Part of the Vector Lab — vector methods for vector theory. Overview and map · Org profile
Tier: single-model scope. Object: a single manifold.
Sibling instruments: Vectorscope · Theoryscope · Manifold Atlas · LLMbench
Intensive reading of a single manifold, in two registers.
Author: David M. Berry Institution: University of Sussex Version: 0.4.0 Date: 17 April 2026 Licence: MIT
Manifoldscope is a web-based research instrument for reading a single manifold intensively, as both a geometric object and an ideological object. It loads or imports a manifold (output embeddings from any provider, a Vectorscope hidden-state export, a Theoryscope corpus map), characterises its intrinsic geometry, and runs manifold-wide critical probes whose findings are bound to the geometric characterisation by a shared provenance record.
The tool is designed for critical and empirical inquiry into the manifold as medium, not for engineering evaluation. Where existing vector-geometry tools are built for engineers tuning retrieval pipelines, and where alignment-research tools are built to inspect circuits and features inside a model, Manifoldscope treats the output geometry as the object of study and asks what shape it has and what that shape does.
Manifoldscope is part of the Vector Lab family of research instruments, alongside Manifold Atlas, Vectorscope, Theoryscope, and LLMbench. The five tools share an editorial design system, an open-weight-friendly methodology, and a commitment to making the geometry of meaning legible for critical analysis. They diverge in their object: Manifold Atlas compares output geometries between models, Vectorscope inspects the internals of a single open-weight model, Theoryscope maps the geometry of a corpus of theoretical texts, LLMbench reads the surface of model outputs as prose, and Manifoldscope reads a single manifold intensively as both geometric and ideological object.
Manifoldscope emerges from the convergence of four research programmes.
Vector theory and the manifold as medium. Berry (2026) Vector Theory develops an account of the manifold as a proprietary medium whose geometry encodes ideology topologically rather than discursively. If that claim is to be more than theoretical assertion, it requires an instrument that can inspect a manifold's shape and describe what the shape does. Manifoldscope is that instrument for the intensive case: one manifold at a time, examined as object.
The provenance layer critical readings require. Atlas-style findings at the level of contested concepts (for instance that freedom sits closer to market-liberalism than to radical democracy) gain defensibility only when the local intrinsic dimension, curvature, and sampling density of the region have been independently characterised. Small cosine differences in high-dimensional space are not, in themselves, findings. Manifoldscope produces the geometric characterisation that strengthens concept-level claims elsewhere in the Vector Lab.
Critical tools of investigation for the manifold. Existing tools either test pointwise concept claims (Atlas) or inspect internal mechanics for alignment purposes (mechanistic interpretability libraries). Neither runs manifold-wide critical probes: ideological topography across regions, hegemonic gravity maps, market-colonisation indices, colonial geometry probes, archaeologies of absence, dead-zone maps, grammatical-ideology probes. Manifoldscope ships these as first-class operations with the same rigour accorded to geometric measurements, and binds them to measurement rather than leaving them free-standing.
Methodological commitment to open-weight embeddings and declared sampling. Commercial embedding APIs do not give researchers what they think they give them: the tokeniser, architecture, training data, and update schedule sit behind an opaque endpoint. Manifoldscope treats open-weight embeddings as the default route for operations that aim to link geometry to training provenance. Closed APIs are supported for measurement operations that need only output vectors. The sample is never treated as preamble: every view declares its sample, and the sample is part of the manifold.
Manifoldscope carries two orientations that are not separable in practice. Each operation can be asked in either key.
Measure. Intrinsic geometry. The mathematical characterisation of shape: intrinsic dimension, curvature, geodesic structure, density field, topological invariants, projection distortion, sampling bias. The posture is descriptive; the outputs are geometric.
Critique. Critical-theoretical investigation of the same manifold as ideological object: what it naturalises, what it marginalises, what it has sedimented, what it refuses to represent. The posture is interpretive; the outputs are readings backed by geometric evidence.
Every Critique finding renders alongside the Measure attestation for the same region. No standalone interpretive claims without geometric characterisation behind them. This binding is what Manifoldscope provides that no other Vector Lab tool currently does.
Manifoldscope works on three kinds of object, and it helps to understand the difference.
A manifold in the instrument's sense is an embedding output plus its sampling. It could be the OpenAI text-embedding-3-large manifold queried with 5,000 concepts, the nomic-embed-text manifold queried with a Zotero corpus, an exported Vectorscope hidden-state cloud from a specified layer of a specified model, or a Theoryscope corpus map under a specified embedder. The manifold is never given abstractly; it is constituted by a sample.
A sample is the finite, explicitly defined set of points that realises the manifold for inspection. A sample is a theoretical claim in its own right: who is in it and who is out, under what criterion, with what filters, determines what the instrument can see. Manifoldscope records the sample definition as part of every result so that findings can be reproduced and contested.
A probe is a curated concept list plus a statistical test. Probes are the unit of critical investigation: the market-colonisation probe, the colonial geometry probe, the archaeology-of-absence probe, the grammatical ideology probe. Each probe list lives in an editable Markdown file and carries its own provenance record and a published partiality note. Curation is political; the note names the politics rather than hiding them.
Manifoldscope is organised as a three-group tabbed workspace: Measure, Critique, and Atlas (curated pre-run analyses on named samples, with provenance and annotations).
| Operation | Core question |
|---|---|
| Intrinsic Dimension Field | What is the local dimension at each point of the manifold? |
| Curvature Estimation | Where is the manifold flat, hyperbolic, positively curved? |
| Geodesic Map | What is the distance under a density-aware metric, and how does it differ from cosine? |
| Density Gradient Field | Where are the dense cores and the sparse shells, as a continuous field? |
| Void Atlas | What are the holes in the manifold, and what concepts bound them? |
| Projection-Distortion Meter | How does the manifold differ under PCA, UMAP, t-SNE, PaCMAP, Isomap? |
| Sampling-Bias Diagnostic | How much of the apparent geometry is the sample, and how much is the manifold? |
| Metric Archaeology | How does the manifold deform between paired versions (base vs instruct; pre vs post RLHF)? |
Ideological and hegemonic
| Operation | Core question |
|---|---|
| Ideological Topography | What is the political orientation of whole regions? |
| Hegemonic Gravity Map | Which concepts are attractors, and which are peripheral? |
| Market-Colonisation Index | How far has commercial vocabulary seeped into non-market domains? |
| Normative Transition Probe | Where does the manifold pass from is to ought? |
Archaeological and forensic
| Operation | Core question |
|---|---|
| Training-Data Fingerprinting | Which corpora left geometric signatures? |
| Temporal Sedimentation | Which regions are shaped by which periods of training data? |
| Synonymic Erosion | Which distinctions are being lost across model versions? |
| Isometry Archaeology | What does alignment reshape? |
Colonial, gendered, and subaltern geometry
| Operation | Core question |
|---|---|
| Colonial Geometry Probe | How are non-Western concepts positioned relative to Western equivalents? |
| Untranslatable Map | Which concepts resist the multilingual manifold? |
| Social-Categorical Topology | What is the full map of gender and race terms? |
| Labour Visibility Field | Where does reproductive, care, and domestic labour sit? |
Limits, refusals, and absences
| Operation | Core question |
|---|---|
| Archaeology of Absence | What is the manifold thin on that it should be thick on? |
| Dead Zones Map | Where does the manifold give up structuring meaning? |
| Refusal to Represent | How does the manifold handle harms, atrocities, and politically sensitive events? |
| Commons Map | Where do concepts that resist commodification sit? |
| Infrastructural Probe | What has the manifold naturalised enough not to distinguish finely? |
Dissensus and conformism
| Operation | Core question |
|---|---|
| Grammatical Ideology Probe | How much does the manifold commit to active-voice vs passive-voice framings of the same event? |
| Dissensus Detector | Where does meaning become volatile under small contextual changes? |
| Counter-Reading Layer | What does the current organisation foreclose? |
All operations carry a provenance record (manifold source, sample hash, provider and model revision, metric, projection, probe list hash, timestamp) that travels with every export. The Critique tab renders a Measure attestation card alongside every reading.
Phase 0 shipped Intrinsic Dimension Field (Measure) and Market-Colonisation Index (Critique), both end-to-end with provenance. Phase 1a added four more Measure operations: Curvature Estimation (Forman-Ricci on k-NN graph), Density Gradient Field (inverse mean kNN distance in ambient space), Geodesic Map (Isomap geodesic-vs-cosine delta), and Sampling-Bias Diagnostic (bootstrap over the TwoNN field with per-point standard deviation and a stability score in the provenance record). Phase 1a.2 completes the Measure core with Void Atlas (H0 and H1 persistent homology over a Vietoris-Rips filtration via ripser, with persistence diagram and H1 barcode) and Projection-Distortion Meter (five projections side-by-side: PCA, UMAP, t-SNE, PaCMAP, Isomap, each scored by normalised stress and trustworthiness). Phase 1b completes the Critique core with six operations, each binding a Measure attestation on the same sample: Ideological Topography (five contested axes projected onto the sample as per-axis heatmaps), Hegemonic Gravity Map (incoming-kNN attractor score per concept), Normative Transition Probe (is/ought gradient plus centroid cosine), Dissensus Detector (per-concept spread across a battery of contextual framings), Grammatical Ideology Probe (per-pair active/passive cosine gap on a curated list of agency-hiding events), and Market-Colonisation Index. Phase 2a adds four archaeological and forensic operations: Training-Data Fingerprinting (per-concept genre distribution over a marker probe covering Wikipedia, Reddit, academic, news, legal, literary, technical, and corporate registers), Temporal Sedimentation (per-concept period distribution over markers from pre-1950 through the 2020s), Synonymic Erosion (distinction-collapse diagnostic on curated pairs such as citizen / consumer, care / service, liberation / freedom), and Metric Archaeology (two-embedder Procrustes alignment plus a Jaccard neighbourhood deformation field that shows where the two manifolds disagree most about what sits close). The remaining operations land in subsequent phases.
Why two registers in one instrument? Existing tools separate measurement from critique. The separation lets critical readings run on thin geometric evidence and lets geometric characterisations go uninterpreted. Manifoldscope binds them by design: every Critique finding renders alongside the Measure attestation for its region. The intrinsic geometry is the provenance layer for the political-theoretical reading.
Why a single manifold as object? Manifold Atlas compares manifolds across models; Vectorscope opens the internals of one model; Theoryscope takes a corpus as geometry. None of the existing tools treats a single manifold as manifold and characterises it in depth. Manifoldscope fills that gap. Single-manifold intensive reading also complements the extensive comparative reading of Atlas and the internal forensic reading of Vectorscope: the three together give within-model, between-model, and manifold-as-object inspection.
Why probe lists in editable Markdown? The critical probes are curated, and curation is political. A probe list in code is opaque; a probe list in a Markdown file with its own provenance and partiality note is inspectable and contestable. The pattern follows Manifold Atlas's public/models/*.md and Vectorscope's backend/config/models.md convention.
Why declared sampling? A manifold in practice is an embedding output plus a sample. Pretending otherwise smuggles the sampling choice past scrutiny. Manifoldscope displays the sample with every view, includes the sample hash in the provenance record, and ships the Sampling-Bias Diagnostic in Phase 1a rather than deferring it.
Why open-weight-friendly rather than open-weight-only? Some Measure operations need only output vectors and run against any embedding API. Critique operations that aim to link geometry to training provenance (fingerprinting, isometry archaeology, synonymic erosion) prefer open-weight backbones. The distinction is recorded per operation.
Why no engineering metrics? Manifoldscope does not answer "which embedding gives the best search relevance?" That question belongs to retrieval evaluation. It answers "what shape is this manifold, and what does that shape do?" — a critical-theoretical question that requires geometric evidence, not benchmark scores.
Why shared provenance records across the Vector Lab? A finding that cannot be cited is not a finding. The provenance record (manifold source, sample hash, provider and model revision, metric, projection, probe list hash, timestamp) is what makes a Manifoldscope result something that can travel into a paper. Without it, the geometry and the reading are both suggestive but not defensible. With it, the reading can be re-run and contested.
Manifoldscope is two coordinated processes: a Python backend for the heavier numerics (intrinsic dimension, curvature, geodesics, persistent homology, bootstrap diagnostics) and a Next.js frontend that renders the interface and holds the embedding provider client. Both need to be running at the same time, in two separate terminals.
- Python 3.11+ for the FastAPI backend.
- Node.js 18+ (20 LTS recommended) and npm.
- Git, to clone the repository.
- At least one of: an embedding provider API key (OpenAI, Voyage, Google, or Cohere), a HuggingFace account with an Access Token, or Ollama running locally with an embedding model pulled.
git clone https://github.com/vector-lab-tools/manifoldscope.git
cd manifoldscope
npm installSet up the Python backend:
cd backend
./setup.shThis creates a local .venv and installs FastAPI, scikit-learn, numpy, scipy, networkx, ripser, and their dependencies.
Start the backend:
cd backend
source .venv/bin/activate
uvicorn main:app --reload --port 8000Start the frontend in a separate terminal:
npm run devOpen http://localhost:3000. Configure at least one embedding provider in Settings. Load the default sample (Philosophy of Technology concept list) and click into the Measure tab to run Intrinsic Dimension Field, or the Critique tab to run the Market-Colonisation Index.
Provider registry lives in public/models/ as one Markdown file per provider. Add or remove models by editing the corresponding file. No rebuild required.
backend/ # Python FastAPI
main.py # FastAPI app, CORS, route registration
provenance.py # ManifoldSource, SampleSpec, ProjectionSpec,
# MetricSpec, ProbeSpec, ProvenanceRecord
sample/ # Sample loading (concept list, Zotero export,
# Vectorscope hidden-state import, Theoryscope
# corpus-map import), sample hashing
embed/ # Embedding pipelines (sentence-transformers
# default; provider proxy for Atlas clients)
geometry/ # Intrinsic dimension estimators (TwoNN, MLE,
# local-PCA), curvature estimators
# (Ollivier-Ricci), geodesic computation
# (Isomap, diffusion distance), bootstrap
operations/
intrinsic_dimension.py # Phase 0 Measure op
market_colonisation.py # Phase 0 Critique op
(curvature, geodesic_map, density_gradient, void_atlas,
projection_distortion, sampling_bias, ideological_topography,
hegemonic_gravity, dissensus, grammatical_ideology, ... in later phases)
probes/
market-colonisation.md # Curated probe list with provenance + partiality
(ideological-axes, colonial, archaeology-of-absence, refusal, commons, ...)
atlas/
entries/ # Pre-computed Atlas entries (later phases)
src/
app/
api/backend/[...path]/route.ts # Next.js proxy to FastAPI on localhost:8000
layout.tsx # Editorial typography and fonts
page.tsx # Tabbed shell: Measure / Critique / Atlas
providers.tsx # ManifoldProvider
components/
layout/ # Header, SampleLoader, StatusBar,
# ProviderSettings
operations/
measure/ # IntrinsicDimensionField (live);
# others stubbed
critique/ # MarketColonisationIndex (live);
# others stubbed
atlas/ # AtlasBrowser, AtlasEntry (later phases)
binding/ # ProvenanceBindingCard (renders a Measure
# attestation next to any Critique view)
viz/ # ScatterPlot, GravityWell, HeatmapOverlay,
# TopologyScene, Plot3DWrapper
shared/ # SampleSelector, ProbeSelector,
# ProvenanceBadge
context/
ManifoldContext.tsx # Sample + provider + metric + projection state
hooks/
useBackend.ts # Thin fetch wrapper for the proxy route
lib/
embeddings/ # Provider client + plugin modules
# (adapted from Manifold Atlas)
geometry/ # cosine, pca, umap, clusters,
# persistent-homology
# (adapted from Manifold Atlas)
provenance.ts # Frontend mirror of backend ProvenanceRecord
streaming.ts # NDJSON client + server helpers
# (adapted from Theoryscope)
utils.ts
version.ts
types/
manifold.ts
react-plotly.d.ts
public/
models/ # Editable Markdown provider/model registry
# (adapted from Manifold Atlas)
The architecture mirrors Theoryscope's and Vectorscope's pattern: a Next.js App Router frontend proxies all /api/backend/* requests to a FastAPI backend on localhost:8000. No CORS. The Python side owns the heavier numerics, the sample cache, and the provenance record; the TypeScript side owns the visualisation, the embedding provider orchestration, and the binding UI.
Heavy visualisations (Plotly 3D scatter, Three.js persistent-homology scenes) are code-split via next/dynamic to keep the initial bundle lean.
| Layer | Technology |
|---|---|
| Framework | Next.js 16 (App Router), React 19 |
| Language | TypeScript 5 (strict), Python 3.11+ |
| Styling | Tailwind CSS 3, editorial design system shared with the rest of the Vector Lab |
| Visualisation | Plotly.js (GL3D), Three.js (@react-three/fiber), custom SVG |
| Backend | FastAPI, uvicorn |
| Embeddings | Pluggable provider client (OpenAI, Voyage, Google, Cohere, HuggingFace, Ollama, OpenRouter); sentence-transformers for local open-weight default |
| Numerics (server) | numpy, scipy, scikit-learn, networkx, ripser, POT (optimal transport for Ollivier-Ricci) |
| Numerics (client) | Custom PCA, custom cosine, umap-js, TypeScript Vietoris-Rips |
| Streaming | NDJSON over FastAPI StreamingResponse |
| Caching | IndexedDB (client) via idb; local disk (server) for computed geometry with provenance |
| Icons | Lucide React |
- Phase 0 — Scaffold, provenance plumbing, tab shell, one Measure op (Intrinsic Dimension Field), one Critique op (Market-Colonisation Index), provenance binding card. version 0.0.1
- Phase 1a — Measure core: Curvature Estimation (Forman-Ricci), Density Gradient Field, Geodesic Map, Sampling-Bias Diagnostic. MeasurePanel sub-nav added. version 0.1.0
- Phase 1a.2 — Measure core continued: Void Atlas (H0/H1 persistent homology via ripser, persistence diagram, H1 barcode), Projection-Distortion Meter (PCA / UMAP / t-SNE / PaCMAP / Isomap side-by-side grid with normalised stress and trustworthiness). New
Plot2DWrapperfor the 2D plots. Header redone to match the LLMbench / Vector Lab family branding pattern (v0.3.1). version 0.3.1 - Phase 1b — Critique core: Ideological Topography, Hegemonic Gravity Map, Normative Transition Probe, Dissensus Detector, Grammatical Ideology Probe. CritiquePanel sub-nav added; every Critique finding carries a bound Measure attestation. version 0.2.0
- Phase 2a — Archaeological and forensic: Training-Data Fingerprinting (genre-marker probe with per-concept softmax), Temporal Sedimentation (period-marker probe with aggregate profile), Synonymic Erosion (pair-distance distinction-collapse diagnostic), Metric Archaeology (two-embedder Procrustes + Jaccard neighbourhood deformation; MiniLM vs MPNet by default). version 0.4.0
- Phase 2b — Subaltern geometry: Colonial Geometry Probe, Untranslatable Map, Social-Categorical Topology, Labour Visibility Field. version 0.4.x
- Phase 3 — Limits, refusals, absences: Archaeology of Absence, Dead Zones Map, Refusal to Represent, Commons Map, Infrastructural Probe. version 0.5.x
- Phase 4 — Composition and advanced: Vectorscope export interchange, Theoryscope corpus-map import, Counter-Reading Layer, Atlas export. version 0.6.x
- Phase 5 — Release: Atlas entries, Stunlaw post, methodology essay, demonstration paper. version 1.0.0
- Berry, D. M. (2026) 'Vector Theory', Stunlaw. Available at: https://stunlaw.blogspot.com/2026/02/vector-theory.html
- Berry, D. M. (2026) 'What is Vector Space?', Stunlaw. Available at: https://stunlaw.blogspot.com/2026/03/what-is-vector-space.html
- Berry, D. M. (2026) 'Brain Numbers', Stunlaw. Available at: https://stunlaw.blogspot.com/2026/03/brain-numbers.html
- Berry, D. M. (2026) 'What Is Theory Space?', Stunlaw.
- Berry, D. M. (2026) 'Renormalising Theory', Stunlaw.
- Berry, D. M. (2026) Artificial Intelligence and Critical Theory, Manchester University Press.
- Impett, L. and Offert, F. (2026) Vector Media, University of Minnesota Press.
- Sohn-Rethel, A. (1978) Intellectual and Manual Labour: A Critique of Epistemology, Macmillan.
- Facco, E., d'Errico, M., Rodriguez, A. and Laio, A. (2017) 'Estimating the intrinsic dimension of datasets by a minimal neighbourhood information', Scientific Reports, 7.
- Ollivier, Y. (2009) 'Ricci curvature of Markov chains on metric spaces', Journal of Functional Analysis, 256(3), pp. 810–864.
Concept and Design by David M. Berry, implemented with Claude Code 4.6. Design system adapted from the CCS Workbench. Manifoldscope shares its editorial design system, geometry library, NDJSON streaming, provenance plumbing, and FastAPI proxy pattern with its sibling instruments Vectorscope, Manifold Atlas, Theoryscope, and LLMbench.
MIT