Bacteria under antibiotic selective pressure that acquire resistance via plasmid copy-number amplification accumulate a disproportionately high mutational load in plasmid-encoded housekeeping functions as a consequence of error-prone replication at high copy number. A two-stage evolutionary trap therapy — stage 1 agent forces resistance via predictable plasmid amplification, stage 2 agent is selectively toxic to high-copy-number cells via amplification-driven toxin-antitoxin imbalance — creates an escape-proof treatment strategy because the only resistance route to stage 2 (reducing copy number) restores susceptibility to stage 1. This is formalizable as a directed acyclic graph over resistance states with no sink node outside the susceptible state, provable by exhaustive enumeration of known plasmid resistance mechanisms in the CARD and ResFinder databases.

Two sub-claims must each be independently falsifiable: (a) Mechanistic claim: In bacterial populations acquiring antibiotic resistance via plasmid copy-number (PCN) amplification, the per-generation mutation rate in plasmid-encoded housekeeping genes increases supralinearly with plasmid copy number (measurable as mutations/Mb/generation at PCN=1x vs PCN≥10x, expected effect size ≥3-fold, attributable to replication-error accumulation at high copy number rather than drift). (b) Trap-therapy claim: A two-stage sequential drug regimen — Stage 1 selecting for PCN amplification (e.g., a plasmid-addicted resistance gene under sub-MIC pressure), Stage 2 selectively toxic to high-PCN cells (via toxin-antitoxin [TA] stoichiometric imbalance) — reduces the standing-variation escape rate to below the detection limit of a fluctuation (Luria-Delbrück) assay (<1×10⁻⁹ survivors per generation) in vitro, across ≥3 clinically relevant plasmid/host combinations, and that any Stage-2-resistant survivors show reversion to Stage-1 susceptibility (PCN reduction) in ≥90% of isolates. The formal DAG/no-escape-sink proof is a combinatorial claim over annotated CARD/ResFinder mechanisms, not an empirical claim — it must be scored separately as a proof-checking exercise, not conflated with the wet-lab result.

Minimum viable test (MVT), 3 phases, single organism first:

• Organism/plasmid system: E. coli MG1655 carrying a well-characterized multicopy plasmid with native TA system (e.g., pUC-derived ColE1 replicon + ccdAB, or a clinical IncF plasmid carrying blaCTX-M with native TA locus) — chosen because copy-number control, TA biology, and CARD/ResFinder annotation are best characterized in E. coli, minimizing confounds before generalizing to Enterobacteriaceae/Klebsiella.
• Stage 1 agent: sub-MIC β-lactam (e.g., ceftriaxone) selecting for blaCTX-M copy-number amplification (established phenomenon, quantifiable via plasmid:chromosome qPCR ratio and droplet digital PCR).
• Stage 2 agent: a small molecule or peptide inducing TA imbalance at high PCN (candidate: antitoxin-degradation inducer, or a synthetic toxin-activating compound; if none exists, use a CcdB-mimetic gyrase poison whose toxicity is copy-number-dependent as a proof-of-concept surrogate, explicitly flagged as non-clinical).
• Design: 3-arm parallel evolution — (A) Stage 1 alone, (B) Stage 2 alone, (C) Stage 1→Stage 2 sequential — each with n=48 independent Luria-Delbrück fluctuation replicates (96-well format), at 3 population sizes (10⁶, 10⁷, 10⁸ CFU) to estimate mutation rate via MSS-MLE (Ma-Sandri-Sarkar maximum likelihood).
• Readout: colony counts on selective plates at 24h/48h; survivors whole-genome + plasmid long-read sequenced (Nanopore, for copy-number and structural resolution) plus qPCR-based PCN quantification.

# STAGE 0: Formal proof (cheap, run first as a gate)
graph = build_resistance_DAG(CARD_db, ResFinder_db, TADB_db)
for mechanism in graph.nodes:
    annotate(mechanism, evidence_level, fitness_cost_known=bool)
sink_nodes = enumerate_paths(graph, start="susceptible",
                              max_depth=6,
                              exclude_return_to="stage1_susceptible")
assert len(sink_nodes) == 0 or all(n.evidence_level == "speculative" for n in sink_nodes)
# --> if assertion fails: ABORT, publish negative result on formal claim only

# STAGE 1: MA mutation-rate scaling assay
for plasmid_system in [ColE1_ccdAB, IncF_relBE, IncN_vapBC]:
    for pcn_level in [1x, 5x, 10x, 20x]:
        lines = mutation_accumulation(plasmid_system, pcn_level, n=20, generations=200)
        mut_rate[plasmid_system][pcn_level] = MSS_MLE(lines)
    fit_scaling_law(mut_rate[plasmid_system])  # test supralinear vs linear vs flat

# STAGE 2: Two-stage fluctuation assay
for plasmid_system in systems:
    for arm in ["stage1_only", "stage2_only", "sequential"]:
        replicates = fluctuation_assay(plasmid_system, arm, n=48, pop_sizes=[1e6,1e7,1e8])
        escape_rate[arm] = MSS_MLE(replicates)
    compare_rates(escape_rate, test="likelihood_ratio")
    survivors = sequence_all(replicates.survivors, ont_long_read=True, illumina_short_read=True)
    mechanism_breakdown = classify_resistance_mechanism(survivors)
    if fraction(mechanism_breakdown, "non_PCN_route") > 0.25:
        FLAG "trap is leaky" -> escalate to Stage-0 re-analysis

# STAGE 3: In vivo (conditional on Stage 2 success)
if escape_rate["sequential"] < 1e-9 in >=2/3 systems:
    run_murine_infection_model(best_system, arms=["mono1","mono2","sequential"], n=15)