{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EQI7V3T5UP4TPEMGGG4YQYZGTR","short_pith_number":"pith:EQI7V3T5","canonical_record":{"source":{"id":"1710.06502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-17T21:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"34a0808bb28f4747e60702eddeb20d2370a1eee4bd7df936884fed09309c3ed8","abstract_canon_sha256":"360bc8753ef6bbcd2894e53d4ea5b6dbd0947ae750a354420589af247e986775"},"schema_version":"1.0"},"canonical_sha256":"2411faee7da3f937918631b98863269c406d345a2f5fbcdd62b0fcdd20d00bc9","source":{"kind":"arxiv","id":"1710.06502","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06502","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06502v2","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06502","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"EQI7V3T5UP4T","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQI7V3T5UP4TPEMG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQI7V3T5","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EQI7V3T5UP4TPEMGGG4YQYZGTR","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-17T21:04:04Z","cross_cats_sorted":[],"title_canon_sha256":"34a0808bb28f4747e60702eddeb20d2370a1eee4bd7df936884fed09309c3ed8","abstract_canon_sha256":"360bc8753ef6bbcd2894e53d4ea5b6dbd0947ae750a354420589af247e986775"},"schema_version":"1.0"},"canonical_sha256":"2411faee7da3f937918631b98863269c406d345a2f5fbcdd62b0fcdd20d00bc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:20.018873Z","signature_b64":"KqoULgDwOvMXJ6JoO/jo/OiEg0rsa7opBVWsY6eesjj3a417hAdpBG8cvxbAmVOEOX85ptjIAVe/4xFQtfclBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2411faee7da3f937918631b98863269c406d345a2f5fbcdd62b0fcdd20d00bc9","last_reissued_at":"2026-05-18T00:32:20.018340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:20.018340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06502","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":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkP9xNjSmX9UMtZXmirpQbtITYEG4Wn+MYHEpuy/rdxwRIkHIbr2mQ5kcD1qx8K9YYY4jqk/XMstxlhidrylDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:53:13.597830Z"},"content_sha256":"c73451082bafd062eeb985cd49d013f821416795f9c33746a0217a9427e05d6e","schema_version":"1.0","event_id":"sha256:c73451082bafd062eeb985cd49d013f821416795f9c33746a0217a9427e05d6e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EQI7V3T5UP4TPEMGGG4YQYZGTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cup length as a bound on topological complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"parth sarin","submitted_at":"2017-10-17T21:04:04Z","abstract_excerpt":"Polynomial solving algorithms are essential to applied mathematics and the sciences. As such, reduction of their complexity has become an incredibly important field of topological research. We present a topological approach to constructing a lower bound for the complexity of a polynomial-solving algorithm, and give a concrete algorithm to do this in the case that $\\mathrm{deg}(f) = 2,3,4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06502","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":"2026-05-18T00:32:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRiuWffRkOyh5S0xyMVGVHGIMOx30IXs23ouHPid/1Vb+Wv682Vfa1k7A9vzyi1IPcFsDnOadsDRv4ALxVLCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T21:53:13.598185Z"},"content_sha256":"9fd34573beca70937d3ee813ea4337c51b48057b7488b7ccdcba393701139b33","schema_version":"1.0","event_id":"sha256:9fd34573beca70937d3ee813ea4337c51b48057b7488b7ccdcba393701139b33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/bundle.json","state_url":"https://pith.science/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/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":"2026-06-23T21:53:13Z","links":{"resolver":"https://pith.science/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR","bundle":"https://pith.science/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/bundle.json","state":"https://pith.science/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQI7V3T5UP4TPEMGGG4YQYZGTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EQI7V3T5UP4TPEMGGG4YQYZGTR","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":"360bc8753ef6bbcd2894e53d4ea5b6dbd0947ae750a354420589af247e986775","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-17T21:04:04Z","title_canon_sha256":"34a0808bb28f4747e60702eddeb20d2370a1eee4bd7df936884fed09309c3ed8"},"schema_version":"1.0","source":{"id":"1710.06502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06502","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06502v2","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06502","created_at":"2026-05-18T00:32:20Z"},{"alias_kind":"pith_short_12","alias_value":"EQI7V3T5UP4T","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EQI7V3T5UP4TPEMG","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EQI7V3T5","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:9fd34573beca70937d3ee813ea4337c51b48057b7488b7ccdcba393701139b33","target":"graph","created_at":"2026-05-18T00:32:20Z","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 solving algorithms are essential to applied mathematics and the sciences. As such, reduction of their complexity has become an incredibly important field of topological research. We present a topological approach to constructing a lower bound for the complexity of a polynomial-solving algorithm, and give a concrete algorithm to do this in the case that $\\mathrm{deg}(f) = 2,3,4$.","authors_text":"parth sarin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-17T21:04:04Z","title":"Cup length as a bound on topological complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06502","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:c73451082bafd062eeb985cd49d013f821416795f9c33746a0217a9427e05d6e","target":"record","created_at":"2026-05-18T00:32:20Z","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":"360bc8753ef6bbcd2894e53d4ea5b6dbd0947ae750a354420589af247e986775","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-10-17T21:04:04Z","title_canon_sha256":"34a0808bb28f4747e60702eddeb20d2370a1eee4bd7df936884fed09309c3ed8"},"schema_version":"1.0","source":{"id":"1710.06502","kind":"arxiv","version":2}},"canonical_sha256":"2411faee7da3f937918631b98863269c406d345a2f5fbcdd62b0fcdd20d00bc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2411faee7da3f937918631b98863269c406d345a2f5fbcdd62b0fcdd20d00bc9","first_computed_at":"2026-05-18T00:32:20.018340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:20.018340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KqoULgDwOvMXJ6JoO/jo/OiEg0rsa7opBVWsY6eesjj3a417hAdpBG8cvxbAmVOEOX85ptjIAVe/4xFQtfclBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:20.018873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c73451082bafd062eeb985cd49d013f821416795f9c33746a0217a9427e05d6e","sha256:9fd34573beca70937d3ee813ea4337c51b48057b7488b7ccdcba393701139b33"],"state_sha256":"934999bd828b6fda33e215575ad1f65e2e5032b0cab652e8de24b2b62abaf7c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tsdTiAEtrPMTq+jZZa5tbD+ZkuyKQIz6fw5G1wjAM5HVFp4X9OxvhODy0tp9PLKbEbJQhZpl7Gv76Ppk7cSBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T21:53:13.600294Z","bundle_sha256":"1ea1f0c0f296e6d5f53a741b1a29623b5d4294e40f087275e2bf9232fcb409e0"}}