{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CYINFG2BMEDYEQUEOHBZJ2QOOL","short_pith_number":"pith:CYINFG2B","canonical_record":{"source":{"id":"1601.00611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-04T19:15:00Z","cross_cats_sorted":[],"title_canon_sha256":"9ec18579bf7c64f96c96a66412465a5c8cfa07dcafd66dc878b34b3253acc6da","abstract_canon_sha256":"21ce0dafe2739b3f2969a043d971504313c5ff9a52839a9a2a5249c24845f3d6"},"schema_version":"1.0"},"canonical_sha256":"1610d29b41610782428471c394ea0e72f905d513c9d0293ddcc05f71c878c619","source":{"kind":"arxiv","id":"1601.00611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00611","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00611v1","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00611","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"CYINFG2BMEDY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYINFG2BMEDYEQUE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYINFG2B","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CYINFG2BMEDYEQUEOHBZJ2QOOL","target":"record","payload":{"canonical_record":{"source":{"id":"1601.00611","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-04T19:15:00Z","cross_cats_sorted":[],"title_canon_sha256":"9ec18579bf7c64f96c96a66412465a5c8cfa07dcafd66dc878b34b3253acc6da","abstract_canon_sha256":"21ce0dafe2739b3f2969a043d971504313c5ff9a52839a9a2a5249c24845f3d6"},"schema_version":"1.0"},"canonical_sha256":"1610d29b41610782428471c394ea0e72f905d513c9d0293ddcc05f71c878c619","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:26.951062Z","signature_b64":"P3wbJypxUW66umii+sMGX0QsDzI/PsuL0hN/y3jgd6DkfvrkdFsSiGOBRonjNaPQMJ70UCh4q4BDGx7vuNtCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1610d29b41610782428471c394ea0e72f905d513c9d0293ddcc05f71c878c619","last_reissued_at":"2026-05-18T01:23:26.950407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:26.950407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.00611","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":"2026-05-18T01:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6BxoA5mVCxr6d8j/4hLzx+FPE6PYbcEIVoDBnEcM8ESxzbtbKd4FGX1gQKHv4KQ58cHQewoFSmHfTSexr9dUBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:33:48.932205Z"},"content_sha256":"1ee8c6af3d204e0839e1647ceb4be07fb6754904c347f169f1bd993f9d7291d0","schema_version":"1.0","event_id":"sha256:1ee8c6af3d204e0839e1647ceb4be07fb6754904c347f169f1bd993f9d7291d0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CYINFG2BMEDYEQUEOHBZJ2QOOL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On deflation and multiplicity structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Agnes Szanto, Bernard Mourrain (GALAAD2), Jonathan D. Hauenstein","submitted_at":"2016-01-04T19:15:00Z","abstract_excerpt":"This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear in each iteration instead of the quadratic increase of previous methods. The second construction gives the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00611","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":"2026-05-18T01:23:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"obaaT+GEggWhYvJy+oNNu/eVyEl3cdlnthMP41Q9ig0tpcLg0f83K+JDHQRRPLJjSmOGbo7WFsFuX8BcUxClBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:33:48.932626Z"},"content_sha256":"d4b062a008758f5a62481feacd0d06b2aea2e4cc51c0da7e74c8537ef7a4679d","schema_version":"1.0","event_id":"sha256:d4b062a008758f5a62481feacd0d06b2aea2e4cc51c0da7e74c8537ef7a4679d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/bundle.json","state_url":"https://pith.science/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/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":"2026-06-01T15:33:48Z","links":{"resolver":"https://pith.science/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL","bundle":"https://pith.science/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/bundle.json","state":"https://pith.science/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYINFG2BMEDYEQUEOHBZJ2QOOL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CYINFG2BMEDYEQUEOHBZJ2QOOL","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":"21ce0dafe2739b3f2969a043d971504313c5ff9a52839a9a2a5249c24845f3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-04T19:15:00Z","title_canon_sha256":"9ec18579bf7c64f96c96a66412465a5c8cfa07dcafd66dc878b34b3253acc6da"},"schema_version":"1.0","source":{"id":"1601.00611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.00611","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"arxiv_version","alias_value":"1601.00611v1","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.00611","created_at":"2026-05-18T01:23:26Z"},{"alias_kind":"pith_short_12","alias_value":"CYINFG2BMEDY","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CYINFG2BMEDYEQUE","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CYINFG2B","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:d4b062a008758f5a62481feacd0d06b2aea2e4cc51c0da7e74c8537ef7a4679d","target":"graph","created_at":"2026-05-18T01:23:26Z","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":"This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is that it does not introduce new variables and the increase in the number of equations is linear in each iteration instead of the quadratic increase of previous methods. The second construction gives the c","authors_text":"Agnes Szanto, Bernard Mourrain (GALAAD2), Jonathan D. Hauenstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-04T19:15:00Z","title":"On deflation and multiplicity structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00611","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":"sha256:1ee8c6af3d204e0839e1647ceb4be07fb6754904c347f169f1bd993f9d7291d0","target":"record","created_at":"2026-05-18T01:23:26Z","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":"21ce0dafe2739b3f2969a043d971504313c5ff9a52839a9a2a5249c24845f3d6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-01-04T19:15:00Z","title_canon_sha256":"9ec18579bf7c64f96c96a66412465a5c8cfa07dcafd66dc878b34b3253acc6da"},"schema_version":"1.0","source":{"id":"1601.00611","kind":"arxiv","version":1}},"canonical_sha256":"1610d29b41610782428471c394ea0e72f905d513c9d0293ddcc05f71c878c619","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1610d29b41610782428471c394ea0e72f905d513c9d0293ddcc05f71c878c619","first_computed_at":"2026-05-18T01:23:26.950407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:26.950407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P3wbJypxUW66umii+sMGX0QsDzI/PsuL0hN/y3jgd6DkfvrkdFsSiGOBRonjNaPQMJ70UCh4q4BDGx7vuNtCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:26.951062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.00611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ee8c6af3d204e0839e1647ceb4be07fb6754904c347f169f1bd993f9d7291d0","sha256:d4b062a008758f5a62481feacd0d06b2aea2e4cc51c0da7e74c8537ef7a4679d"],"state_sha256":"520dc2530378254a51aa953581c44e21b03296ce4cec22b64da5b3d26d524cb6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U8h7JniS5Eo/b8tO5KqOgPRQswQ+DaRx8/LiUecQo0PBOZDOjNXvlDcVk2JhDs/BP93eiiLJOl39xoANhZcYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:33:48.935131Z","bundle_sha256":"8396aa7beacf49deaf5f478b8edea88576cdb57a2b7b0f6d0d97cb09b957ecb3"}}