Journal

The last note owned environment lighting as a multiply: a GGX-prefiltered cube times a DFG LUT, plus distant irradiance. Display was a named footnote there:

TM was Khronos PBR Neutral, exposure 1.05, identical on every IBL comparison row, not baked into the cubemaps. The IBL out-of-scope line was explicit: deep tone-map bake-off (TM is one named operator). This note owns that operator. Tone mapping allocates display codes; it does not create lighting.

The same loft still the IBL note already earned: cream stoneware (dielectric $F_0=0.04$, glaze roughness $0.14$–$0.30$) and measured brass $F_0=(0.910,\,0.778,\,0.423)$ on a board-formed concrete catcher, loft window behind, grounded contact. Named operator, exposure 1.05. The metal still carries mullions. The glaze still reads cream. HUD: Khronos PBR Neutral exposure=1.05, photo-only - no metric. Caption on the plate: tone mapping allocates display codes; it does not create lighting. Do not hang a clip-fraction on this photograph.

Controlled failure on the identical float buffer. Left burns any channel $\ge 1$ to display white. Right compresses the peak and keeps brass hue. Same $e=1.05$. Caption on the plate: not IBL-10: that plate clipped $L_i$ before prefilter. this clips $L_e$ after shading. Photo only. The full-frame pair does not make the mullion crush obvious.

Pin this. Tight crop of the brass window specular, nearest upscale. Left CLIP — blown: channel-1 pancake, mullion grid gone. Middle NEUTRAL — structure: $4\times 5$ bars still there, brass tint still there. Right $|\mathrm{diff}|$: heat where clip and Neutral disagree. If the L/R pair looked similar from across the room, this crop is the proof.

Hero, Mesa 25.0.7 llvmpipe, linear working space, Khronos PBR Neutral ($F_{90}=0.04$, $K_s=0.76$, $K_d=0.15$), exposure 1.05: env solid-angle mean luma 1.628; linear plate $Y_{\max}$ 48.22, $Y_{\mathrm{mean}}$ 1.302. Before TM at $e=1.05$: clip_frac 0.13355, highlight RMS 7.660, midtone mean 0.481. After clip/sat: sat_frac 0.134, highlight RMS 0.686, midtones unchanged 0.481. After Neutral: clip_frac 0, highlight RMS 0.625, midtone 0.441. Assertions 31 pass / 0 fail.

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What you are seeing

Working space is scene-referred linear Rec.709 radiance. One RGBA32F loft still, shaded once. Camera, materials, env, and split-sum tables are IBL-continuous (eye (1.30, 0.54, 1.98) → (0.05, 0.25, 0.02), fov $30^\circ$). This note does not re-derive Karis, DFG, or distant $E(\mathbf{n})$. It changes the display operator.

Presentation hook. Product still, $1920\times 1080$, GL photograph, CPU tone map. Named display operator. Photo only.

Controlled failure. L/R, $1920\times 660$. Identical float buffer, same exposure, only TM differs. The full-frame pair is a quiet product still. The brass-window mullion crush lives in the teaching zooms.

Four-up of the same crop, $5\times$ nearest. (1) hard clip/sat, specular is a flat white pancake. (2) Neutral, mullion bar + brass hue still there. (3) clip with fail pixels marked: red = channel-1 white where Neutral keeps structure. (4) $|\mathrm{clip}-\mathrm{Neutral}|$ heat. Caption on the plate: if panel 1 vs 2 still looks similar from afar, trust panel 4.

Same L/R as the controlled failure, callouts on the brass specular: left hard clip/sat, hue crushed to channel-1; right Neutral, mullion / brass color kept.

Two facts, never mixed:

1. Beauty plates (hero, clip-vs-Neutral, exposure ladder, Reinhard / ACES / luma controls) are GL-rendered split-sum, then a named CPU TM, then sRGB OETF. HUD photo-only means do not invent a clip-fraction or RMS theorem from the JPEG.
2. Instruments (false-color $Y(L_o)$, curve-on-hist of $Y(L_e)$, clip-mask of $L_e>1$, and the CSV) are the float buffer. The teaching zooms are nearest-upscale crops of the L/R pair so the failure is readable.

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Scene-referred, display-referred, then 8-bit

Three spaces. Mixing them is how people “fix lighting” with a tone curve.

1. Scene-referred linear. $L_o$ is radiance after shading. Values $\gg 1$ are legal. This plate: $Y_{\max}=48.22$, $Y_{\mathrm{mean}}=1.302$. At $e=1.05$, 276928 pixels have any $L_e$ channel $>1$ (clip_frac 0.13355).
2. Display-referred linear. After TM, $L_d\in[0,1]$ (Neutral and per-channel Reinhard land here; luma-ratio Reinhard can still overshoot a channel and needs a final sat). This is what a display code of 1 means in this note.
3. 8-bit sRGB PNG. The OETF is IEC 61966-2-1 piecewise, not $\gamma=2.2$. PNG 255 is not linear 1. Measurement is the float buffer / CSV. Do not FFT or energy-integrate the JPEG.

IBL-10 is not this failure. That plate authored $L_i\le 1$ before prefilter: the environment never had HDR, so the metal lost punch and the interior collapsed. These plates clip $L_e$ after shading, on a float loft that does have HDR (env mean luma 1.628). Same visual family, different theorem. Stated on the L/R pair and the clip-mask.

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Why: expose, then a named curve, then OETF

Shade once into RGBA32F. Operator rows change only TM + encode. $e$ is a stated gain, not Neutral’s $F_{90}$, not an auto-exposure meter.

Exposure is a separate pre-TM gain

Default lock $e=1.05$ on every operator comparison (IBL continuity). The exposure ladder varies $e\in\{0.50,\,1.05,\,2.00\}$ under one fixed curve. Neutral’s $K_s$ is not retuned.

Clip / saturate — controlled failure

No shoulder. Any channel $\ge 1$ becomes display white. Hue of a clipped brass highlight is whatever channel survived. Shiny white and matte white become the same code. The product still dies. That is the left panel of the L/R pair, and the pancake in the teaching zoom.

Reinhard — labeled control

Global form:

Never reaches 1. Two application modes, one control plate:

• Per-channel. Apply to $R,G,B$ independently. Highlights desaturate toward grey; brass hue walks. Midtones on this crop: 0.325 (pulled vs Neutral’s 1:1-ish band).
• Luminance-ratio. Rec.709 luma $Y=0.2126R+0.7152G+0.0722B$, $Y'=Y/(1+Y)$, $RGB'=RGB\cdot(Y'/Y)$. Hue-preserving; a channel can still exceed 1 before the final sat (clip_frac 0.056 on $L_d$).

Extended white-point Reinhard $L(1+L/L_w^2)/(1+L)$ is mention-only, not a hero.

Narkowicz ACES — labeled control (album continuity)

Older sampling notes displayed with ACES (Narkowicz) then $\gamma=2.2$. Keep that operator as a labeled control, not the hero. No silent $0.6$ pre-scale.

Per-channel. On this midtone crop ACES mean 0.604 sits above Neutral 0.441 and even above $L_e$ 0.481: Narkowicz around $Y\approx 0.48$ has gain $>1$. That is filmic contrast, not a Neutral defect, and not a claim that ACES is wrong.

Khronos PBR Neutral — named hero

Linear Rec.709 in, linear Rec.709 in $[0,1]$ out. Constants from the Khronos spec / pbrNeutral.glsl, not re-fit. Cite KhronosGroup/ToneMapping PBR_Neutral. No gamut mapping in this note.

Three stages:

• Toe. Offset from $x=\min(R,G,B)$ so darks are not a raw 1:1 that looks desaturated under Fresnel-aware PBR. $F_{90}=0.04$ is the dielectric normal-incidence term Neutral is built around:

• Mid. 1:1-ish after that offset for base colors in the band $0.08\le RGB\le 0.8$ (sRGB 80–231 under unitary white). Peak $P=\max(c)$. If $P<K_s$, return $c$. That band is why Neutral is the product-still operator. On this ceramic/catcher crop the midtone is $L_e$ mean minus the $0.04$ offset exactly: 0.4815 − 0.04 = 0.4415. Gray slice asserted: Neutral$(0.50,0.50,0.50)\to 0.46$.

• Shoulder. Peak compression starts at $K_s=0.76$. Let $d=1-K_s$:

Then mix $c$ toward $(P',P',P')$ at mix $g$. Desaturation toward the compressed peak at rate $K_d=0.15$.

Neutral is the named product-still display operator, not “correct cinematography.”

Display-referred range, then OETF

After TM, $L_d\in[0,1]$ is display-referred linear. Then the sRGB OETF (IEC 61966-2-1 piecewise):

PNG write is this encode. GL_FRAMEBUFFER_SRGB is off. Measurement is the float buffer, not the PNG.

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Unique artifact: this plate’s histogram, these curves

This is the thing this note exists to draw. Log-$x$ scene-referred $Y(L_e)$, same loft buffer as the beauty rows, clip drawn as a wall at 1. Overlay: clip/sat (hits 1 and stays), Neutral (gold, 1:1-ish through the mid, shoulder after $K_s$), Narkowicz ACES (magenta, gain $>1$ in the mids on this plate), Reinhard $L/(1+L)$ (cyan, never reaches 1). Thumbnail of this still so it cannot be a stock filmic screenshot.

Honesty on the overlay: Neutral’s peak compression plus desat-toward-white is RGB. The plotted curve is grayscale Neutral(Y,Y,Y), labeled on the plate. Gold band on the legend is $0.08\ldots 0.8$, the 1:1-ish claim.

Instrument, not a hero. $\log_{10} Y(L_o)$ before exposure and TM, turbo, color bar in linear $Y$ from 0.01 to 31.6, tick at $Y=1$. Window glass and the brass reflection sit well above 1. Values $\gg 1$ are legal scene-referred radiance.

False-color is $Y(L_o)$ before exposure. The histogram is $Y(L_e)$ with $e=1.05$ so the wall at 1 matches the clip operator. Do not mix those two $Y$s.

Neutral photograph plus red overlay where any $L_e$ channel $>1$, plus a brass/window crop: clip flattens, Neutral keeps highlight structure. Red is the pixels $\mathrm{sat}()$ burns to channel-1. Neutral compresses the peak. Same theorem as the teaching zoom, painted on the whole plate.

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Quote the CSV. Do not quote the beauty photographs as meters.

Float buffer, Mesa llvmpipe. Highlight crop: brass window specular $(1125,475)$–$(1345,635)$, $n=35200$. Midtone crop: ceramic/catcher away from the window spec $(421,239)$–$(601,399)$, $n=28800$. $e=1.05$ unless the row is the Neutral ladder.

Neutral exposure ladder (curve fixed, $K_s$ not retuned):

Env solid-angle mean luma 1.628. Linear plate $Y_{\max}$ 48.22, $Y_{\mathrm{mean}}$ 1.302. FBO RGBA32F $1920\times 1080$; 8-bit fallback not hit.

Hero rounding used in the lede: clip_frac 0.13355; highlight RMS 7.660 → 0.686 (clip) / 0.625 (Neutral); midtones 0.481 (clip, unchanged) / 0.441 (Neutral) / 0.325 (Reinhard RGB); ladder 0.189 / 0.441 / 0.817. Do not invent a clip-fraction or RMS theorem from the hero, the L/R pair, or the Reinhard plate. Those frames are photo-only.

Highlight RMS is photometric, not a structure meter. After clip, crop RMS is 0.686 (many pixels parked at 1). After Neutral it is 0.625 (shoulder below 1). Clip RMS $>$ Neutral RMS is not Neutral “losing” highlights. Structure (mullions in the brass reflection) is the clip-mask and the teaching zoom, not the RMS ranking.

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Failures / controls

Clip vs Neutral

The L/R pair plus the obvious zooms plus the clip-mask. Clip-fraction of $L_e$ is the input fact (0.13355). After clip, that fraction is burned into channel-1 (sat_frac 0.134, midtones untouched at 0.481). After Neutral, clip-fraction of $L_d$ is 0; sat_frac is $4.2\times 10^{-5}$ (a handful of pixels at the compressed peak $\ge 0.999$), highlight structure remains. This is the controlled failure, not a contestant.

The zooms exist because the full-frame L/R is a quiet product still. The tight crop is the brass-window mullion grid: clip is a white rectangle; Neutral still has bars. The four-up panel 4 is the heat proof if the photographs still look close. The clip-mask paints the same $L_e>1$ pixels red on the Neutral plate (window, glaze rims, brass spec) and repeats the crop.

Exposure ladder under one curve

Neutral only. $e=0.50$ underexposes the glaze (midtone 0.189). $e=1.05$ is the lock (midtone 0.441). $e=2.00$ drives more of the window into Neutral’s shoulder (midtone 0.817, highlight RMS 0.758). Clip-frac after Neutral stays 0 at all three gains. Not auto-exposure. $K_s$ is not retuned. The scientific point is the split: gain first, curve second.

Reinhard vs Neutral

Same buffer, same $e=1.05$. Reinhard $L/(1+L)$ per RGB never reaches 1 and pulls cream glaze / concrete midtones down (0.325 vs Neutral 0.441 vs $L_e$ 0.481). Neutral keeps a 1:1-ish base-color band. Reinhard is a labeled control, not a second hero.

ACES vs Neutral

Same buffer, same $e$. ACES is the older album default. Caption on the plate: not a claim that ACES is wrong cinematography. Midtone mean 0.604 is the filmic contrast already quoted. No $0.6$ input pre-scale.

Per-channel vs luminance Reinhard (brass hue)

Control plate, not a second hero. Measured brass $F_0$ is colored. Per-channel Reinhard greys the highlight (the crop walks toward white-grey). Luma-ratio keeps $F_0$ hue; a channel can still exceed 1 before final display sat (clip_frac 0.056). Per-channel TM is a hue operator in disguise. Neutral’s peak-based compression plus desat-toward-white is a different, stated choice.

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Two paths, do not mix the instruments

The L/R pair is a photograph of the control and the source of the teaching zooms. Quote the CSV for clip-frac and RMS. Do not quote the 8-bit panel as 0.13355.

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Honesty gaps

1. Neutral is the named product-still display operator, not “correct cinematography.” ACES is a labeled control (older album default). Reinhard is a labeled control. Clip is the controlled failure.
2. Highlight RMS is photometric, not a structure meter. Clip RMS 0.686 vs Neutral 0.625 does not rank highlight quality. Structure is the clip-mask and the teaching zoom.
3. ACES midtone mean (0.604) sits above Neutral (0.441) and even above $L_e$ (0.481) on this crop. Narkowicz around $Y\approx 0.48$ has gain $>1$. Filmic contrast, not a Neutral defect.
4. Neutral sat_frac is $4.2\times 10^{-5}$, not identically 0. A handful of pixels sit at the compressed peak $\ge 0.999$. clip_frac (any channel $>1$) is 0.
5. Reinhard luma-ratio still needs a final display sat for PNG (clip_frac 0.056 on $L_d$ before sat). Per-channel Reinhard never reaches 1.
6. Curve overlay on the histogram is grayscale TM(Y,Y,Y). Neutral’s peak compression + desat-toward-white is RGB; the overlay is labeled Neutral(Y,Y,Y).
7. False-color is $Y(L_o)$ before exposure. Histogram is $Y(L_e)$ with $e=1.05$ so the wall at 1 matches the clip operator.
8. This clip is post-shading $L_e$, not IBL-10. IBL-10 clipped $L_i$ before prefilter (source never had HDR). Same visual family, different theorem.
9. TM does not create lighting. Same $L_o$, same env, same materials. The curve only allocates display codes.
10. Contact AO is a planar cosine term, not a shadow map. Env is procedural loft HDR, not a captured EXR.
11. No hardware tonemap unit, no PQ/HDR10, no OCIO cinema LUT, no local adaptive TM as hero. Neutral’s current spec is sRGB. Local TM exists; it is not this plate.
12. JPEG / PNG is 8-bit display-referred. Do not FFT or energy-integrate the file. Midtone mean and highlight RMS are linear-crop meters.
13. IBL tables are reused, not proven here. Seamless-cube face edges, glGenerateMipmap, prefilter spp caveats stay in the IBL note.

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Mesa / llvmpipe — what this run can claim

Can claim: on this llvmpipe build, one linear HDR loft buffer, exposed by a stated gain, produces these photographs under clip / Reinhard / ACES / Neutral; clip-fraction, highlight RMS, and midtone mean move as the CSV says; Neutral is the named display operator carried forward from IBL.

Cannot claim: that Neutral is “correct cinematography,” that ACES is wrong, that a JPEG histogram is the scene histogram, that PNG 255 is linear 1, that changing the curve invented lighting, or that this is how a display chip’s tonemap unit works. Discrete-GPU metrics, occupancy, bandwidth, HDR10/PQ encode, OCIO cinema LUTs.

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Assertions

This run: 31 pass / 0 fail.

No assert tolerances were loosened for the photoreal plates.

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Out of scope

Full cinema LUT pipelines, OCIO shows, film print emulations, AgX / Hable / Uncharted2 as additional heroes. HDR10 / PQ / HLG / Rec.2020 mastering (Neutral’s current spec is sRGB). Local adaptive / operator-TMO / bilateral / photographic-zone TM as the hero. Auto-exposure meters, key-value, histogram-centering as the primary subject ($e$ is a stated gain). Color-management ICC / display-profile rabbit hole. sRGB-vs-linear texture decode. TAA, temporal accumulation, firefly-suppression as TM. Re-deriving IBL: Karis prefilter, DFG LUT, roughness→mip, distant $E(\mathbf{n})$. Cite the live note. Toksvig, anisotropic GGX, sheen, clearcoat, layered metals. Shadow-map bias. Hardware “tonemap unit,” real-time cost, occupancy, bandwidth.

Album sequence:

1. Perspective-correct — what you interpolate
2. Z-fighting — how depth is encoded
3. Mipmaps — which frequencies survive an isotropic minify
4. Anisotropic — which UV ellipse that pixel covers
5. Parallax occlusion — fake depth from a height field; the silhouette is still the quad
6. Split-sum IBL — environment lighting as a multiply: GGX-prefiltered cube $\times$ DFG, plus distant $E(\mathbf{n})$
7. Tone mapping — scene-referred to display-referred; the curve allocates codes, it does not create lighting

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Display lock

Le = e * Lo
Ld = TM(Le)          // Neutral hero; clip / Reinhard / ACES are labeled
sRGB = OETF(sat(Ld))

Locked Neutral constants (not re-fit): $F_{90}=0.04$, $K_s=0.76$, $K_d=0.15$. Rec.709 in/out. Pin the hero as the presentation. Pin the tight crop as the failure. Pin the histogram as the unique artifact. The formula is the caption. Same $L_o$. The curve only allocates display codes.