce184e179a8479c58c81783eeda2f0e30f9adddbe8f083be45","last_reissued_at":"2026-05-18T00:54:57.909606Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:57.909606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.04860","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":"2026-05-18T00:54:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EGnXfV9M1yFGwEitaDe5UtK0n7MTu/TtqhJKy8HhcddZkGC739shMcKbAbYniqt476Aqot06D4Mo8i5Mc/RdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:50:12.570774Z"},"content_sha256":"09bd5d7f02c537d944ebabd7d68f6b59dc346d521571a177156bde0299fa9b0f","schema_version":"1.0","event_id":"sha256:09bd5d7f02c537d944ebabd7d68f6b59dc346d521571a177156bde0299fa9b0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GTOLJZ4SHZB44GCOC6NII6OFRS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intersection multiplicity, Milnor number and Bernstein's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Pinaki Mondal","submitted_at":"2016-07-17T12:33:16Z","abstract_excerpt":"We explicitly characterize when the Milnor number at the origin of a polynomial or power series (over an algebraically closed field k of arbitrary characteristic) is the minimum of all polynomials with the same Newton diagram, which completes works of Kushnirenko (Invent. Math., 1976) and Wall (J. Reine Angew. Math., 1999). Given a fixed collection of n convex integral polytopes in R^n, we also give an explicit characterization of systems of n polynomials supported at these polytopes which have the maximum number (counted with multiplicity) of isolated zeroes on k^n, or more generally, on a un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04860","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":"2026-05-18T00:54:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bscRU7SwlcWWWTIp7d6PtT743xFK8k90R3NbOMzQAh5z5qEiDLtpOtjhqm7yPeYNe1QEFtDspGyqrh+qipHfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:50:12.571124Z"},"content_sha256":"a68970bdc8d1be6fca48727fc349dc984409bde0418f69c18ad622b61ab063b7","schema_version":"1.0","event_id":"sha256:a68970bdc8d1be6fca48727fc349dc984409bde0418f69c18ad622b61ab063b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/bundle.json","state_url":"https://pith.science/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/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":"2026-06-25T12:50:12Z","links":{"resolver":"https://pith.science/pith/GTOLJZ4SHZB44GCOC6NII6OFRS","bundle":"https://pith.science/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/bundle.json","state":"https://pith.science/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTOLJZ4SHZB44GCOC6NII6OFRS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GTOLJZ4SHZB44GCOC6NII6OFRS","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":"3033e85f512048af72da20b9050f93b8e62c899d38d4a68a76cfe1c25100a2f3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-17T12:33:16Z","title_canon_sha256":"3d232150e24d7474b80e786096e1ec746a946c33acc79be088c9b5dc11fe59b2"},"schema_version":"1.0","source":{"id":"1607.04860","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.04860","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"arxiv_version","alias_value":"1607.04860v4","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04860","created_at":"2026-05-18T00:54:57Z"},{"alias_kind":"pith_short_12","alias_value":"GTOLJZ4SHZB4","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GTOLJZ4SHZB44GCO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GTOLJZ4S","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:a68970bdc8d1be6fca48727fc349dc984409bde0418f69c18ad622b61ab063b7","target":"graph","created_at":"2026-05-18T00:54:57Z","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 explicitly characterize when the Milnor number at the origin of a polynomial or power series (over an algebraically closed field k of arbitrary characteristic) is the minimum of all polynomials with the same Newton diagram, which completes works of Kushnirenko (Invent. Math., 1976) and Wall (J. Reine Angew. Math., 1999). Given a fixed collection of n convex integral polytopes in R^n, we also give an explicit characterization of systems of n polynomials supported at these polytopes which have the maximum number (counted with multiplicity) of isolated zeroes on k^n, or more generally, on a un","authors_text":"Pinaki Mondal","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-17T12:33:16Z","title":"Intersection multiplicity, Milnor number and Bernstein's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04860","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":"sha256:09bd5d7f02c537d944ebabd7d68f6b59dc346d521571a177156bde0299fa9b0f","target":"record","created_at":"2026-05-18T00:54:57Z","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":"3033e85f512048af72da20b9050f93b8e62c899d38d4a68a76cfe1c25100a2f3","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-17T12:33:16Z","title_canon_sha256":"3d232150e24d7474b80e786096e1ec746a946c33acc79be088c9b5dc11fe59b2"},"schema_version":"1.0","source":{"id":"1607.04860","kind":"arxiv","version":4}},"canonical_sha256":"34dcb4e7923e43ce184e179a8479c58c81783eeda2f0e30f9adddbe8f083be45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34dcb4e7923e43ce184e179a8479c58c81783eeda2f0e30f9adddbe8f083be45","first_computed_at":"2026-05-18T00:54:57.909606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:57.909606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kU3jpqJVz78LaJF0pVV1yIqCpQjm/dYO6lXK66CTbqfSjMjyK1aA4HTFKB3FbKDYlDytwRPCzaa+o81tttnRAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:57.910050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.04860","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09bd5d7f02c537d944ebabd7d68f6b59dc346d521571a177156bde0299fa9b0f","sha256:a68970bdc8d1be6fca48727fc349dc984409bde0418f69c18ad622b61ab063b7"],"state_sha256":"19f47324ef21b860e1fc7f46000b37f93662c9f4c30bd5794ff75fef76736666"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0RGxmd08RBBekCyqPfYctB9QjcAMI9X81QvCO95lCAkmW5/Bu3kdcQ/xLwUi5FZ/T3HZS8WiXTgF+A+xPhgCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:50:12.573120Z","bundle_sha256":"458f49391ee719784c035b27f28b7740ebbc7203b5602894d638c65badb34313"}}