v4cat 0.3.0

Symmetry-break cataloguing — ISA + SQLite schema + MCP server for accumulating named structural distinctions about a domain (Klein-four-equipped, self-hosting)

v4cat — Symmetry-break cataloguing framework

A Python ISA + SQLite schema + MCP server for accumulating named structural distinctions ("breaks") about a domain, with witnesses, refinements, lineage edges, and the Klein-four read primitive.

The framework is domain-agnostic. The ISA's introduce_object, introduce_break, witness, refine verbs and the analytic views work the same whether the witness objects are programming languages, processors, cryptographic primitives, file systems, formal systems, ML architectures, or anything else with structure worth cataloguing. See examples.md for domain templates.

See methodology.md for the design.

Layout

v4cat/
├── __init__.py              public API
├── catalogue.py             SymmetryCatalogue class (the ISA)
├── views.py                 kquery + analytic queries
├── mcp_server.py            FastMCP server exposing tools/resources/prompts
├── schema.sql               generic framework schema (S0-S11)
├── cells.py                 Cell tagged union + Kinds enum (theory.md § 14.5.1)
├── theory.py                framework signature, the IMPL referent (§ 14.5.2)
├── bootstrap.py             closure check (§ 14.5.4); SelfHostingViolation
├── framework_seed.sql       framework self-cataloguing seed data (§ 14.5.5)
├── methodology.md           operational design — ISA, schema, KQUERY, MCP
├── theory.md                foundations — shadow architecture, Klein-four, Yoneda+Derrida, magma+pointfree, Theorem 14.5
├── tutorial.md              LLM-friendly walk-through, empty → small worked domain
├── examples.md              domain templates (languages, processors, crypto, …)
├── README.md                this file
├── pyproject.toml           pip-installable package metadata
└── tests/
    ├── test_isa.py          framework tests, synthetic data
    ├── test_mcp.py          MCP server tests, synthetic data
    └── test_self_hosting.py regression test for Theorem 14.5

Documentation

The framework is documented at four levels of depth:

• README.md (this file): quick start. Installation, layout, first commands.
• tutorial.md: walk-through from empty catalogue to a small worked domain. Best first read for an LLM operating the catalogue.
• methodology.md: full operational design — ISA, schema breaks, the Klein-four read primitive, MCP interface, philosophical lineage.
• theory.md: foundations — shadow architecture, the temporal axis as normal to symmetry planes, magma + pointfree topology, Yoneda + Derrida, the recursive schema, convergence, trace-thickening.
• examples.md: domain templates — programming languages, cryptographic primitives, databases, file systems, network protocols, mathematical structures, OS designs, ML architectures.

All five files are exposed as MCP resources at catalogue://readme, catalogue://tutorial, catalogue://methodology, catalogue://theory, and catalogue://examples. There's also catalogue://docs — an index resource that lists everything available, suitable as the entry point for an LLM encountering the framework.

Quick start

from v4cat import SymmetryCatalogue, kquery, agree, blind

with SymmetryCatalogue('/tmp/cat.db') as cat:
    # Introduce objects with year + lineage
    cat.introduce_object('alpha', 'Alpha', year=1980)
    cat.introduce_object('beta',  'Beta',  year=1985,
                         lineage=[('alpha', 'descended-from')])

    # Introduce a break with axis classification
    cat.introduce_break('F1', 'My first break', axes=['spatial'])

    # Witness and refine
    cat.witness('alpha', 'F1', 'origin')
    cat.witness('alpha', 'F1', 'catalogue-introduces')
    cat.witness('beta',  'F1', 'inherits')
    cat.refine('F1', 'beta', 'extension', description='details')

    # Derived attribution (always a query, never stored)
    print(cat.origin('F1'))            # → originator: alpha
    print(cat.lineage('beta'))         # → ancestor chain
    print(cat.inherited_breaks('beta'))  # → F1 inherited from alpha

# Klein-four read primitive: every read is a comparison
result = kquery(['a', 'b'], ['b', 'c'], universe=['a', 'b', 'c', 'd'])
# {
#   '11': ['b'],     # both — agreement
#   '10': ['a'],     # left only
#   '01': ['c'],     # right only
#   '00': ['d']      # shared blindness
# }

Run the MCP server

Two persistence modes, mutually exclusive:

# Pinned-file: server pinned to one SQLite file. Slot tools error;
# the LLM has no string to redirect.
python -m v4cat.mcp_server --db /path/to/cat.db

# Named-slot: server confined to a sandbox directory. Slot tools
# become available; clients address catalogues by slug, never path.
python -m v4cat.mcp_server --root /path/to/dir [--default mydomain]

In named-slot mode the server only ever opens files matching <root>/<slug>.db, where <slug> is [A-Za-z0-9][A-Za-z0-9_-]{0,63}. The slug regex rules out .., /, \, leading dots, and NUL bytes; post-resolve the parent must equal the resolved root, catching symlink-escape attempts. See v4cat/sandbox.py for the validation.

Connects via stdio (the standard MCP transport). Configure your MCP-aware client (Claude Desktop, Claude Code, custom agents) to talk to it.

The server exposes:

• tools: every ISA verb (introduce_break, introduce_object, witness, refine, defer, promote, boundary, kquery, query_origin, query_lineage, etc.) plus, in named-slot mode, list_catalogues, open_catalogue, create_catalogue.
• resources: addressable views (catalogue://breaks, catalogue://objects/{id}, catalogue://retroactive, catalogue://axes, catalogue://lineages/{id}, catalogue://self_hosting, ...)
• prompts: workflow templates (analyze_new_object, audit_md_vs_sql, next_object, snap_to_grid_check)

Loading a domain on top

The framework schema (schema.sql) is generic. Domain-specific schema extensions (per-break detail tables, per-domain views, seed data) load via load_extension:

cat = SymmetryCatalogue('/tmp/proc.db')
cat.load_extension('path/to/my_domain.sql')

Domain extensions are responsible for their own idempotence (CREATE TABLE IF NOT EXISTS, INSERT OR IGNORE).

Run the tests

python -m v4cat.tests.test_isa
python -m v4cat.tests.test_mcp

Both use synthetic data only and don't depend on any specific domain. 50 tests; all green on Python 3.13.

Methodology

The brief version:

1. Identity is relational (Yoneda). An object is its participation in the witness graph; nothing more.
2. Time and lineage are breaks-themselves. A metric field (e.g. year) and lineage are recorded once per object as primary data; attribution emerges via tropical MIN over the chosen axis, restricted to origin-class edges. There's no RETRO verb.
3. Every read is a comparison (Klein-four). kquery(A, B; U) classifies the universe into four cells (11, 10, 01, 00). query, wedge, coverage, blind are named selections.
4. Schema breaks are additive. Don't drop columns; add new ones. The schema's own evolution mirrors the methodology.
5. Global structure is always derived, never imposed. Status, origin, retroactive gaps, consistency violations — all live in views.

The full case for these commitments — and their alignment with Derridean traces, Yoneda relationality, and pointfree topology — is in methodology.md.

Naming

The package is v4cat — "the category of V₄-equipped domain catalogues." The name is licensed by Theorem 14.5 (theory.md § 14) being operative by default: SymmetryCatalogue(...) runs the closure check on every open, and the regression test in tests/test_self_hosting.py passes against every shipped catalogue. The renaming was triggered by a runtime invariant, not by an act of nomination — see theory.md § 14.8.

Earlier candidate names from the lifting work, kept here for reference:

• kfour/ — earlier name committing only to V₄ as the read primitive at level 0, used while the closure check was opt-in.
• sbc/ — Symmetry-Break Cataloguing (descriptive but generic).
• traces/ — Derridean reading.
• cotype/ — after the snap-to-grid accumulator concept.

The MCP URI scheme (catalogue://...) is unchanged: it identifies addressable catalogue resources by purpose, not by package name.

License

MIT. See LICENSE at the repo root.