{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:KKU22T5XADEFZ3AU5B2EP4G66K","short_pith_number":"pith:KKU22T5X","schema_version":"1.0","canonical_sha256":"52a9ad4fb700c85cec14e87447f0def2bb89a51dd684101db08a63e105719cef","source":{"kind":"arxiv","id":"1603.04606","version":1},"attestation_state":"computed","paper":{"title":"Some Complete and Intermediate Polynomials in Algebraic Complexity Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Meena Mahajan, Nitin Saurabh","submitted_at":"2016-03-15T09:22:25Z","abstract_excerpt":"We provide a list of new natural $\\mathsf{VNP}$-intermediate polynomial families, based on basic (combinatorial) $\\mathsf{NP}$-complete problems that are complete under parsimonious reductions. Over finite fields, these families are in $\\mathsf{VNP}$, and under the plausible hypothesis $\\mathsf{Mod}_p\\mathsf{P} \\not\\subseteq \\mathsf{P/poly}$, are neither $\\mathsf{VNP}$-hard (even under oracle-circuit reductions) nor in $\\mathsf{VP}$. Prior to this, only the Cut Enumerator polynomial was known to be $\\mathsf{VNP}$-intermediate, as shown by B\\\"{u}rgisser in 2000.\n  We next show that over rationa"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1603.04606","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-03-15T09:22:25Z","cross_cats_sorted":[],"title_canon_sha256":"ca6cefad35415138eeb53467821cce03ef68c3543de00dc70b97acf2af237800","abstract_canon_sha256":"7e1e8d812d1e42d9192ab960aee731af76a1230a07f7406a795be7dc5d910222"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:04.389835Z","signature_b64":"nxDXU9ioiHgTihec8MvRvWWEfuAsT9ZncOPqbxwnGrHgs4FZnI8pGfV4MaryRHoRolnWhI/EmpkSOj0qmAD0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52a9ad4fb700c85cec14e87447f0def2bb89a51dd684101db08a63e105719cef","last_reissued_at":"2026-05-18T01:19:04.389327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:04.389327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Complete and Intermediate Polynomials in Algebraic Complexity Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Meena Mahajan, Nitin Saurabh","submitted_at":"2016-03-15T09:22:25Z","abstract_excerpt":"We provide a list of new natural $\\mathsf{VNP}$-intermediate polynomial families, based on basic (combinatorial) $\\mathsf{NP}$-complete problems that are complete under parsimonious reductions. Over finite fields, these families are in $\\mathsf{VNP}$, and under the plausible hypothesis $\\mathsf{Mod}_p\\mathsf{P} \\not\\subseteq \\mathsf{P/poly}$, are neither $\\mathsf{VNP}$-hard (even under oracle-circuit reductions) nor in $\\mathsf{VP}$. Prior to this, only the Cut Enumerator polynomial was known to be $\\mathsf{VNP}$-intermediate, as shown by B\\\"{u}rgisser in 2000.\n  We next show that over rationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04606","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.04606","created_at":"2026-05-18T01:19:04.389404+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04606v1","created_at":"2026-05-18T01:19:04.389404+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04606","created_at":"2026-05-18T01:19:04.389404+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKU22T5XADEF","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKU22T5XADEFZ3AU","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKU22T5X","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K","json":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K.json","graph_json":"https://pith.science/api/pith-number/KKU22T5XADEFZ3AU5B2EP4G66K/graph.json","events_json":"https://pith.science/api/pith-number/KKU22T5XADEFZ3AU5B2EP4G66K/events.json","paper":"https://pith.science/paper/KKU22T5X"},"agent_actions":{"view_html":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K","download_json":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K.json","view_paper":"https://pith.science/paper/KKU22T5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04606&json=true","fetch_graph":"https://pith.science/api/pith-number/KKU22T5XADEFZ3AU5B2EP4G66K/graph.json","fetch_events":"https://pith.science/api/pith-number/KKU22T5XADEFZ3AU5B2EP4G66K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K/action/storage_attestation","attest_author":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K/action/author_attestation","sign_citation":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K/action/citation_signature","submit_replication":"https://pith.science/pith/KKU22T5XADEFZ3AU5B2EP4G66K/action/replication_record"}},"created_at":"2026-05-18T01:19:04.389404+00:00","updated_at":"2026-05-18T01:19:04.389404+00:00"}