Every claim, and where it came from

1. Agent purchases settled on withzero rails since 2026-05-19: 39,044 calls, $714.05, 171 distinct paying wallets, 23 capabilities active in the week of 2026-08-17.BigQuery `withzero.withzero_analytics.capability_invocations` (one row per HTTP request), queried 2026-08-21. Metered routes record no amount, and proof-intent identity routes record zero-amount settlements that are excluded here, so the dollar figure is a floor and the call count a ceiling.
2. ORA's live agent-readiness index reported 14,616 sites scanned, an average score of 34/100 and 2% graded B or above on 2026-08-24; payment support was the weakest published layer at 6% average fill.ORA Research, `How ready is the web for agents?`, https://ora.ai/research, and scoring methodology, https://ora.ai/methodology, retrieved 2026-08-25. ORA is an external, continuously updated index; its measurements provide public context and do not seed, calibrate or validate this simulation.
3. x402 is the volume leader among agent payment rails: roughly 165M payments from ~69k agents by April 2026.agenticplug.ai protocol tracker (secondary), April 2026; the x402 Foundation under the Linux Foundation listed 40 members in July 2026. Primary Coinbase figures were not independently verified for this page.
4. UCP (Google + Shopify, January 2026) is the merchant-side standard; OpenAI retired ChatGPT Instant Checkout in March 2026 after in-chat conversion ran about 3× below discover-in-AI, buy-on-site.withzero research note `docs/research-readiness-2.1-audit.md` A4, compiled 2026-08-13 from public announcements.
5. All major US card networks now ship agent payment tokens: Mastercard Agent Pay (announced 2025-04-29, live) and Visa Intelligent Commerce (Agent Score, Agentic Registry at Visa Payments Forum 2026); Google AP2 launched September 2025 with 60+ partners.aimmediahouse.com, eco.com, agenticplug.ai, retrieved 2026-08-21.
6. Forecasts for agent-driven commerce diverge mostly by definition: Bain $300–500B US by 2030 (15–25% of e-commerce); Morgan Stanley 10–20% of US e-commerce; Gartner 20% of digital commerce via AI platforms; McKinsey $3–5T globally.Bain 2030 snap chart (Dec 2025), Digital Commerce 360 on McKinsey (2025-10-20), Stellagent integrated analysis; retrieved 2026-08-21.
7. Every curve on this page comes from a deterministic mean-field simulation: purchase intents → instrument-to-rail match → outcome, stepped quarterly, with seller adoption and buyer instrument migration as share movements. Interoperability has an explicit cross-rail conversion rate, and platform take is reported as merchant-retained GMV. No LLM computes a value; uncertainty bands come from 4,096 seeded Latin-hypercube runs that cover every assumed range densely and evenly.`capabilities/futures/sim/engine.ts`, `sim/ledger.ts`, `sim/sweep.ts` and `sim/sensitivity.ts`. `npm run sim -- run --branch open` reproduces the open-rails series; `npm run sim:sweep` reproduces the bands.
8. The three scenarios share every parameter except nine lever values: rail interoperability, the chance a chat runtime blocks third-party rails, platform take rate, relative integration cost for five rails, and which rail the agent-native incumbents push after the fork.`npm run sim -- check` prints the differing keys and `non-lever diffs: 0`.
9. The near-term simulation starts from disclosed scenario priors rather than a readiness score. Before a run is accepted, four accounting checks require seller-capability, buyer-instrument and runtime shares to conserve to one and first-quarter outcomes to close.`npm run sim -- run --branch open` prints the model-internal start-state checks. `sim/validate.ts` defines them; they validate accounting, not empirical fit.
10. An LLM was tried as the seller-adoption decision model and rejected: at temperature 0 it returned the same x402 adoption probability (0.72) for every lost-sales level from 0% to 95%, and pushed wallet-holding buyers to 79–87% in both tested scenarios regardless of the levers.Spike run 2026-08-21, claude-haiku-4.5 via openrouter, 20-step monotonicity sweep; total spend under $0.50. The LLM now drafts prose only.
11. A 402 Payment Required response is the agent-commerce handshake: the seller names a price and accepted rails; the buyer's agent pays and retries the same request with proof of payment.HTTP 402 as used by x402 (Coinbase) and MPP (mpp.dev); withzero's gateway answers 402 with a machine-readable challenge on every paid route.
12. ZeroClick publishes this scenario and has a commercial interest in open agent commerce. ZeroClick itself is not a modeled actor: no scenario assumes that its current products persist, supply the coordination layer or win future market share.Disclosure. The simulation models market capabilities and actor classes, not company valuation or product-market fit.
13. The chapter architecture adapts AI 2027's scenario method: repeatedly ask what happens next, and begin each chapter with a compact state of the world. Here that method is applied to commerce institutions and purchasing interfaces rather than general AI capability.AI 2027, scenario and methodology, https://ai-2027.com/ and https://ai-2027.com/scenario.pdf, retrieved 2026-08-24.
14. Delegation is better treated as a curve than a ladder: the useful degree of agent autonomy varies with category, stakes and reversibility, and higher-authority actions require bounded, auditable and reversible controls.McKinsey, `The automation curve in agentic commerce`, https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-automation-curve-in-agentic-commerce, retrieved 2026-08-24.
15. Agentic product search can shift scarce human effort from inspecting products toward articulating preferences; platform capability may therefore advance faster than consumer delegation, creating an adoption lag.Dong, Luo and Xu, `From Product Search to Preference Articulation: The Economics of Agentic Search`, arXiv:2608.08395, https://arxiv.org/abs/2608.08395, August 2026.
16. The four commerce-arena profiles are counterfactual lenses, not empirical category estimates. Their repeatability, reversibility, consequence and preference-articulation values alter purchasing-interface thresholds, autonomy and exception risk without changing the aggregate market path.Disclosed unanchored scenario priors in `capabilities/futures/sim/horizon.ts`; each selected arena prints its values and evidence status in HTML and Markdown.
17. Each structural chapter exposes the model transition that precedes it. The 2029 trace shows the explicit near-term-to-structural mapping; later traces report exact percentage-point changes between simulated states. These traces describe the equations, not observed real-world causal attribution.`buildHorizonTransitionTrace` in `capabilities/futures/sim/horizon.ts`; HTML and Markdown render the returned run values without recomputing or rewriting them.
18. Each structural chapter opens with a deterministic authored institutional event selected from the actual branch, year and published model thresholds. The page exposes the exact selection rule and a trigger sentence with run values; the title, interpretation and consequence are scenario narration, not measurements or forecasts. The 512 range-covering structural draws also report how often every threshold-defined alternate event is selected; those shares diagnose rule sensitivity and are not event probabilities.`buildHorizonChapterEvent` and `simulateLongHorizonEnsemble` in `capabilities/futures/sim/horizon.ts`; the selected event and full event coverage are carried into HTML, Markdown and the narrator dossier with the evidence status `model-triggered authored event`.
19. Long-horizon ribbons are conditional sensitivity bands, not probabilities or confidence intervals. For each branch, 512 paired seeded Latin-hypercube draws cover all nine disclosed unanchored structural ranges while holding the published 2029 branch handoff fixed; the page reports p10, p50 and p90 of the resulting model outputs. The same draws report the complete share distribution across all four purchase surfaces by arena and epoch; that coverage is a robustness and sensitivity diagnostic, not a probability. A published preset can sit outside its ribbon because the coverage design spans every range stratum rather than centering on that preset.`simulateLongHorizonEnsemble` in `capabilities/futures/sim/horizon.ts`, using the deterministic sampling primitives in `capabilities/futures/sim/sampling.ts`; generated bands and full surface distributions are rendered directly in the `/2040` frontier, companion, chapters, chart and Markdown.
20. Physical agents are becoming a technically distinct frontier rather than an extension of browser automation: current embodied-reasoning systems can plan multi-step physical tasks, coordinate multiple robots and detect task completion. This is evidence for possible building blocks, not evidence of commercial diffusion or a 2040 adoption rate.Google DeepMind, `Gemini Robotics ER 2`, https://deepmind.google/models/gemini-robotics/embodied-reasoning/ and model card https://deepmind.google/models/model-cards/gemini-robotics-er-2/, retrieved 2026-08-24. The model card restricts safety-critical production uses; the simulation's physical-execution values remain unanchored priors.
21. Current agent-payment specifications already distinguish human-present approval from human-not-present autonomous mandates, but delegation from one shopping agent to another remains explicitly outside the current AP2 specification. The gap between a secure purchase mandate and a durable economy of delegated agents is therefore still open.Google Agent Payments Protocol v0.2 specification, https://github.com/google-agentic-commerce/AP2/blob/main/docs/ap2/specification.md, retrieved 2026-08-24.
22. Emerging agent registries separate agent identity, reputation and task validation, suggesting that future machine counterparties may need trust infrastructure independent of a seller site. These are proposed standards, not measured adoption.ERC-8004 `Trustless Agents`, https://eips.ethereum.org/EIPS/eip-8004, retrieved 2026-08-24.
23. The present Universal Commerce Protocol covers discovery profiles, checkout and asynchronous order lifecycle updates. Pooled demand, commissioned production and physical multi-operator outcomes go beyond that transaction-centered surface and are modeled here only as disclosed structural possibilities.Universal Commerce Protocol specification overview and roadmap, https://ucp.dev/2026-01-11/specification/overview/ and https://ucp.dev/documentation/roadmap/, retrieved 2026-08-24.
24. Visa's 2025 surveys of 3,700 monthly online shoppers across the United States, Australia and New Zealand found stated willingness to substitute an AI shopping assistant across the buyer journey: 73% for discovery, 69% for evaluation, 62% for cart and checkout and 64% for post-purchase tasks; 85% said control over agent-accessible data was important.Visa, `Earning consumer trust in the age of agentic commerce`, https://corporate.visa.com/en/products/intelligent-commerce/earning-trust-report.html, retrieved 2026-08-25. These are survey responses to illustrated use cases, not observed transaction rates.
25. PayPal's 2026 Agentic Commerce Pulse Report surveyed 498 U.S. merchants across small-business, mid-market and large-enterprise segments about preparation for AI-influenced shopping.PayPal, `What merchants really think about agentic commerce`, https://www.paypal.com/us/brc/article/agentic-commerce-pulse-report-findings, published 2026-04-27 and retrieved 2026-08-25. Merchant expectations are directional survey evidence, not measured adoption.
26. The economic layer starts from $340.2 billion of seasonally adjusted U.S. retail e-commerce sales in Q2 2026, annualized to $1.3608 trillion. Census reported that quarterly e-commerce represented 17.1% of total U.S. retail sales. Only this baseline is observed; every later dollar value is a conditional scenario estimate.U.S. Census Bureau, `Quarterly Retail E-Commerce Sales`, https://www.census.gov/retail/ecommerce.html, released 2026-08-18 and retrieved 2026-08-25. The published figure is adjusted for seasonal variation but not price changes.
27. McKinsey estimated that U.S. B2C retail could see $900 billion to $1 trillion of revenue orchestrated by agentic commerce in 2030, and $3 trillion to $5 trillion globally. The estimate covers goods, not services or B2B, and is shown only as an external comparison; it does not seed, calibrate or validate the simulation.McKinsey, `The agentic commerce opportunity: How AI agents are ushering in a new era for consumers and merchants`, https://www.mckinsey.com/capabilities/quantumblack/our-insights/the-agentic-commerce-opportunity-how-ai-agents-are-ushering-in-a-new-era-for-consumers-and-merchants, published 2025-10-17 and retrieved 2026-08-25.

Anchored values cite a measurement. Assumed values are our best guess with the range the uncertainty sweep samples. Lever rows are the only parameters that differ between scenarios.