{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EJED64LA6H4RWUY42QVUXXESG6","short_pith_number":"pith:EJED64LA","canonical_record":{"source":{"id":"1407.2799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-10T14:23:28Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"5c055a30aefad049d4fa12c314de63c86858f0360a024c1d3245633ab1d121e4","abstract_canon_sha256":"aa85c14ff2ecae400414837d160a9cb9720f208ef36b0000de86b54b5dcea0ee"},"schema_version":"1.0"},"canonical_sha256":"22483f7160f1f91b531cd42b4bdc9237a488d690fc0269471aa84bd792d208f5","source":{"kind":"arxiv","id":"1407.2799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2799","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2799v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2799","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"EJED64LA6H4R","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJED64LA6H4RWUY4","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJED64LA","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EJED64LA6H4RWUY42QVUXXESG6","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-10T14:23:28Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"5c055a30aefad049d4fa12c314de63c86858f0360a024c1d3245633ab1d121e4","abstract_canon_sha256":"aa85c14ff2ecae400414837d160a9cb9720f208ef36b0000de86b54b5dcea0ee"},"schema_version":"1.0"},"canonical_sha256":"22483f7160f1f91b531cd42b4bdc9237a488d690fc0269471aa84bd792d208f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.639038Z","signature_b64":"ok9aULd0Q2PHjpXHwcJXN4X5wuNfdqhKP8rCmWLCc0JZRyU3NNTdhtDj7JUsduuYtCdQ85dfnuYbhpLKhJlEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22483f7160f1f91b531cd42b4bdc9237a488d690fc0269471aa84bd792d208f5","last_reissued_at":"2026-05-18T02:47:53.638567Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.638567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2799","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":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lkSi65nOcKAJmPRbVX1mKlk9E3vlB0efurKa5MXMTWcQjChjvq43u3hzICdlC23/itu42rHeeTjyFDyGBFgsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:58:40.847398Z"},"content_sha256":"6d25f15c2c48485af9bcb32f41c46cd82244036361be3159154894c1c50440e5","schema_version":"1.0","event_id":"sha256:6d25f15c2c48485af9bcb32f41c46cd82244036361be3159154894c1c50440e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EJED64LA6H4RWUY42QVUXXESG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Resultant of an equivariant polynomial system with respect to the symmetric group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Anna Karasoulou (Athens), Laurent Bus\\'e (INRIA Sophia Antipolis)","submitted_at":"2014-07-10T14:23:28Z","abstract_excerpt":"Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be decomposed into a product of several smaller resultants that are given in terms of some divided differences. As an application, we obtain a decomposition formula for the discriminant of a multivariate homogeneous symmetric polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2799","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":"2026-05-18T02:47:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PZp61cVaBRy2ahXm4X7pdR8uiutIqP2QEkuAdYUZSfd8cDFHCa/VWCXVMyUvQs94UzTiaYS1Y2kFibkCtgX/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:58:40.847787Z"},"content_sha256":"9a041a21d60426f87935d6732549ecabbd91d67a51f7f500b47b079cf0e5712a","schema_version":"1.0","event_id":"sha256:9a041a21d60426f87935d6732549ecabbd91d67a51f7f500b47b079cf0e5712a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJED64LA6H4RWUY42QVUXXESG6/bundle.json","state_url":"https://pith.science/pith/EJED64LA6H4RWUY42QVUXXESG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJED64LA6H4RWUY42QVUXXESG6/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":"2026-06-06T08:58:40Z","links":{"resolver":"https://pith.science/pith/EJED64LA6H4RWUY42QVUXXESG6","bundle":"https://pith.science/pith/EJED64LA6H4RWUY42QVUXXESG6/bundle.json","state":"https://pith.science/pith/EJED64LA6H4RWUY42QVUXXESG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJED64LA6H4RWUY42QVUXXESG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EJED64LA6H4RWUY42QVUXXESG6","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":"aa85c14ff2ecae400414837d160a9cb9720f208ef36b0000de86b54b5dcea0ee","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-10T14:23:28Z","title_canon_sha256":"5c055a30aefad049d4fa12c314de63c86858f0360a024c1d3245633ab1d121e4"},"schema_version":"1.0","source":{"id":"1407.2799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2799","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2799v1","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2799","created_at":"2026-05-18T02:47:53Z"},{"alias_kind":"pith_short_12","alias_value":"EJED64LA6H4R","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EJED64LA6H4RWUY4","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EJED64LA","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9a041a21d60426f87935d6732549ecabbd91d67a51f7f500b47b079cf0e5712a","target":"graph","created_at":"2026-05-18T02:47:53Z","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":"Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be decomposed into a product of several smaller resultants that are given in terms of some divided differences. As an application, we obtain a decomposition formula for the discriminant of a multivariate homogeneous symmetric polynomial.","authors_text":"Anna Karasoulou (Athens), Laurent Bus\\'e (INRIA Sophia Antipolis)","cross_cats":["cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-10T14:23:28Z","title":"Resultant of an equivariant polynomial system with respect to the symmetric group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2799","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":"sha256:6d25f15c2c48485af9bcb32f41c46cd82244036361be3159154894c1c50440e5","target":"record","created_at":"2026-05-18T02:47:53Z","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":"aa85c14ff2ecae400414837d160a9cb9720f208ef36b0000de86b54b5dcea0ee","cross_cats_sorted":["cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-10T14:23:28Z","title_canon_sha256":"5c055a30aefad049d4fa12c314de63c86858f0360a024c1d3245633ab1d121e4"},"schema_version":"1.0","source":{"id":"1407.2799","kind":"arxiv","version":1}},"canonical_sha256":"22483f7160f1f91b531cd42b4bdc9237a488d690fc0269471aa84bd792d208f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22483f7160f1f91b531cd42b4bdc9237a488d690fc0269471aa84bd792d208f5","first_computed_at":"2026-05-18T02:47:53.638567Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:53.638567Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ok9aULd0Q2PHjpXHwcJXN4X5wuNfdqhKP8rCmWLCc0JZRyU3NNTdhtDj7JUsduuYtCdQ85dfnuYbhpLKhJlEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:53.639038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d25f15c2c48485af9bcb32f41c46cd82244036361be3159154894c1c50440e5","sha256:9a041a21d60426f87935d6732549ecabbd91d67a51f7f500b47b079cf0e5712a"],"state_sha256":"20daa5f908d50cc6275c4ef17b05c29e76f24b9940571eeb9fc76dddabfca431"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"30o344NZc3Q+dejyy/X5X8ZPM/knmOAgEMsI8vFrlXydIaES3XE3ABGMO29799rXcCuF6mHHMX1t57KNx4+3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:58:40.849897Z","bundle_sha256":"420c6764d11064c065b25cd9212c9b2897a5b333a60f241d3e471ebd99dc46ad"}}