"""Exact finite geometric ranking and filter example; not HNSW implementation."""
import json,math
SLUG="ann-recall-contracts"
def run():
    # True distance d_i=i/100 for deterministic1D corpus, q=0.
    points=[(i,i/100) for i in range(1,101)]
    truth=[i for i,d in points[:10]]
    budgets=[1,2,5,10,20,40,60,80,100]
    # Candidate order is even identifiers followed by odd: intentionally biased.
    order=list(range(2,101,2))+list(range(1,100,2))
    recall=[]
    for b in budgets:
        candidates=order[:b]
        top=sorted(candidates)[:10]
        recall.append(len(set(top)&set(truth))/10)
    assert recall[3]==.5 and recall[-1]==1
    # Filter eligible iff index>=91; postfilter top20 yields none, eligible exacttop5 exist.
    eligible=[i for i,d in points if i>=91]
    assert len([i for i in range(1,21) if i>=91])==0 and eligible[:5]==[91,92,93,94,95]
    # Additive per-distance error bounded eps: reversal impossible when gap>2eps.
    epss=[0,.001,.0025,.005,.01,.02,.04]
    gap=.01
    margins=[gap-2*e for e in epss]
    assert abs(margins[3])<1e-12 and margins[4]<0
    checks=0
    for eps in [.001,.002,.004]:
        for e1 in [-eps,0,eps]:
            for e2 in [-eps,0,eps]:
                assert .10+e1<.11+e2;checks+=1
    return {"slug":SLUG,"checks":[{"name":"Candidate recall against exhaustive ground truth","passed":True,"cases":len(budgets),"detail":"Biased even-first candidate sequence: at budget 10, recall@10 = 0.5; at full budget, recall@10 = 1."},{"name":"Filtering after truncation counterexample","passed":True,"cases":1,"detail":"Eligible IDs 91..100: the unfiltered top 20 contains no eligible item, although 10 exist."},{"name":"Bounded-distance-error ranking margin","passed":True,"cases":checks,"detail":"All finite endpoint/zero perturbation pairs preserve the 0.01 gap when 2 * epsilon < 0.01."}],"figures":[{"id":"candidates","title":"Recall is controlled by which candidates survive","x_label":"Number of candidates inspected","y_label":"Recall@10 against exact top 10","series":[{"name":"Even-first constructed candidate ordering","x":budgets,"y":recall}],"caption":"A deterministic 100-point one-dimensional example. This candidate policy is deliberately simple and is not HNSW, DiskANN, Faiss or ScaNN.","assumptions":["Euclidean distance toquery 0; point i at i/100","Stable identifier tie-break; no equal distances"],"kind":"Constructed analytical model; not a measured benchmark"},{"id":"margin","title":"Distance error matters relative to the ranking gap","x_label":"Maximum absolute distance error epsilon","y_label":"Certified residual gap (distance units)","series":[{"name":"0.01 - 2 epsilon","x":epss,"y":margins}],"caption":"Positive values certify the order of two items under an assumed uniform error bound. Negative values mean the certificate is inconclusive, not that every ranking reverses.","assumptions":["True distance gap 0.01","Each approximate distance deviates by at most epsilon"],"kind":"Constructed analytical model; not a measured benchmark"}],"result_summary":{"recall_at_budget10":recall[3],"recall_at_full_budget":recall[-1],"postfilter_top20_eligible_count":0,"eligible_exact_top5":eligible[:5],"strict_margin_epsilon_threshold":.005}}
if __name__=="__main__":print(json.dumps(run(),indent=2))