CPI-U month-over-month, June 2026 (first print, SA)

Population stdev of headline MoM over the last 24 months = 0.189pp. This is elevated by the recent oil-shock spike; a typical pre-shock month was ~0.1pp stdev. Using ~0.20-0.24pp as the 1-sigma scale, the 80% band (z=1.28) is roughly point +/- ~0.27pp.

Trailing-3 mean = +0.66%, but the sequence is monotonically decelerating (0.87 -> 0.64 -> 0.47). Linear extrapolation of the deceleration points to roughly +0.35-0.40% for June as the initial energy spike's monthly contribution fades while levels stay high.

Base rate (pre-shock 12-month run-rate, mid-2025): headline MoM clustered around +0.2-0.3%. The oil shock has lifted the conditional mean above that; June should sit between the shock-elevated recent prints and the calmer base, i.e. ~+0.3-0.5%.

Outside [0.1, 0.7] if: a renewed oil spike (escalation) or a large shelter/airfare jump pushes the print to +0.8%+; or, conversely, an abrupt energy pullback (ceasefire, falling gasoline) drops it toward +0.1% or below. Headline is the most energy-sensitive of the four CPI/labor cells, so its band is the widest.

Decelerating energy contribution + firm core floor + PPI pipeline pressure -> point +0.4%. 80% CI = +0.4 +/- ~0.27 -> [0.1, 0.7].

The control sees the recent headline CPI deceleration but treats energy risk as generic residual volatility rather than a structured component.

Energy and pipeline-price packs keep the center a touch above the aggregate control while the release pack prevents the interval from becoming too wide.

The resolver is the BLS first print for CPI-U all items, U.S. city average, seasonally adjusted percent change from May 2026 to June 2026, released in the CPI Summary and Table A.

Base-rate/reference-class: the last six published all-items monthly changes average about 0.47 percent and have a median of 0.4 percent, but that reference class includes an unusually large energy impulse in March through May.

Counter-consideration: if gasoline or energy prices remain as strong as in May, headline CPI could print above 0.5 percent even with core near 0.2 percent; if energy mean-reverts, headline could fall toward 0.2 percent.

Use the six-month headline median of 0.4 as the anchor; lean slightly below the 0.47 average because May core was 0.2 and food was 0.2, while keep a wide 80% interval of 0.1 to 0.8 to reflect energy volatility.

The resolver is the BLS first print for CPI-U, U.S. city average, all items, seasonally adjusted percent change from May 2026 to June 2026. This is a data-release target, not a later revised time-series value.

Base-rate/reference-class: recent one-month headline CPI prints before the target were 0.2, 0.3, 0.9, 0.6, and 0.5. Their simple average is 0.5, but the median is also 0.5 and the latest core reading of 0.2 suggests headline pressure is being pulled up by volatile energy rather than a broad acceleration.

Counter-consideration: if the energy shock persists into June, gasoline and energy could keep headline CPI near the recent 0.5-0.6 pace or higher; if energy retraces or core softness dominates, the rounded print could fall toward 0.2-0.3.

Use a reference-class center near 0.5, shade down by 0.1 because May core CPI was 0.2 and some mean reversion is likely after March 0.9, April 0.6, and May 0.5. Set pointEstimate = 0.4. An 80% interval of 0.1 to 0.8 covers a soft core-led month through a renewed energy-led upside surprise and respects one-decimal BLS rounding.

Framing and exact resolver: this is BLS CPI-U all items, U.S. city average, seasonally adjusted month-over-month percent change for June 2026, first print. The series variant is headline CPI-U SA MoM; all CPI anchors below use the same BLS headline SA table, not NSA index levels or core CPI as the target.

Base rate/reference class: the six available BLS headline SA prints from Dec 2025 through May 2026 average 0.47 percent, but that reference class is elevated by a large energy shock: March 0.9, April 0.6, and May 0.5 coincided with energy monthly increases of 10.9, 3.8, and 3.9 percent in the BLS release.

Current-release adjustment: EIA gasoline prices declined each week from June 1 through July 6, so the June CPI energy contribution should be below May's large positive energy contribution. Core CPI at 0.2 percent, food at 0.2 percent, and shelter at 0.3 percent in May keep the non-energy center positive but not high enough to preserve a 0.5 percent headline print if gasoline turns down.

Prior/update/interval: persistence prior is the BLS recent headline SA MoM reference class Dec 2025-May 2026 values [0.3, 0.2, 0.3, 0.9, 0.6, 0.5], mean = 0.47; adjustment components are about -0.20 for gasoline/energy reversal, -0.05 for core mean reversion from April, and 0.00 to +0.05 for shelter/food persistence, giving an unrounded center near 0.20. Interval method uses realized dispersion of those change values themselves: sample sigma = 0.258, so 1.28*sigma = 0.330; 0.20 +/- 0.33 implies about -0.13 to 0.53, rounded to a first-print-style 80 percent interval of -0.1 to 0.5.

Counter-consideration and scenarios: upside risk would land above the interval if June gasoline seasonal adjustment or renewed oil disruption keeps energy CPI positive while shelter/core services reaccelerate, pushing headline above 0.5. Downside risk would land below the interval if gasoline, airfares, and vehicle-related prices fall together enough to offset core services and food, pushing headline below -0.1.

The target is BLS CPI-U all items, U.S. city average, seasonally adjusted percent change from May 2026 to June 2026. This is the first-print BLS CPI news release value, not a FRED mirror or later revised seasonal-adjustment vintage. The prior June thesis.analyst runs were centered at 0.4 with a 0.1 to 0.8 interval; I use them only as strategy context and keep the center because no newer official CPI print is available before the July 14 release.

Base-rate/reference class: the recent official first-print headline sample for Dec 2025 through May 2026 is 0.3, 0.2, 0.3, 0.9, 0.6, and 0.5 percent. The mean is 0.47 percent and the median is 0.4 percent, but the March-May run was unusually energy-heavy, so I anchor on the median rather than chase the mean higher.

Level, momentum, and mechanism split: level and recent momentum remain high for headline CPI, with 0.9, 0.6, and 0.5 percent in March-May. The one-off mechanism is energy: May gasoline at +7.0 percent and energy at +3.9 percent made headline stronger than core. The policy and pass-through mechanism is a smaller upside tail through goods prices, while core, shelter, and food momentum argue for a lower central print than March.

Prior/update/interval: Use a persistence prior from the Dec 2025-May 2026 first-print headline reference class with median 0.4 and mean 0.47; update +0.05 for June gasoline still elevated in level, -0.05 for late-June EIA gasoline declines, and -0.05 for May core CPI at 0.2, then round the one-decimal first-print point back to 0.4. For the 80% interval, because this is a monthly change/flow series, compute dispersion from the fetched values themselves: sigma = 0.258 using the six official monthly changes; 1.28*sigma = 0.330. Around 0.4 this gives about 0.07 to 0.73, widened modestly for energy volatility and BLS one-decimal rounding to 0.1 to 0.8.

Upside risk: gasoline or broader energy prices could keep the June monthly average strong despite late-month declines, and tariff pass-through could add to core goods, which would land above the interval if headline rounds to 0.9 or higher. Downside risk: a sharper gasoline retracement, soft airfares/lodging, or another subdued core print could put the release near 0.0 or outside the interval below 0.1.

Framing and exact resolver: this is the BLS CPI-U U.S. city average all-items index, seasonally adjusted, month-over-month percent change for June 2026, first print. I use the same SA headline variant for the resolver, anchors, and historical values; series code is CUSR0000SA0 for the all-items CPI-U SA index.

Base rate/reference class: the recent same-variant BLS headline CPI-U monthly changes available in the current release are 0.3, 0.2, 0.3, 0.9, 0.6, and 0.5 from December 2025 through May 2026, averaging about 0.47. That base rate is elevated by the March-May energy shock, so I do not simply persist the latest 0.5.

Level, momentum, one-off, and mechanism split: core momentum near 0.2 plus food near 0.2 and shelter near 0.3 point to a positive underlying June print. The one-off adjustment is energy: the EIA gasoline drop from a 4.479 May average to a 4.050 June average should reverse much of May's gasoline CPI strength, pulling headline materially below the recent all-items average.

Prior/update/interval: persistence prior is the recent official BLS headline CPI-U SA MoM reference class, December 2025-May 2026 values [0.3, 0.2, 0.3, 0.9, 0.6, 0.5], mean 0.467. Update components: underlying core/food/shelter contribution keeps the point positive around +0.35 to +0.40, while the EIA gasoline decline of -9.6% subtracts roughly 0.15 to 0.25 percentage point from headline, giving 0.20. Interval method: realized dispersion of the fetched change values themselves gives sigma = 0.258, so 1.28*sigma = 0.330; 0.20 - 0.33 = -0.13 and 0.20 + 0.33 = 0.53.

Counter-consideration and falsification: upside risk is broader tariff or services pass-through plus a smaller-than-expected CPI gasoline drag, which would land above the interval near 0.6 or higher. Downside risk is a larger seasonally adjusted gasoline reversal or airfares/used vehicles weakness, which would land below the interval near -0.2 or lower. Outside the interval would likely require energy or tariff effects larger than the recent component evidence implies.

Framing and exact resolver: this is BLS CPI-U all items, U.S. city average, seasonally adjusted month-over-month percent change for June 2026, first print. The series variant is headline CPI-U SA MoM from BLS CPI Summary Table A; anchors below use that same variant, not NSA index levels or core CPI as the target.

Base rate/reference class: the six same-variant BLS headline SA MoM prints from Dec 2025 through May 2026 average 0.47 percent, with latest persistence at 0.5. That base rate is inflated by the energy shock: BLS reported energy monthly increases of 10.9 in March, 3.8 in April, and 3.9 percent in May.

Update from previous run/context: an older catalog forecast was centered higher before the full June gasoline decline was visible; I treat that only as strategy context, not evidence. The public EIA price path since June 1 makes the energy contribution materially lower than in May, while May core 0.2, food 0.2, and shelter 0.3 keep a positive non-energy floor.

Ladder: P(X <= -0.3) = 0.03; P(X <= -0.2) = 0.06; P(X <= -0.1) = 0.10; P(X <= 0.0) = 0.23; P(X <= 0.1) = 0.36; P(X <= 0.2) = 0.50; P(X <= 0.3) = 0.65; P(X <= 0.4) = 0.78; P(X <= 0.5) = 0.90; P(X <= 0.6) = 0.96; P(X <= 0.7) = 0.98. Linear interpolation gives p10 = -0.1, p50 = 0.2, and p90 = 0.5, each already at one-decimal print precision.

Prior/update/interval: persistence/base-rate prior is the chosen simple time-series prior from the BLS recent headline SA MoM reference class Dec 2025-May 2026 values [0.3, 0.2, 0.3, 0.9, 0.6, 0.5], mean = 0.467; I do not use a richer model because this near-term release is dominated by energy component timing and current public component data. Adjustment components are about -0.20 for gasoline/energy reversal, -0.05 for core mean reversion from April, and 0.00 to +0.05 for shelter/food persistence, giving center near 0.20. Interval method uses realized dispersion of the six fetched recent change values themselves: sigma = 0.258, so 1.28*sigma = 0.330. The ladder-implied 80% half-width is 0.30 around 0.2, close to the recent realized-volatility half-width, so no extra widening is applied.

Counter-consideration and scenarios: upside risk would land above the interval if June gasoline seasonal adjustment or renewed oil disruption keeps energy CPI positive while shelter/core services reaccelerate, pushing headline above 0.5. Downside risk would land below the interval if gasoline, airfares, and vehicle-related prices fall together enough to offset core services and food, pushing headline below -0.1. An outside the interval miss would most likely come from an energy seasonal-adjustment surprise rather than the stable core categories.

Review disposition: accepted the optional clarifications by naming the simple persistence/base-rate time-series prior, ruling out a richer model for this near-term energy-timing forecast, and stating that the volatility estimate is intentionally based on six recent monthly prints rather than a long-run CPI distribution; no required fixes were raised.

Derived run: the pointwise median of the CDFs of 3 independent thesis.analyst fast rollouts on this target — median prediction sampling per Turtel et al. 2025 (arXiv:2505.17989). No new model call; this run is a deterministic aggregate of the recorded rollouts at 2026-07-08T02:46:59Z, 2026-07-08T02:47:33Z, 2026-07-08T02:48:25Z. Drivers and resolver fields mirror the rollout closest to the median.

Median CDF quantiles: q10 = -0.1, q50 = 0.2, q90 = 0.53. Constituent points [0.2, 0.4, 0.2] with 80% widths [0.6, 0.7, 0.66]; the median interval inherits the central rollout mass rather than averaging tails.