I · Measured
The same question, asked of everything.
Studies, papers and lab books. Each field has its own instrument, but every instrument makes the same commitment: deterministic, interpretable coordinates, read before meaning is assigned.
Paintings, photographs & calligraphy · Image Structure Reader
It recognises nothing.
A pre-semantic instrument aimed at works whose meaning is already argued over. Each study has a lab book, the working record with every correction kept, and a critique, the essay it earned. The full corpus, with notes on what each study taught the instrument, is on the studies page.
The sixteen studies
The instrument
Image Structure Reader: a place to point
What the reader is, and why it recognises nothing: it measures what is geometrically there, so critical language can be checked against it.
Reading a reading
One painting taken down all four layers of the reader, with every metric named where it appears on the canvas.
Why trust a structure reader
Null controls, seed sweeps, pre-registration, and a register that records its declines.
Compare any two works
Two works, one coordinate space. Pick any pair from the corpus and read their coordinates side by side.
ISR technical reference
The fields the reader computes (luminance gradient, OKLab chroma, cone-opponent channels, committed and soft edges, structural mass) and how regions are read as one system.
Also: July edition, 12 studies
Earlier readings
Where the many-digited sum solves into zero
A training-free structural reading of Picasso's Family of Saltimbanques (1905), and what a measuring instrument can and cannot say about a painting.
Also: Lab book
Image generation, attempt 1
Can a generator reproduce a composition it cannot read? Eight AI renders of the Saltimbanques structure, each scored by the instrument.
ImagePlot: careers in structure space
Whole careers plotted on colour and structure axes. Cézanne's 428 paintings by period and series, and five more painters.
ImagePlot: load your own folder
Load a folder of images and plot them on any pair of the lens's axes.
Also: Saliency version
The Met gallery: islands and corridors
Each image read as a system of structural islands, a mass centre, conduits and resistant corridors, beyond frame-centre balance.
Structural Predictive Gate
Does the structure reader add predictive information beyond simple pixel, regional and frequency features? Six pre-registered tests with planted controls. The decisive one, 859 steered images in 106 groups, found +0.003: structure added nothing there.
Depth Holonomy
A reader of pictorial space: one picture in, readings of its planes, groups and field, and where its own local readings refuse to agree. Its pre-registered claim, that the relief mask reproduces beyond a trivial mask, did not hold, and the page says why.
Generative image models · Visual Thinking Lens
Image models repeat the same geometry.
The lens measures the compositional prior that image generators apply to every output, whatever the prompt asks for. It is the field this work began in.

The Visual Thinking Lens
6,000+ images across Midjourney, GPT, SDXL, Firefly and Sora. Semantic diversity explains less than 10% of spatial variance.
Narrower paint, same placement
A label-free count of compositional vocabulary. AI-default portraits use a narrower vocabulary of surface and colour than pre-modern oil portraits, and an equally wide vocabulary of placement.
Treatment, not position
Image-system independence in authored and generative portraiture: 1,341 images across pre-modern oil, Midjourney default and Midjourney steered.
Smaller than the dice
What prompt steering actually moves, measured on 927 generated portraits and 125 paintings, and why the instrument agreed with it at first.
Steering authority
Do the steering clauses in a prompt move a picture's composition, or only its tone? 106 paired Midjourney sitters; 1 of 11 predictions held.
What a prompt controls
The operating windows of one image generator, measured object-level and mass-level: 864 Z-Image Turbo images, two frozen tests and three exploratory dives.
Same words, two engines
What changes when only the generator changes: one bet, one set of prompts and seeds, one frozen instrument, 810 images measured twice.
When the words stop steering
A pre-registered bet about prompt control, killed on FLUX.1-schnell: 324 images, one measurement pass, six referee checks.
The spatial blind spot
Standard image metrics read what a picture contains, not its visual vocabulary. CLIP and the kernel side by side on two subjects, each made three ways: CLIP is indifferent; the kernel separates them.
Measuring spatial priors in generative image models
Geometry-based field metrics for attractor basins, perturbation drift and geometric collapse, independent of semantic content.
Parallax Ensemble
Compare two complete sets of generated images on 17 pixel-traceable axes, with effect sizes and bootstrap intervals. Images never leave your device; no model judges another.
Where the mass is
A pre-registered test on 1,080 images: the placement measures transfer to two held-out engines (46 of 48 directions), but the same prompt words make different compositions on different engines.
VTL kernel metrics: behavioural drift detection
A seven-metric geometric framework for detecting compositional drift in image generators, with no model access required.
Compositional attractor basins
Spatial instruction compliance as a geometric probe of Midjourney v6 and Recraft V4: one neutral subject, eight placement prompts, 48 outputs.
Mass, not subject
Gradient-field analysis of 400 Midjourney images, explained in three vocabularies: the artist's, the researcher's and the engineer's.
NCD × VTL atlas, track 1
Compression rejects byte-level sameness across the set, while the lens finds many near relationships in spatial structure: different substrates, kindred composition.
Runs: 134Kinship readout
Normalized compression distance
A model-free similarity: two things share structure when they compress better together than apart.
VOID the CENTER
A disagreement instrument for two images. Literal sameness is not structural kinship; drop in a pair and inspect the gap.
Interestingness field
The choice detector. A line pressed far from the middle is improbable by luck, the fingerprint of a choice; every line dead centre is a prior.
Vector steering lab book
A traceable record of vector image steering, geometric verification and bounded repair, captured as a reproducible snapshot.
Cull: the portrait corpus
The curation sheet for the 476-portrait corpus: every candidate laid out, with genre scenes and bad scans marked to drop.
Recognition test: which one holds?
Sixty portrait pairs. Pick the one that reads as a considered, authored composition rather than a default.
The Crit
Upload an image, get a structural critique: mass, void, drift, radial gravity, and whether the image was authored or settled. Runs in the browser.
The Field
A colour critique that reads palette, value and hue breadth, and whether colour rides the structure or floats free of it.
The Synth
The inverse of the instrument. Set target coordinates and it generates a composition that lands on them, then measures its own output to prove it.
Also: The Synth II
Foreshortening recipe book
Ordered, near-to-far prompt capsules that make an image model earn its depth, with Sora examples and the full recipe book as a PDF.
Deformation operator playbook
Controlled figure warps: treat the distortion as its own object, then integrate it. Sora examples and the full playbook as a PDF.
Film & 3D scenes · VTL in the render loop
Measurement becomes direction.
Connected to Blender or Unreal, the lens's readings of a rendered frame can choose the next camera move or scene edit.
VTL Evidence Observatory
VTL as a visual measurement and directorial control instrument, with evidence from Blender, film and Unreal.
Can VTL steer a release shot?
Early evidence from a closed-loop camera experiment in Blender: of 24 deterministic paths, the searched one met the release brief at 24.8% lower loss than the best ordinary moving control. Not yet tested against random search.
Courier: revise the scene, not the frames
One authored Blender shot revised four ways through the scene itself (relight, blue, gold, cleared), set beside frame-by-frame FLUX image editing and a masked baseline. The scene keeps what the frames lose.
Settlers: coordinated body and feet
Same controls, same available poses, different selection: picking frame by frame passes 17 of 24 mechanical checks; choosing the sequence as a whole passes 24 of 24. One development shot; artist review still open.
What a camera controls
Across 495 rendered frames, the camera moves 25 of 38 measured coordinates, mostly through geometry rather than light; focal length is the strongest control. Two pre-registered conclusions were overturned by later checks, and both corrections are shown.
Language models · Linguistic Kernel
Text has shape.
The same move applied to text: reduce an output to a small set of structural coordinates and measure it, without asking another model what it means.

The Linguistic Kernel
Eight-dimensional structural measurement for LLM outputs, measured across Claude, GPT and Gemini, with no judge model.
Text has shape
What a deterministic text reading can tell apart: prompt against run, engines under batch load, answers cut off mid-formula, and which instruction wins when instructions collide.
Structural residue
Clause density in a finished answer tracks how unevenly GPT-4o's own token-level uncertainty moved, with no access to the model: r = 0.36 after controlling for length and prompt family.
Structural telemetry for LLM outputs under batch load
1,200 Gemini, GPT and Claude responses under twenty-prompt batch load: how each engine allocates output, and the rendering-intensive derivations that cut off mid-formula.
Parallax Telemetry
Stop using LLMs to judge LLMs. Score outputs, gate prompt changes and monitor drift in CI with a deterministic kernel.
The Code Lens
The lens turned on source code: weigh each structural dimension against a corpus norm, and read where this code departs from the middle.
Histopathology · Parallax Pathology
The pathology is the absence of normal form.
Tissue architecture read as geometry: how far a section departs from the organisation of normal form.

Parallax Pathology
58 deterministic axes and zero trained parameters. 91.5% nine-class accuracy on CRC-VAL-HE-7K; hazard ratio 1.872 on TCGA-COAD survival.
A deterministic structural measurement framework for H&E histology
The full framework: nine-class tissue accuracy with no training, plus a survival signal in 180 TCGA-COAD patients.
Architectural persistence across related sections
A methods paper on coordinate-free structural persistence across serial histology sections.
Structural address in explicit H&E measurements
A methods paper showing that where a measurement is taken conditions what task-relevant information it carries.
Semiconductor inspection · VTL coordinates & PTD-Z
Semiconductor patterns have topology.
The same fifteen physics-grounded coordinates, carried from paintings to wafers without redesign.

Visual Topology of Light
93.4% SEM balanced accuracy with no learned parameters. The same coordinates transfer across SEM, wafer maps and aerial lithography without retraining.
A modality-agnostic image coordinate framework
93.4% on production SEM and 94.9% on wafer maps with no retraining; coordinate dominance shifts with the physics of image formation.
PTD-Z: pattern topology drift monitor
Asks whether an organised pattern has stopped behaving like the structure it was expected to be, routed across geometry, pitch, material and contrast.
Seismic arrays · Ω structural agreement
The field supports multiple answers.
Ω measures how many competing organisations a field supports at once, by asking physically independent reads whether they agree.

Parallax Seismology
A 6.9× independence gain over correlated transforms; Cohen's d = 1.78 against the P-window; 15 FK beamforming failure cases documented.
What the signal is competing with
Independent structural agreement as a field-coherence diagnostic: the pre-arrival Ω signal separates into a floor, and the layers above it.
FK reliability failure on compact arrays
A slowness-ratio diagnostic across three arrays, including an artifact peak 46° from the expected Tōhoku P arrival.
Precipitation observers · Structural collocation
Disagreement as a measurement.
Radar, infrared, microwave and rain gauges read the same rain field. Their disagreement about its geometry estimates each one's error, and shows when two of them share one, without ground truth.
Structural collocation of precipitation observers
Triple collocation on rain-field geometry over CONUS: the observer ranking depends on the triplet, and replacing either satellite with gauges reverses it.
Precipitation disagreement lab book
A domain-qualification test that closed negative, and the collocation thread it opened, replicated on an unseen month with all six pre-registered predictions met.
How a synthetic control manufactured shared error
A coarsening step that did not conserve mass gave independent observers correlated errors, and a finding built on it was withdrawn. The mechanism, the checks that would have caught it, and a checklist.
Materials microstructure · Structural Topology Kernel
One representation. Three tasks. No training.
A fixed descriptor asked to classify microstructure, predict a physical property and say how ambiguous its own labels are.

The Structural Topology Kernel
A fixed 50-coordinate descriptor: 0.832 AUC on microstructure classification and R² = 0.939 on 2D permeability, from a single representation.
STK: an interpretable multi-task descriptor for materials
Classification, taxonomy alignment, measurable label ambiguity, and a fair field-governed property test.
Embodied AI & robotics · Spatial Kernel & relational auditor
Does it look right, or is it right?
Checking whether a spatial instruction became a geometric fact, and keeping a learned judge from certifying what the pixels do not support.

The Spatial Kernel
A two-view geometric check caught 10 flat printed decoys that a frontier embodied VLM certified as real 3D objects. 19 object types, real phone pixels.
The VTL Spatial Kernel
On real photographs, a deterministic two-view check separates real 3D objects from flat printed decoys.
Confidence without correctness
A frontier success judge returns confident false passes: an object's box moved 2.4% while its true visible extent moved 67.7%.
The authority-separated auditor
A pre-registered specification: which parts of the false-pass firewall are established, and the single experiment that would settle the rest.
Relational auditor lab book
The full record behind the auditor: existence proof, authority projection, boundary map, and results on real public pixels.
Robotics success verifier lab book
The backward trail: what it started with, what was wrong with it, what was built, and where it honestly loses.
Human movement · ZTOYBOX Biomechanical
A negative result, kept on the record.
Can organisational measurements reveal something about the body that produced them, beyond the complete conventional read? The computational phase closed without earning that claim, and says so.
Biomechanical research lab book
552 trials from 28 participants and 29 linked questions, each attacked by an adversary. The physical claim is not earned; what remains needs a prospective physical experiment.
Financial markets · Ω, multi-family
Concentration beyond amount.
A transfer test: does the seismic idea of independent structural reads carry over to the cross-section of stock returns?
Cross-characteristic dispersion and the cross-section of stock returns
A working manuscript: frozen Stage 1 evidence plus a pre-registered Stage 2 characterisation of economic magnitude.
Parallax Markets lab book
The transfer test in full, including the failed first construction and an adversarial audit that corrected a hasty "non-replication".
The Human Exchange
An interactive terminal arguing for an AI-free stock market as a protected space for judgment, dissent, apprenticeship and accountability.
Credit & provenance · Patch ledger
Exact credit, by construction.
A generator built so every output carries an exact record of what it drew on, and what that means for paying contributors.
Exact counterfactual credit in a patch-mosaic diffusion generator
Every number is read programmatically from the saved results; each finding is labelled by the strength of its evidence. Version 2 lists what changed since the first draft.
Also: First draft
Patch ledger findings
The study record: a generator whose every output pixel is an exact, owner-labelled blend of training pixels, after Kamb & Ganguli's patch-mosaic result.
Steering Exposure Statement
How far can steering move a contributor's expected credit while every receipt stays honest? A per-contributor bound passed a frozen test in 95% of pairs; a simulated $10,000 settlement moved $266.89, and the largest single loss stayed inside its stated exposure.
Face / Pixel Lab
Why this pixel? Rebuild a damaged face from source portraits and explicit rules, then remove any one and see what changes. An exact-duplicate test shows that a large matching weight does not mean a source was necessary.
Similar how?
Six experiments in what "similar" means: move, shuffle and recolor an image, then see which scores notice. A second lab trains a small diffusion model in the browser and traces outputs back to images and patches.
Attribution Stack
What "credit" can mean, formally and in plain language, across transformer and diffusion stacks, with small-model controls. Toy quantities, not production influence or legal allocations.
Diffusion Microscope
Eleven linked chapters over sixteen synthetic images: watch a toy denoiser draw on an indexed source memory, with exact, estimated and logged quantities kept apart.
The Training Data Ledger
Lifecycle, lineage, toy influence methods, observability and accounting schemas, with lineage and influence kept as separate questions.
Take It Out
An exact, owner-labelled generator and an instrument for taking a source out. The October run tested whether a collection's creditability can be predicted from its make-up: neither predictor could, and under pixel error exact credit came out nearly uniform.
Take an artist out
A picture from an exact generator trained on six public-domain draughtsmen and a pool of museum paintings. Remove an artist, see what changes, and compare who gets paid under exact Shapley, usage and leave-one-out.
From conditional denoising to learned information
A mathematical response proposing an exact observation law for a learned attention block, with two propositions, proofs, numerical checks and a testable programme. Draft for technical review.
II · Made
The measurements, turned into things to use.
Tools for painters and draughtsmen, instruments for the ear, and games that make an idea walkable. Each is built on a measurement from Part I.
Drawing & painting · Studio tools
A machine that can make. And reconsider.
Making systems where every move is recorded and a critic argues back, plus pocket looking devices for the gallery and the easel.
Making systems
VTL Studio
An experimental practice for machine drawing and visual critique, moving between mark-making instruments, generators and source material.
Drawing Machine
Generators, a learned charcoal hand, an eraser and a critic built from the lens. A drawing stops only at an argued Hold.
Study Wall
Reads a brief before any picture exists, lays out a wall of studies, argues a choice and hands it to a painting simulator.
In Turn
A drawing partner. You make a mark; it answers a few marks at a time, in one of seven learned hands, and you decide what belongs.
Vector Workbench
Edit the relationships, not the points: open an artwork as addressable parts and change it while keeping its possibilities.
Intent Studio
A composition editor where decisions persist: change emphasis, frame, arrangement or spacing, drag to propose a position, then see the conflicts and choose how to resolve them.
Declared Change Receipt
Before, after, and a declaration of what was allowed to change: a reproducible receipt of what an SVG edit actually touched. The final code flagged all 4 edits reviewers called material and none of the other 20.
Coordinate Control
Move a painting's color center while locking hue-family chroma, lightness and a protected region. 22 of 42 requests solved under the full contract; the other 20 refused as infeasible, with a check for each refusal.
Composition Contracts
Recolor one layer and move the fewest others to keep the composition's color center: 9.6% fewer collateral layer changes than a strong baseline, for 2.9% more movement, across 48 Photoshop requests.
know between
A drawing hand that can only learn new marks from what it looks at: nine views of Mont Sainte-Victoire, then yours.
Hand Studio
Learned drawing hands as files, and a studio that draws with them and says whose marks made each drawing.
Afterimage
A picture that remembers: retained source-derived marks whose origins travel with the material.
The Mixing Painter
Composition as attention: masses average toward each other and disagreement provably shrinks. Anchors hold a composition open.
Looking devices for phone and tablet
Sketchbook
Point the camera and a master's learned hand draws what it sees, stroke by stroke.
Counterweight
A viewfinder that reads the picture instead of drawing a grid on it: a value squint, visual weight and crops with receipts.
Two Drawings
Every picture is drawn twice, by light and by colour. Separates the edges a grey value study keeps from those that exist only as colour.
Relief
Take the receding plane out, and see what stands off the ground.
Reach
Can this box of paint mix that picture? Choose the tubes and see what is out of reach, with a recipe for any colour you tap.
Touch of Paint
Your pile is almost right. Say what it needs by eye and see what to add, how much, and what else it will do; it learns your tubes, scales the batch, and shows the geometry underneath.
Value Plan
Squint at a reference, cut it into a few value masses, and get one pile per mass from a short shared palette, each checked so it stays in its value; with accents kept and a sheet to print for the easel.
The Mixing Room
Eight paints and a world between them. Find a starting mixture, see which way it leans, and make it your own; studies and reference images stay in your browser.
Mixing Notes
Tap a colour in a painting or your own photo and get an estimated oil-paint recipe from the paints you actually have. Adjust it, push it lighter, warmer or quieter, and save the mixes worth keeping.
Studio Diary
Photograph a painting session by session, straighten it, and see what changed.
Painting Notebook
A working notebook for painters: find a way into an image through line, mass, value and colour studies, keep a direction, and follow the painting through its sessions.
Thumbnails
Thumbnail sketching on the go: pages of frames for a phone in a gallery or an iPad with a pencil.
Sound instruments
Structure, heard.
Noise machines after Russolo, and rigs that let you hear an image or a measurement.
The Walked Painting
A painting heard in the order the eye walks it: each fixation a note, each saccade a glide. Where the field collapses, silence.
Intonarumori
Russolo's six families of noise from 1913, rebuilt and extended with six more: sirens, electrical, granular, motors, crowd, radio.
Noise Orchestra
A noise beat maker: pads, a sequencer, and controls that reshape the same sounds.
p3r4mancer
A living music box. Five voices, six seeds, endless little returns. Touch a sound; leave a little future.
russ-riss-et reader
A tone built to climb forever tells you almost nothing about where it is. This rig reads back what it can.
Song of Irreverence
A score for human and machine. A machine counts; you interrupt; the interruption becomes another rule.
The Other Thing You Could Have Done
A playable appendix answering Russell Foltz-Smith's irreverence in a computer. Load a tape, change one recorded decision, and hear both versions.
Games & thought experiments
Ideas you can walk around in.
Games and small machines built on real mathematics: holonomy, evidence, eigenmodes, reaction and diffusion.
The Impossible Architect
A book of stairs that do not close. Walk, build and break Penrose stairs on a real lozenge tiling.
Also: The Unfinished City
Held
A town with no ground, and a Mill that wants it. A turn-based town builder drawn in pen and ink, where anything that loses its path to an anchor falls.
Same Room Twice
A detective game about object permanence. Looking tells you nothing; only acting does. You're scored on how honest your belief is.
Who Gets Paid?
Peek at real combinations of six artists, split 100 coins, then see the exact answer. In every round and under every measure, paying by usage or by leave-one-out scores worse than splitting evenly.
The Other Light
A shadow mystery in twelve rooms. Choose where to shine the light on a hidden sculpture, rule out the forms that don't fit, and learn when light alone cannot decide.
The Conservatory
Interactive habitats for observing, learning and testing what changes a decision.
Continuum
The vibration modes of a folded sculpture. Blend eigenfunctions, trace nodal lines, reshape its spectrum.
Impossible Objects
A copper loop that makes sense at every point and climbs all the way around, yet arrives where it started. The depth it gains is what the picture cannot hold.
Held Space
Three sculptural studies in knots, linked ribbons and single-sided surfaces: an interactive geometry atelier.
Relational field notes
An interactive notebook about what changes when "same" changes: geometry, perception, topology, symmetry, averages.
The replay world
Fifty frozen ecology runs, and an answer-blind search that tries to reach the verdict from the record.
the residual
Two chemicals, one rule, iterated until something forms. Draw to seed it.
Cell Mirror
Your camera image breaks into a grid of moving cells. Each cell measures its own motion and stretches its piece of you along it; the more you move, the further the mirror comes apart.
Thrombo / Duchamp engine
A machine that does not work. It clots: flow becomes obstruction, obstruction becomes medium.
Also: First version
the scribbler
Growth tips navigate the page reading local ink density: heavy contour at the frontier, fine hatching within.
Also: One teacher
One Thousand Twenty-Eight
A contradiction instrument after Foltz-Smith: a clock made of words becomes a machine for measuring where the measurements refuse to agree.
Three Addresses
One field counted three ways, drawn as lights on paper and sonified so the three counts beat against each other.
The Meter
The layer the GPT-chip deletes: an external audit loop set against a closed loop that only validates itself.
the paperclip / the question
Form without content.
Nothing matches that. Clear the filters