VOL. 01 / NO. 01 MAY 2026 A MATHEMATICAL WARNING
â THE PREMISE
Debt service, revenue, and borrowing costs are coupled through standard macro mechanisms: the Phillips curve, Fed reaction, fiscal response. Most shocks move them in offsetting directions, which is why fiscal cascades are rare. The question is what happens when a single shock moves them together instead.
â THE MODEL
A single ratio: federal debt service divided by available revenue, where the revenue itself shrinks as unemployment and inflation rise. Move the sliders to see how the ratio responds under any combination of the three variables, at any horizon.
â THE ALARM BELL
AI displacement is the first shock that plausibly overrides those offsetting mechanisms and drives the three together. Adoption sits in single digits today. If it scales as the labor-exposure research suggests, the cascade the model describes moves on a timeline of years, not decades.
DEBT HELD BY PUBLIC $32.0T Owed to outside investors, not the $40T total. The gap is debt Treasury owes itself.
CRISIS RATIO 0.241 Debt service over stress-adjusted receipts, at live conditions.
STRUCTURAL THRESHOLD 0.30
STATUS APPROACHING
Under ordinary conditions, unemployment, inflation, and interest rates are coupled through standard macroeconomic mechanisms â the Phillips curve, the Federal Reserve's reaction function, and fiscal-policy feedback â and those mechanisms move the variables in the canonical inverse pattern. Recessions raise u and lower i; supply shocks raise i without raising u; rate cycles trail both with a lag. The fiscal arithmetic absorbs each shock in turn because the canonical mechanisms drive the variables in offsetting directions.
What changes the picture is a shock that overrides those canonical mechanisms â one that pushes all three variables in the same direction at the same time through a different coupling pathway. AI-driven cognitive displacement is the first plausible such shock in modern macroeconomic history. The model below shows what the fiscal math does if it fires.
REVENUE FUNCTION
Y(u, i) = Yâ à [ 0.55 + 0.45 · max(0, 1 â 0.05·u â 0.04·max(0, i â i*)) ]
The bracket smoothly interpolates between the floor (0.55·Yâ) at extreme stress and full baseline (Yâ) at zero stress. Each percentage point of unemployment reduces the inner term by 5%; each point of inflation above the 2% target reduces it by 4%. The 0.55 floor encodes the worst peacetime federal-receipts contraction on record (1932â33). The coefficients are stylized sensitivities calibrated to the 2008â09 episode and post-1985 indexed-bracket experience, respectively â not regression estimates.
DEBT SERVICE
DS = D Ã r
Annual debt service equals debt held by the public multiplied by the weighted-average rate. Each 1% increase in r adds approximately $323 billion to annual servicing costs at current debt levels ($32.3T held by public).
SUSTAINABILITY THRESHOLD
Crisis Ratio = DS ÷ Y(u, i)
Stress band begins at Crisis Ratio ⥠0.30
The 0.30 threshold mirrors the IMF MAC-DSA "elevated risk" band on interest-to-revenue for advanced economies. Above 0.30, discretionary fiscal capacity erodes. Above 0.50, non-mandatory spending is crowded out and rollover risk dominates. Above 1.0, the math reverses â borrowing finances borrowing.
FY2025 ACTUALS
Debt held by public $30.28T +$1.97T YoY
Federal receipts $5.24T +$317B YoY
Net interest $970B +$80B YoY
Interest ÷ receipts 0.185 +0.006 YoY
The ratio rose again in FY2025, though only by six thousandths, because revenue growth from customs duties (+$118B) and individual income tax (+$230B) absorbed most of the rise in interest costs. Roughly half of the customs duty growth came from tariffs imposed under the International Emergency Economic Powers Act, which the Supreme Court ruled unlawful in Learning Resources v. Trump (February 20, 2026). The refund liability is unresolved but potentially in the $100â200B range. The favorable revenue dynamic was therefore partly produced by a fiscal action subsequently ruled to exceed statutory authority. The cascade scenarios below describe what happens when that revenue growth stops absorbing the rise; the structural fragility this represents is exactly what the model is designed to make legible. Sources: Treasury MTS; Joint Economic Committee, U.S. Senate (October 2025); Supreme Court, Learning Resources, Inc. v. Trump, February 20, 2026; Penn Wharton Budget Model, "IEEPA Revenue and Potential Refunds" (February 2026).
FY2026 THROUGH JUNE â MOST RECENT DATA
Debt held by public $31.7T
Receipts (annualized) ~$5.53T first 9 months
Net interest (annualized) ~$1.14T first 9 months
Interest ÷ receipts 0.206 +0.023 vs FY25
Unemployment (Jun 2026) 4.2%
Through the first ten months of FY2026, net interest reached $931.4 billion, up 10.8 percent on the same period last year, while receipts reached $4.485 trillion, up 3.2 percent. Interest as a share of receipts stands at 0.208 against 0.193 for the same ten months of FY2025. That share has risen in every full fiscal year since 2022 (0.097, 0.149, 0.179, 0.185), and FY2026 is running above all of them. This is the fragility the model describes: the revenue tailwind from tariffs and nominal growth is not keeping pace with the interest it has to cover. The measured reading is still inside the "approaching" band, a trajectory and not a cascade. Sources: U.S. Treasury Monthly Treasury Statement (July 2026); BLS Employment Situation and CPI (July 2026).
The Crisis Ratio is computed at a point in time using current inputs, but debt accumulates: every year that conditions persist, debt held by the public grows by roughly $2 trillion in baseline conditions and significantly more under stress. Use the horizon control to see how the same configuration evolves when conditions don't reverse. The static ratio shows the present state. The 3-year ratio shows the cascade.
CRISIS RATIO STATIC
Project forward: â
0.241
APPROACHING THRESHOLD
+3 YEARS
0.286
D = $38.3T
Revenue Y(u,i) $4.62T
Revenue contraction from unemployment â20.0%
Revenue contraction from inflation â4.0%
Projected debt D(t) $32.30T
Annual debt service DS $1.11T
Revenue gap +$3.51T
INTERPRETATION
Debt service consumes 21% of federal receipts â inside the sustainable band but approaching the IMF-style stress threshold of 0.30. AI displacement has not yet materially begun; the canonical macroeconomic mechanisms still govern.
Fig. 01 / Sixty MonthsAug 2021 – Jul 2026
The Inputs & The Output.
Monthly. Ratio computed on trailing-twelve-month net interest over trailing-twelve-month receipts.
Unemployment (u) Inflation, CPI YoY (i) Avg rate on debt (r) Interest ÷ receipts (TTM)
The Inputs · Percent
The Output · Interest ÷ Receipts
SOURCES: TREASURY MTS T4/T9 · TREASURY AVG INTEREST RATES · BLS LNS14000000 · BLS CUUR0000SA0 · OCT 2025 GAP: DATA NOT PUBLISHED
- iAI displaces cognitive workers at scale
- iiA high-MPC consumer cohort loses earned income
- iiiAggregate demand contracts; capital captures the productivity gains
- ivWealth concentration drives asset inflation; goods inflation may stay muted
- vThe Fed faces a trap: cut and fuel asset bubbles, or hold and accelerate fiscal compression
- viEither choice creates conditions for a credibility event on Treasuries
- viiTerm premium rises; weighted-average r climbs with the rollover stack
- viiiThe Crisis Ratio accelerates past 0.30 toward critical bands
EVIDENCE LOG
What partial credibility events look like in real time
The cascade described above is conditional. None of it has fully fired. But the conditions favorable to it have measurably accumulated over the past eighteen months. Three recent examples worth pointing to:
- Moody's downgraded U.S. sovereign debt from Aaa to Aa1 on May 16, 2025 â the first downgrade in the agency's 108-year history of rating U.S. debt.
- The Supreme Court ruled the IEEPA tariffs unlawful in February 2026, producing a $100â200B potential refund liability and demonstrating how rapidly fiscal arithmetic can move on a single court decision.
- Treasury auctions in March 2026 saw primary dealers absorbing twice their normal share of 2-year notes, alongside weak demand for 5- and 7-year securities â indicators of softening demand at the duration where credibility premiums show up first.
None of these is the cascade. Each is a piece of evidence that the conditions favorable to it are accumulating.
01 Phillips Curve
Q. Doesn't the Phillips curve already explain this?
The Phillips curve couples unemployment and inflation in offsetting directions through wage-driven price inflation: tight labor markets raise wages, wages raise prices, the Fed responds. The cascade described here does not run through that channel. It runs through asset inflation and a Fed policy trap, with goods inflation potentially muted by automation's downward pressure on costs. The Phillips curve is not wrong; it is silent on this configuration. That the curve has been empirically flat since roughly 2010 â with the 2021â2022 inflation arriving without prior labor-market tightening â only reinforces that it is not a binding constraint here.
02 Japan
Q. Doesn't Japan prove this is wrong?
Japan has run debt above 250% of GDP for decades with near-zero rates and no cascade. The objection is fair, and the answer clarifies what the cascade actually requires. Japan does not cascade because the conditions that drive the U.S. cascade are largely absent there.
-
i
Debt is held at home. Japanese debt is overwhelmingly held domestically â by its own central bank and savers â rather than by foreign holders. That insulates it from the credibility dynamics that run through foreign capital.
-
ii
A savings base the U.S. does not have. Japan financed its debt with a high domestic savings rate and current account surpluses. The U.S. has neither.
-
iii
Not the reserve currency issuer. Japan's experiment stayed idiosyncratic rather than systemic precisely because the yen is not the global reserve asset.
-
iv
No coupling shock. Japan never faced the specific coupling shock the cascade requires â a single mechanism that pushes u, i, and r in the same direction at once.
The lesson of Japan is not that high debt is safe. It is that high debt is survivable under conditions â domestic financing, high savings, no coupling shock â that the U.S. does not meet. The U.S. configuration is the photographic negative of the Japanese one.
03 Yield Curve Control
Q. Can't the Fed just cap yields (yield curve control)?
Capping yields does not escape the cascade; it relocates it. Holding yields below the level the market demands requires the central bank to buy unlimited quantities of debt with newly created money â and to do so in an already-inflationary environment, which accelerates the revenue erosion on the other side of the ratio.
-
i
For the reserve currency issuer, the cascade migrates. A yield cap drives capital out of the dollar, so the cascade runs through the exchange rate and reserve status instead of through the nominal yield. The pressure does not vanish; it changes which gauge it shows up on.
-
ii
Japan's YCC is not a precedent for the U.S. Japan could sustain yield curve control partly because the yen is not the global reserve asset and its debt is domestically financed. Both conditions are absent for the dollar.
-
iii
The trade is arguably worse. For the dollar, yield curve control trades a Treasury-market cascade for a currency-and-reserve cascade. That is not obviously a better failure mode.
Yield curve control is not an escape mechanism. It changes which wall the system hits, not whether it hits one.
UNEMPLOYMENT SENSITIVITY
α = 0.05
Revenue contraction per percentage point of unemployment, applied to the inner bracket term. A disclosed stress value: historical central estimate â 0.03; CBO cyclically-adjusted range 0.04 to 0.06. Calibrated to the 2008â09 episode (federal receipts fell ~17% against a 4.3-pt unemployment increase); the cascade conclusion holds even at 0.03.
INFLATION SENSITIVITY
β = 0.04
Fiscal-capacity erosion per percentage point of inflation above the 2% target. Calibrated to the post-1985 indexed-bracket era â modern indexation substantially mutes the inflation-revenue channel relative to pre-1985 episodes.
RATE MULTIPLIER
+$323B
Additional annual debt service per percentage point increase in the weighted-average rate on debt held by the public ($32.3T, current). Each percentage point now carries more fiscal weight than at any time since the early 1990s.
EXPLORE THE FULL SCENARIO BREAKDOWNS
Three modeled futures, with the math worked out step by step.
REFRESHED 18 JULY 2026 · FY2026 THROUGH JUNE (9 MONTHS)
Debt held by public $31.7T +$0.4T since Apr
Net interest (9-mo) $857B +13% YoY
Receipts (9-mo) $4.15T +3.5% YoY
Interest ÷ receipts 0.206 +0.017 vs FY25 9-mo
Unemployment / CPI 4.2% / 3.5% Jun 2026
This page previously carried FY2026 data through June. The ten-month figures in the July Monthly Treasury Statement extend that reading. Sources: U.S. Treasury Monthly Treasury Statement (July 2026); U.S. Treasury Debt to the Penny; BLS Employment Situation and CPI (July 2026).
What changed. Net interest reached $931.4 billion for the first ten months of FY2026, up 10.8 percent year over year. Receipts reached $4.485 trillion, up 3.2 percent, slower than the pace carried through June. On a like-for-like ten-month basis, interest as a share of receipts stands at 0.208 against 0.193 a year ago. Debt held by the public reached $32.3 trillion. Headline CPI eased to 3.4 percent and unemployment fell to 4.1 percent.
How it affects the trajectory. The measured reading is still well below the 0.30 structural threshold, and nothing here fires the coupling mechanism. What the ten-month data settles is the direction of the denominator: receipts are growing at roughly a third the rate of the interest they have to cover. Run on current conditions rather than a fixed baseline, the model returns 0.241. The scenarios are unchanged. The distance between where the model stands and where they begin has narrowed again, which is precisely the fragility the model was built to make legible.