{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QLKPB3CYESXEV53VII3S77FR37","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":"8fb810cd836775dc3280572ae5e0ca9da049b8802643dfab1b7d1edf192d6601","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-29T13:54:45Z","title_canon_sha256":"25d7f1caa59cf7b57754063f973f94323388a9a54921739d34f7408b269082a1"},"schema_version":"1.0","source":{"id":"1705.10185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.10185","created_at":"2026-05-18T00:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1705.10185v1","created_at":"2026-05-18T00:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.10185","created_at":"2026-05-18T00:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"QLKPB3CYESXE","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QLKPB3CYESXEV53V","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QLKPB3CY","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:879de51c3b95db7bc665e1e8006d006485a31248b7dd27d95ba3c4f0b96f304a","target":"graph","created_at":"2026-05-18T00:25:01Z","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":"About two decades ago, Tsfasman and Boguslavsky conjectured a formula for the maximum number of common zeros that $r$ linearly independent homogeneous polynomials of degree $d$ in $m+1$ variables with coefficients in a finite field with $q$ elements can have in the corresponding $m$-dimensional projective space. Recently, it has been shown by Datta and Ghorpade that this conjecture is valid if $r$ is at most $m+1$ and can be invalid otherwise. Moreover a new conjecture was proposed for many values of $r$ beyond $m+1$. In this paper, we prove that this new conjecture holds true for several valu","authors_text":"Mrinmoy Datta, Peter Beelen, Sudhir R. Ghorpade","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-29T13:54:45Z","title":"Maximum Number of Common Zeros of Homogeneous Polynomials over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10185","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:c4c1b80f9a341181646e5865b74b0de127721e312752eac7349a98a298b111f5","target":"record","created_at":"2026-05-18T00:25:01Z","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":"8fb810cd836775dc3280572ae5e0ca9da049b8802643dfab1b7d1edf192d6601","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-05-29T13:54:45Z","title_canon_sha256":"25d7f1caa59cf7b57754063f973f94323388a9a54921739d34f7408b269082a1"},"schema_version":"1.0","source":{"id":"1705.10185","kind":"arxiv","version":1}},"canonical_sha256":"82d4f0ec5824ae4af77542372ffcb1dfee13d3be3ba4dd1d04e9066e06667e97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82d4f0ec5824ae4af77542372ffcb1dfee13d3be3ba4dd1d04e9066e06667e97","first_computed_at":"2026-05-18T00:25:01.719059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:01.719059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"85G51UowPjF4K1pBN3vLsIDqkFxNYHk9EV5qXB69kFntfpsnF1XvLuhYTkWrBlDB/0zP2q6d32StK2a4S/7wBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:01.719468Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.10185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4c1b80f9a341181646e5865b74b0de127721e312752eac7349a98a298b111f5","sha256:879de51c3b95db7bc665e1e8006d006485a31248b7dd27d95ba3c4f0b96f304a"],"state_sha256":"c7b3925395ebb02f075334b99dc0877dcba9f709643b984735ee3a3bd06d9ce0"}