The smallest change in price, in month-over-month growth, or in burn that reaches a declared goal: a runway of N months, solvency through the horizon, breakeven by a month, or a closing cash amount, ranked by least effort. A fixed monthly cash model walks every combination of your three lever grids; the all-zero scenario is always reported as the baseline.
Goal-SeekInteger Minor UnitsZero PIIClient-side only
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Scope & reliance
Month 1 uses the declared revenue (optionally price-uplifted); growth applies from month 2 at a constant rate; burn is derived once and held constant. The first month where cash goes below zero is the cash-out month, interpolated in basis points of a month as (m−1)·10000 + floor(prev_cash·10000/(−net)); cash landing exactly on zero is not a cash-out. Effort is the half-up integer division by 100 of the sum of weight times lever; ties break by burn_cut, then price_uplift, then growth_add, all ascending. Scope limits: one revenue line, constant burn, no financing events, no churn model, and no tax. No formal correctness proof exists for this node yet (compute_proof_ready: deferred); see the proof-status note below the results.
Cash model and goal
Edit any field and run. The sample is fixture F1, the baseline-meets-goal seal vector from the conformance set.
Result
Proof status
This node ships compute_proof_ready: deferred. No formal correctness proof has been produced for this kernel; the result above is a deterministic recompute, verified by a property-test floor, not a proven one.
Execution Hash & §4 Artifact
SHA-256 execution hash (JCS canonical, RFC 8785):
Ask your agent
Copy this paragraph into Claude, OpenClaw, or any MCP-aware agent to run this exact tool, with this sample, and verify the artifact.
Run the AINumbers MCP tool `find_runway_goal_path`. Task: Goal-seek over a monthly cash model: the smallest change in price, growth or burn that reaches a runway, solvency, breakeven or ending-cash goal, ranked by least effort with ties by burn cut, then price uplift, then growth.
Call it with arguments: {"policy_parameters":{"cash_minor":100000000,"monthly_revenue_minor":2000000,"monthly_burn_minor":6000000,"revenue_growth_bp":800,"horizon_months":36,"goal":{"type":"runway_months","value":18},"levers":{"price_uplift_bp":[0,500,1000,1500,2000,3000],"growth_add_bp":[0,100,200,300,500],"burn_cut_bp":[0,500,1000,1500,2000,3000]},"effort_weights":{"price_uplift_bp":1,"growth_add_bp":2,"burn_cut_bp":1},"max_candidates":4}}
Verify before trusting: call `verify_execution_hash` on mcp.ainumbers.co (https://mcp.ainumbers.co/mcp) with the parameter `claimed_hash` set to the returned `execution_hash`, passing the full artifact the run returned (the object containing `policy_parameters` + `output_payload` + `execution_hash`; equivalently `policy_parameters` + `output_payload` with `claimed_hash`), not the bare hash string, or re-run the in-page WebMCP tool `find_runway_goal_path`.
Return the ledger link https://ledger.ainumbers.co/ so a human can re-verify without contacting us.
PII rule: All inputs are processed locally in your browser. No data is transmitted. Do not enter real personal data — use synthetic or anonymised inputs only.
Open the tool with the sample prefilled: https://ainumbers.co/chaingraph/art-702-runway-goal-path.html#p=v1.H4sIAAAAAAAA_wGPAXD-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