{"id": "card_chain_bhargava_skinner_zhang_2014", "kind": "reference", "title": "Bhargava 2014 — A majority of elliptic curves over Q satisfy the Birch and Swinnerton-Dyer conjecture", "body": "M. Bhargava, C. Skinner, W. Zhang (2014). A majority of elliptic curves over Q satisfy the Birch and Swinnerton-Dyer conjecture. arXiv (2014). Canonical: https://arxiv.org/abs/1407.1826. Free copy: https://arxiv.org/abs/1407.1826. License as found: arXiv.org non-exclusive license to distribute — free to read, cited. What it gave the chain: at least 66.48% of elliptic curves over Q, ordered by height, satisfy the conjecture.", "source": {"label": "M. Bhargava, C. Skinner, W. Zhang (2014), arXiv (2014)", "url": "https://arxiv.org/abs/1407.1826", "domain": "mathematics", "authority_tier": "reference"}, "shelf": "codex", "box": "chain", "bands": ["chain", "record", "2014", "bhargava", "mathematics"], "subject": "A majority of elliptic curves over Q satisfy the Birch and Swinnerton-Dyer conjecture", "connections": [{"to_card_id": "card_chain_kolyvagin_1989", "relationship": "builds_on", "evidence": "at least 66.48% of elliptic curves over Q, ordered by height, satisfy the conjecture"}, {"to_card_id": "card_src_mill_wiles_1995", "relationship": "builds_on", "evidence": "at least 66.48% of elliptic curves over Q, ordered by height, satisfy the conjecture"}, {"to_card_id": "card_question_bsd", "relationship": "enables", "evidence": "a later work standing on an earlier one"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.chain", "facets": {"subject": ["2014", "bhargava", "mathematics", "record"]}, "presentation": {"glyph": "•", "kind_label": "chain", "by": "M. Bhargava, C. Skinner, W. Zhang (2014), arXiv (2014)", "authority": "reference", "posted": "", "standing": "", "link": {"url": "https://arxiv.org/abs/1407.1826", "host": "arxiv.org", "provider": "arXiv preprint", "titled": "Bhargava 2014 — A majority of elliptic curves over Q satisfy the Birch and Swinnerton-Dyer conjecture", "waybill_line": "", "reach": "", "embed": ""}}, "neighbors": [{"id": "card_chain_kolyvagin_1989", "title": "Kolyvagin 1989 — Finiteness of E(Q) and Sha(E, Q) for a subclass of Weil curves", "relationship": "builds on", "why": "at least 66.48% of elliptic curves over Q, ordered by height, satisfy the conjecture", "href": "/card/card_chain_kolyvagin_1989", "resolved": true}, {"id": "card_src_mill_wiles_1995", "title": "A. Wiles 1995 — Modular elliptic curves and Fermat's last theorem", "relationship": "builds on", "why": "at least 66.48% of elliptic curves over Q, ordered by height, satisfy the conjecture", "href": "/card/card_src_mill_wiles_1995", "resolved": true}, {"id": "card_question_bsd", "title": "The Birch and Swinnerton-Dyer conjecture", "relationship": "enables", "why": "a later work standing on an earlier one", "href": "/card/card_question_bsd", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_chain_bhargava_skinner_zhang_2014", "next_step": {"do": "read the source itself", "door": "FIND", "web": "/reader.html?card=card_chain_bhargava_skinner_zhang_2014"}, "ends": "a verdict or a card · the trail · a seal · one next step"}}