{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PIWB3BBIU5NVOBSQET4GEYWMST","short_pith_number":"pith:PIWB3BBI","canonical_record":{"source":{"id":"1112.1012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","cross_cats_sorted":["cs.SC","math.CO"],"title_canon_sha256":"45fabde5b1ab747168521873719d3acf6423d28ce84b516cb5346937c36de531","abstract_canon_sha256":"46d86ba2fdc5fa30040e8ecc60b74a9a8765edf86168d4c80c8df5f6a3a520cf"},"schema_version":"1.0"},"canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","source":{"kind":"arxiv","id":"1112.1012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1012","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1012v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1012","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"PIWB3BBIU5NV","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PIWB3BBIU5NVOBSQ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PIWB3BBI","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PIWB3BBIU5NVOBSQET4GEYWMST","target":"record","payload":{"canonical_record":{"source":{"id":"1112.1012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","cross_cats_sorted":["cs.SC","math.CO"],"title_canon_sha256":"45fabde5b1ab747168521873719d3acf6423d28ce84b516cb5346937c36de531","abstract_canon_sha256":"46d86ba2fdc5fa30040e8ecc60b74a9a8765edf86168d4c80c8df5f6a3a520cf"},"schema_version":"1.0"},"canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:57.234911Z","signature_b64":"Cyv2Anf79W6+CulDMoclsNw5JxD16vC/AeSIFJXrXHZSI63fpTOO7R5wknM5dcnMhIZ16B9CPVddgXRyeN2+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","last_reissued_at":"2026-05-18T04:06:57.234198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:57.234198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.1012","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+4mdH4h6/6LNGhnia2omT556LzBqj93iO02ATRc98JH6fnyIGODo3D0fGXHRR6tm9FQa1t7ftMF9Q3gbpeoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:10:42.600587Z"},"content_sha256":"6b85424128cd16f7f967d8657b33570b281028df87a504352dce6c94dd864296","schema_version":"1.0","event_id":"sha256:6b85424128cd16f7f967d8657b33570b281028df87a504352dce6c94dd864296"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PIWB3BBIU5NVOBSQET4GEYWMST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixed Discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.CO"],"primary_cat":"math.AG","authors_text":"Alicia Dickenstein, Bernd Sturmfels, Eduardo Cattani, Maria Angelica Cueto, Sandra Di Rocco","submitted_at":"2011-12-05T17:39:08Z","abstract_excerpt":"The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plucker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1012","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZNaT9JE16ATYg+NiopTOfCuGLNfiuWsWnON8u6Mv8Mo7/++4/KC6ffYg1XC1xroqNo6Kmt7bSETmExCHZDkpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:10:42.600968Z"},"content_sha256":"0056046fe25685dd7e68b6b17b20eada4388ee4ba73ea3ead916aa4e6f0659a9","schema_version":"1.0","event_id":"sha256:0056046fe25685dd7e68b6b17b20eada4388ee4ba73ea3ead916aa4e6f0659a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/bundle.json","state_url":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PIWB3BBIU5NVOBSQET4GEYWMST/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":"2026-06-11T21:10:42Z","links":{"resolver":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST","bundle":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/bundle.json","state":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PIWB3BBIU5NVOBSQET4GEYWMST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PIWB3BBIU5NVOBSQET4GEYWMST","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":"46d86ba2fdc5fa30040e8ecc60b74a9a8765edf86168d4c80c8df5f6a3a520cf","cross_cats_sorted":["cs.SC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","title_canon_sha256":"45fabde5b1ab747168521873719d3acf6423d28ce84b516cb5346937c36de531"},"schema_version":"1.0","source":{"id":"1112.1012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1012","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1012v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1012","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"PIWB3BBIU5NV","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PIWB3BBIU5NVOBSQ","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PIWB3BBI","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:0056046fe25685dd7e68b6b17b20eada4388ee4ba73ea3ead916aa4e6f0659a9","target":"graph","created_at":"2026-05-18T04:06:57Z","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":"The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plucker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves.","authors_text":"Alicia Dickenstein, Bernd Sturmfels, Eduardo Cattani, Maria Angelica Cueto, Sandra Di Rocco","cross_cats":["cs.SC","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","title":"Mixed Discriminants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1012","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":"sha256:6b85424128cd16f7f967d8657b33570b281028df87a504352dce6c94dd864296","target":"record","created_at":"2026-05-18T04:06:57Z","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":"46d86ba2fdc5fa30040e8ecc60b74a9a8765edf86168d4c80c8df5f6a3a520cf","cross_cats_sorted":["cs.SC","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","title_canon_sha256":"45fabde5b1ab747168521873719d3acf6423d28ce84b516cb5346937c36de531"},"schema_version":"1.0","source":{"id":"1112.1012","kind":"arxiv","version":1}},"canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","first_computed_at":"2026-05-18T04:06:57.234198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:57.234198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cyv2Anf79W6+CulDMoclsNw5JxD16vC/AeSIFJXrXHZSI63fpTOO7R5wknM5dcnMhIZ16B9CPVddgXRyeN2+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:57.234911Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b85424128cd16f7f967d8657b33570b281028df87a504352dce6c94dd864296","sha256:0056046fe25685dd7e68b6b17b20eada4388ee4ba73ea3ead916aa4e6f0659a9"],"state_sha256":"394f7c495bb807bdf99064d4f9e8815d98bfc4f54e1445f57b69ae3f5f6a51c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+4jSM5Y1u0mXwda8QSHKS7WmYzRt5BGfBPeP4P5N1pN17zyA5n3DQ05GiBe3JApMcccJnIwkwv4RPMYJasyrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:10:42.603059Z","bundle_sha256":"9d50e2f6ec4ffd21335aa73b663e6b7bb71b9b5f72bf2912a60d125754ca6c64"}}