{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:T6JF2IRXZTZPPE5SRYCZYAT4ZX","short_pith_number":"pith:T6JF2IRX","canonical_record":{"source":{"id":"1605.02912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-10T09:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"79dae048f8dae20daf71f214415b067ede5f7220e42e271591bf0d41395424ba","abstract_canon_sha256":"6ecb65700336b3f58aa79a4b3096b3901494e5efa751ef42f24188e089fb4d25"},"schema_version":"1.0"},"canonical_sha256":"9f925d2237ccf2f793b28e059c027ccdcb6f7a11ab4c172b964dca2f3a1bd998","source":{"kind":"arxiv","id":"1605.02912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02912","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02912v1","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02912","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"T6JF2IRXZTZP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6JF2IRXZTZPPE5S","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6JF2IRX","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:T6JF2IRXZTZPPE5SRYCZYAT4ZX","target":"record","payload":{"canonical_record":{"source":{"id":"1605.02912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-10T09:54:16Z","cross_cats_sorted":[],"title_canon_sha256":"79dae048f8dae20daf71f214415b067ede5f7220e42e271591bf0d41395424ba","abstract_canon_sha256":"6ecb65700336b3f58aa79a4b3096b3901494e5efa751ef42f24188e089fb4d25"},"schema_version":"1.0"},"canonical_sha256":"9f925d2237ccf2f793b28e059c027ccdcb6f7a11ab4c172b964dca2f3a1bd998","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:59.050200Z","signature_b64":"riIl1ctz09GABNhdnCAw1ShqD3n09xzpa/zLbnMCN6Yi20V42gJApEtA+lfkuj7PhKH/PzNXYG5gmrEolIWVDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f925d2237ccf2f793b28e059c027ccdcb6f7a11ab4c172b964dca2f3a1bd998","last_reissued_at":"2026-05-18T01:10:59.049621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:59.049621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.02912","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":"2026-05-18T01:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KHxpoTfwe48skyQmY6FHtPLdGI3RDZVMfxlypnBeYODtpNVoIXg6GiNuLGqycmiRW7mXCiC8chMHtl3MrQeZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:54.558541Z"},"content_sha256":"94c193096e5fb12d072b362167d2761ef9deae31624e202279e436927e5803af","schema_version":"1.0","event_id":"sha256:94c193096e5fb12d072b362167d2761ef9deae31624e202279e436927e5803af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:T6JF2IRXZTZPPE5SRYCZYAT4ZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Need Polynomial Systems be Doubly-exponential?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"James H. Davenport, Matthew England","submitted_at":"2016-05-10T09:54:16Z","abstract_excerpt":"Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled?\n  We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\\\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02912","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":"2026-05-18T01:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+RfwT55xxD5M5OIkPwkNekajBDNIQ7/kVXTCVgYNF5hZ0590mTkuWO10sm9+rDOAFN269SFwUkE3Kh94QJNnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:54:54.558886Z"},"content_sha256":"5d444819f9f70e5ae891d724ffcb93d47c7d30278dcd8169856fe0f3ab358a7d","schema_version":"1.0","event_id":"sha256:5d444819f9f70e5ae891d724ffcb93d47c7d30278dcd8169856fe0f3ab358a7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/bundle.json","state_url":"https://pith.science/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/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":"2026-06-02T03:54:54Z","links":{"resolver":"https://pith.science/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX","bundle":"https://pith.science/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/bundle.json","state":"https://pith.science/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T6JF2IRXZTZPPE5SRYCZYAT4ZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T6JF2IRXZTZPPE5SRYCZYAT4ZX","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":"6ecb65700336b3f58aa79a4b3096b3901494e5efa751ef42f24188e089fb4d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-10T09:54:16Z","title_canon_sha256":"79dae048f8dae20daf71f214415b067ede5f7220e42e271591bf0d41395424ba"},"schema_version":"1.0","source":{"id":"1605.02912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.02912","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1605.02912v1","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.02912","created_at":"2026-05-18T01:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"T6JF2IRXZTZP","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6JF2IRXZTZPPE5S","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6JF2IRX","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:5d444819f9f70e5ae891d724ffcb93d47c7d30278dcd8169856fe0f3ab358a7d","target":"graph","created_at":"2026-05-18T01:10:59Z","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":"Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled?\n  We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\\\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done ","authors_text":"James H. Davenport, Matthew England","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-10T09:54:16Z","title":"Need Polynomial Systems be Doubly-exponential?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.02912","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":"sha256:94c193096e5fb12d072b362167d2761ef9deae31624e202279e436927e5803af","target":"record","created_at":"2026-05-18T01:10:59Z","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":"6ecb65700336b3f58aa79a4b3096b3901494e5efa751ef42f24188e089fb4d25","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-10T09:54:16Z","title_canon_sha256":"79dae048f8dae20daf71f214415b067ede5f7220e42e271591bf0d41395424ba"},"schema_version":"1.0","source":{"id":"1605.02912","kind":"arxiv","version":1}},"canonical_sha256":"9f925d2237ccf2f793b28e059c027ccdcb6f7a11ab4c172b964dca2f3a1bd998","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f925d2237ccf2f793b28e059c027ccdcb6f7a11ab4c172b964dca2f3a1bd998","first_computed_at":"2026-05-18T01:10:59.049621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:59.049621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"riIl1ctz09GABNhdnCAw1ShqD3n09xzpa/zLbnMCN6Yi20V42gJApEtA+lfkuj7PhKH/PzNXYG5gmrEolIWVDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:59.050200Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.02912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94c193096e5fb12d072b362167d2761ef9deae31624e202279e436927e5803af","sha256:5d444819f9f70e5ae891d724ffcb93d47c7d30278dcd8169856fe0f3ab358a7d"],"state_sha256":"7eaf1fb68b5b312e9754898fef5ca2eedb8089b0c1761fea2e0babb2274393ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ZEXTAtLjq9c9mv6+2v1srGM3vYylIedhP2PUhBUJFYA45Bh8YqHeO+EgdodmBMwXIL5VNM4mMBTI7uD4yTbBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:54:54.560811Z","bundle_sha256":"b7f7f846347efaf6e55322b458982700019ec2a4c74d3bc0512699504c14a28b"}}