{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JIJOG5WQZ5WAHVRZHTCTZRG6MH","short_pith_number":"pith:JIJOG5WQ","canonical_record":{"source":{"id":"1608.03740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-12T10:27:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7a1e0b1829162828743f81603a7ce42707c83b93d7294050431cf5141f90dfbe","abstract_canon_sha256":"746722f7ac438ff0f3ee0b057df5b11277946df4da695c2b0fe1db2f056df2f9"},"schema_version":"1.0"},"canonical_sha256":"4a12e376d0cf6c03d6393cc53cc4de61cbba600d9a8af7e70dab922036b2b2a2","source":{"kind":"arxiv","id":"1608.03740","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03740","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03740v2","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03740","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"JIJOG5WQZ5WA","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JIJOG5WQZ5WAHVRZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JIJOG5WQ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JIJOG5WQZ5WAHVRZHTCTZRG6MH","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-12T10:27:26Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7a1e0b1829162828743f81603a7ce42707c83b93d7294050431cf5141f90dfbe","abstract_canon_sha256":"746722f7ac438ff0f3ee0b057df5b11277946df4da695c2b0fe1db2f056df2f9"},"schema_version":"1.0"},"canonical_sha256":"4a12e376d0cf6c03d6393cc53cc4de61cbba600d9a8af7e70dab922036b2b2a2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:16.464283Z","signature_b64":"0lPPRCJ2uzy4MnEVMONE46etsdK8zDGQynuhd0t8N3Pc0HOnxK8UdCiGIy+gzePgsNqbL3yLftrBzKjZHaCaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a12e376d0cf6c03d6393cc53cc4de61cbba600d9a8af7e70dab922036b2b2a2","last_reissued_at":"2026-05-18T00:46:16.463777Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:16.463777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03740","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZdGXVewLl/FCk8KkpqZufCDGSnbO2T1TKUE4V4JxQl3rCSD+edZbRQn4xUmsnCkYSGIpm6dysPpYR+ZyDmhDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:28:14.300797Z"},"content_sha256":"daf625a9cdc5866efefaa2a0d3e1acd4b68e35980274a856b31d7ac9e0d9f42c","schema_version":"1.0","event_id":"sha256:daf625a9cdc5866efefaa2a0d3e1acd4b68e35980274a856b31d7ac9e0d9f42c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JIJOG5WQZ5WAHVRZHTCTZRG6MH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subresultants in multiple roots: an extremal case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Agnes Szanto, Alin Bostan, Carlos D'Andrea, Marcelo Valdettaro, Teresa Krick","submitted_at":"2016-08-12T10:27:26Z","abstract_excerpt":"We provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\\alpha)^m and (x-\\beta)^n with respect to the set of Bernstein polynomials \\{(x-\\alpha)^j(x-\\beta)^{d-j}, \\, 0\\le j\\le d\\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03740","kind":"arxiv","version":2},"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":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UzmI5nr0NMZ9V3DP+ASJtl0F2dgb21IWsTcM1SfZS7RoFUCYqmg0UAYjKAH9txpgM7iEd0l5dsZOG+clkJkKBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:28:14.301151Z"},"content_sha256":"0a865979bb99410505d8e80ab49c6491119c2f3d7ec84662677972e481dd6cbd","schema_version":"1.0","event_id":"sha256:0a865979bb99410505d8e80ab49c6491119c2f3d7ec84662677972e481dd6cbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/bundle.json","state_url":"https://pith.science/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/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":"2026-06-01T04:28:14Z","links":{"resolver":"https://pith.science/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH","bundle":"https://pith.science/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/bundle.json","state":"https://pith.science/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JIJOG5WQZ5WAHVRZHTCTZRG6MH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JIJOG5WQZ5WAHVRZHTCTZRG6MH","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":"746722f7ac438ff0f3ee0b057df5b11277946df4da695c2b0fe1db2f056df2f9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-12T10:27:26Z","title_canon_sha256":"7a1e0b1829162828743f81603a7ce42707c83b93d7294050431cf5141f90dfbe"},"schema_version":"1.0","source":{"id":"1608.03740","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03740","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03740v2","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03740","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"JIJOG5WQZ5WA","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JIJOG5WQZ5WAHVRZ","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JIJOG5WQ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:0a865979bb99410505d8e80ab49c6491119c2f3d7ec84662677972e481dd6cbd","target":"graph","created_at":"2026-05-18T00:46:16Z","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 provide explicit formulae for the coefficients of the order-d polynomial subresultant of (x-\\alpha)^m and (x-\\beta)^n with respect to the set of Bernstein polynomials \\{(x-\\alpha)^j(x-\\beta)^{d-j}, \\, 0\\le j\\le d\\}. They are given by hypergeometric expressions arising from determinants of binomial Hankel matrices.","authors_text":"Agnes Szanto, Alin Bostan, Carlos D'Andrea, Marcelo Valdettaro, Teresa Krick","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-12T10:27:26Z","title":"Subresultants in multiple roots: an extremal case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03740","kind":"arxiv","version":2},"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:daf625a9cdc5866efefaa2a0d3e1acd4b68e35980274a856b31d7ac9e0d9f42c","target":"record","created_at":"2026-05-18T00:46:16Z","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":"746722f7ac438ff0f3ee0b057df5b11277946df4da695c2b0fe1db2f056df2f9","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-08-12T10:27:26Z","title_canon_sha256":"7a1e0b1829162828743f81603a7ce42707c83b93d7294050431cf5141f90dfbe"},"schema_version":"1.0","source":{"id":"1608.03740","kind":"arxiv","version":2}},"canonical_sha256":"4a12e376d0cf6c03d6393cc53cc4de61cbba600d9a8af7e70dab922036b2b2a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a12e376d0cf6c03d6393cc53cc4de61cbba600d9a8af7e70dab922036b2b2a2","first_computed_at":"2026-05-18T00:46:16.463777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:16.463777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0lPPRCJ2uzy4MnEVMONE46etsdK8zDGQynuhd0t8N3Pc0HOnxK8UdCiGIy+gzePgsNqbL3yLftrBzKjZHaCaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:16.464283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03740","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daf625a9cdc5866efefaa2a0d3e1acd4b68e35980274a856b31d7ac9e0d9f42c","sha256:0a865979bb99410505d8e80ab49c6491119c2f3d7ec84662677972e481dd6cbd"],"state_sha256":"43f11049f2c667cfa4691b22b8f1d420530974ec2bf56b9562842f99b2d0950e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yogg+ZukugI2AoZfc+XxonX4PaqBz5ZDSXrNESaZINDSjsFP7Ow2lM26EfM4BWdq2cLQ+MMJY4tdZEhD7Zq+AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:28:14.303423Z","bundle_sha256":"14498de3d702a6118ad5a1df4cbb25a2d60eb510ac009d7215e15c627e3345ff"}}