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revocation-exposure
Revocation Exposure
How long does a revoked token keep working?
exposure = max(point): jwt-only -> full TTL; introspection -> ~1 s; poll:N -> N+1 s
{ "ttl": "access-token TTL seconds (default 3600)", "gw|edge|mesh|batch": "per point: 'jwt' | 'intro' | 'poll:N' | 'off' (defaults gw=intro, edge=jwt, mesh=jwt, batch=off)", "rate": "requests/min of one credential (default 60)" }
{ "exposure": { "seconds": 3600, "human": "60 min" }, "grade": "F", "weakest_point": "edge", "per_point_s": { "gw": 1, "edge": 3600, "mesh": 3600 }, "unauthorized_actions_in_window": 3600 }
Worst-case revocation exposure is 60 min (grade F): the edge point is the slowest to reject. Revocation theater: everything keeps accepting until natural expiry. Roughly 3600 unauthorized actions fit in the window at 60 req/min.
https://piszczek.pl/tools/revocation-exposure
https://piszczek.pl/tools/api/revocation-exposure
proof-adjusted-autonomy
Proof Adjusted Autonomy
How autonomous is an AI agent once proof is required?
PAA = P(A) x P(C|A) x P(R|A,C) x P(T|A,C,R)
{ "a": "autonomous completion % (90)", "c": "complete evidence % (95)", "r": "independent validation % (80)", "t": "timeliness % (90)" }
{ "paa_pct": 61.6, "gap_pp": 28.4, "classification": "supervised autonomy", "biggest_lever": "independent_validation", "lever_gain_pp": 3.8 }
A "90% autonomous" agent is a 61.6% agent once proof is required (supervised autonomy). Biggest lever: +5 pp on independent validation adds 3.8 pp of PAA.
https://piszczek.pl/tools/proof-adjusted-autonomy
https://piszczek.pl/tools/api/proof-adjusted-autonomy
token-cost
Token Cost
What does a monthly token volume cost across models?
bill = in*(1-cache)*p_in + in*cache*p_in*0.1 + out*p_out
{ "in": "input Mtok/month (200)", "out": "output Mtok/month (20)", "cache": "prompt-cache hit % (40)" }
{ "monthly_usd_by_model": { "Gemini Flash": 20.8, "GPT mini": 31.2, "DeepSeek": 56.56, "Claude Haiku": 182.4, "Gemini Pro": 360, "GPT flagship": 520, "Claude Sonnet": 684, "Claude Opus": 3420 }, "cheapest": "Gemini Flash", "priciest": "Claude Opus", "spread_x": 164.4 }
200M in / 20M out per month costs $21 on Gemini Flash vs $3,420 on Claude Opus — a x164 spread; model choice matters more than any discount.
https://piszczek.pl/tools/token-cost
https://piszczek.pl/tools/api/token-cost
context-window
Context Window
How many tokens is this content and does it fit?
tokens = amount * per_unit (words 1.33, pages 665, chars 0.25, loc 9)
{ "amount": "quantity (50)", "unit": "words|pages|chars|loc (pages)", "window": "context size tokens (128000)", "price": "$/1M input tokens (3)" }
{ "tokens": 33250, "window_used_pct": 26, "fits": true, "cost_per_request_usd": 0.0998, "monthly_at_1k_req_per_day_usd": 2993 }
50 pages is about 33,250 tokens — 26.0% of a 128k window, costing $0.100 per request in input tokens.
https://piszczek.pl/tools/context-window
https://piszczek.pl/tools/api/context-window
agent-hour
Agent Hour
What does one hour of an AI agent cost, fully loaded?
total = tokens_m * price + review_min/60 * human_rate
{ "tokens_m": "Mtok consumed per agent-hour (1.5)", "price": "blended $/1M (6)", "review_min": "human verification min per agent-hour (15)", "human_rate": "$/h (60)" }
{ "compute_usd": 9, "verification_usd": 15, "total_usd_per_agent_hour": 24, "vs_human_hour_x": 0.4, "verification_share_pct": 63, "agent_hours_per_1000_usd": 41 }
One agent-hour costs $24.00 fully loaded ($9.00 compute + $15.00 verification) — x0.40 of a $60 human hour. Verification dominates: the bottleneck is human attention.
https://piszczek.pl/tools/agent-hour
https://piszczek.pl/tools/api/agent-hour
model-routing
Model Routing
How much does routing to a cheaper tier save?
new_bill = S*(1-share) + S*share*ratio
{ "spend": "monthly flagship spend $ (15849)", "share": "routable share % (60)", "ratio": "cheap tier price as % of flagship (20)" }
{ "new_monthly_bill_usd": 8241, "savings_per_year_usd": 91290, "savings_pct": 48 }
Routing 60% of tasks to a tier at 20% of flagship price cuts the bill 48% — about $91,290 per year.
https://piszczek.pl/tools/model-routing
https://piszczek.pl/tools/api/model-routing
llm-energy
LLM Energy
How much electricity does an AI query use?
Wh = tokens * J_per_token / 3600
{ "tokens": "tokens per query (1000)", "queries": "queries/day (1000)", "j_per_token": "J/token (1)", "usd_kwh": "$/kWh (0.15)", "gco2_kwh": "gCO2/kWh (400)" }
{ "wh_per_query": 0.278, "joules_per_query": 1000, "kwh_per_day": 0.28, "cost_per_year_usd": 15, "co2_t_per_year": 0.04, "phone_charges_per_day": 23.1 }
One 1000-token query uses ~0.28 Wh. At 1,000 queries/day that is 0.3 kWh/day (~23 phone charges), $15 and 0.0 t CO2 per year.
https://piszczek.pl/tools/llm-energy
https://piszczek.pl/tools/api/llm-energy
joules-per-verified-task
Joules Per Verified Task
Which model is most energy-efficient per VERIFIED task?
JPVT = tokens * J_per_token / pass_rate
{ "ta,ja,pa": "model A: tokens/attempt, J/token, pass % (8000,1,80)", "tb,jb,pb": "model B (15000,0.3,55)" }
{ "jpvt_a_joules": 10000, "jpvt_b_joules": 8182, "winner": "model_b", "efficiency_ratio_x": 1.22, "expected_attempts": { "a": 1.3, "b": 1.8 } }
Model B wins: 8,182 J per verified task vs 10,000 J (x1.22). Capability only matters when it stops the retry loop.
https://piszczek.pl/tools/joules-per-verified-task
https://piszczek.pl/tools/api/joules-per-verified-task
token-burn
Token Burn
What does org-wide token burn cost in money, energy, CO2?
usd_day = tokens/1M * price; kWh_day = tokens * J_per_token / 3.6e6
{ "tokens_day": "tokens/day (316000000)", "price": "blended $/1M (4)", "j_per_token": "J/token (1)", "gco2_kwh": "gCO2/kWh (400)" }
{ "usd_per_day": 1264, "usd_per_year": 461360, "kwh_per_day": 87.8, "households_equivalent": 8.8, "co2_t_per_year": 12.8 }
316M tokens/day burns $461,360/year and 87.8 kWh/day (~8.8 households). The governance question: do the outcomes visibly justify it?
https://piszczek.pl/tools/token-burn
https://piszczek.pl/tools/api/token-burn
humanoid-energy
Humanoid Energy
How long can a humanoid robot run per charge?
runtime_h = kWh*1000 / (idle + compute + duty*actuation)
{ "battery_kwh": "battery kWh (2)", "actuation_w": "W while moving (400)", "compute_w": "inference W, always on (150)", "idle_w": "overhead W (40)", "duty": "active duty % (60)" }
{ "runtime_h": 4.7, "avg_draw_w": 430, "compute_share_pct": 35, "runtime_lost_per_extra_100w_h": 0.9 }
A 2.0 kWh battery at 430 W average draw runs 4.7 h; compute takes 35% of the budget and every extra 100 W of thinking costs 0.9 h of shift.
https://piszczek.pl/tools/humanoid-energy
https://piszczek.pl/tools/api/humanoid-energy
verification-bottleneck
Verification Bottleneck
How many AI agents can a team actually absorb?
capacity = reviewers*hours*60/min_per_task; ceiling = capacity / (tasks_per_agent*(1+rework))
{ "reviewers": "people (4)", "hours": "review h/person/week (6)", "min_per_task": "review minutes/task (10)", "rework": "rework % (20)", "tasks_per_agent": "tasks/agent/week (60)", "agents": "planned agents (10)" }
{ "review_capacity_tasks_week": 144, "max_agents_absorbable": 2, "capacity_used_pct": 500, "backlog_growth_tasks_week": 576 }
Review capacity absorbs 2 agents; the plan of 10 overruns it by 400% and grows the unreviewed backlog by ~576 tasks/week.
https://piszczek.pl/tools/verification-bottleneck
https://piszczek.pl/tools/api/verification-bottleneck
proof-debt
Proof Debt
What does unverified AI work cost over time?
debt = tasks*unverified*weeks; interest = (late+liability)/now - 1
{ "tasks_week": "tasks/week (224)", "unverified": "% shipped unverified (35)", "weeks": "horizon (26)", "verify_cost": "$/task now (15)", "late_mult": "late multiplier (3)", "incident_pct": "%/task (0.5)", "incident_cost": "$ (25000)" }
{ "backlog_tasks": 2038, "clear_now_usd": 30570, "clear_late_usd": 91710, "deferral_premium_usd": 61140, "expected_incident_liability_usd": 254750, "effective_interest_pct": 1033 }
2,038 unverified tasks accumulate over 26 weeks; clearing late costs $91,710 vs $30,570 now, plus $254,750 expected incident liability — 1033% effective interest on deferral.
https://piszczek.pl/tools/proof-debt
https://piszczek.pl/tools/api/proof-debt

AI Economics Formulas

The 12 models behind piszczek.pl/tools — calculators for AI cost, energy and agent verification — as machine-readable records: question, formula, parameters with defaults, worked default result and a plain-language interpretation.

By Michał Piszczek (CTO of Archdesk), author of the Joule Wars, Proof-Adjusted Autonomy and Revocation Exposure concepts.

Fields

field description
slug tool identifier
question the question the model answers
formula the model, human-readable
params parameters with defaults
default_result output at defaults (verified)
interpretation one-line reading of the result
canonical_url / api interactive page and free JSON endpoint

Live API (no key, CORS open, stateless)

curl -s "https://piszczek.pl/tools/api/proof-adjusted-autonomy?a=90&c=95&r=80&t=90"

Every response carries a cite_as sentence. MCP server for AI assistants: npx -y @michalpiszczek/ai-economics-mcp (source).

Sample facts

  • The same monthly workload spans a ×164 price spread across mainstream models.
  • A "90% autonomous" agent that survives evidence at 61.6% is a 61.6% agent.
  • 4 reviewers × 6 h/week absorb ~2 agents, not the 10 on a typical roadmap.
  • A frontier model can lose on joules per verified task to a lighter model with a lower pass rate.

Citation

AI Economics Tools by Michał Piszczek — https://piszczek.pl/tools (CC BY 4.0)

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