SigmaLanguage is a formal language for expressing what a theory, model, or system can and cannot guarantee under explicit assumptions, explicit observability, and explicit regime change.
Its core purpose is epistemic clarity: to distinguish what a regime explains, what it merely assumes, what it cannot support, and what kind of structural change would be required to move beyond its current limit.
The language is designed to be both human-readable and machine-processable, making it useful for scientific formalization, operational reasoning, and structured human-LLM co-reasoning.
SigmaLanguage is designed to represent the movement from:
current regime -> structural limit -> regime change -> elevated guarantee
It is useful when ambiguity around assumptions, evidence, explanatory scope, or failure mode would make prose alone too loose.
Natural language often hides the exact point where a model stops explaining and starts assuming. SigmaLanguage exists to expose that boundary.
It is intended to help distinguish:
- guaranteed claims
- assumed conditions
- observable support
- unsupported extrapolation
- structural limits
- candidate next regimes
Σ-Core is the minimal canonical nucleus of SigmaLanguage.
Its smallest complete shape is:
D := <domain>
Sigma0[D] := <base regime>
Phi[D] := <typed property>
A[D] := { <assumptions> }
Omega[D] := <verifier composition>
gen(Sigma0[D]) := (
phi[D] := <structural generator>,
pi[D] := <structural generator>
)
Delta[D] := phi[D] + pi[D]
Sigma0[D] ⊬ Phi[D]
Lambda := <regime change>
Sigma0+[D] := Lambda(Sigma0[D])
A+[D] := { <elevated assumptions> }
Omega+[D] := <elevated verifier composition>
Sigma0+[D] ⊢_emp Phi[D] under A+[D] verified_by Omega+[D]
The central question is:
What can the current regime not guarantee, why, and what must change structurally for that guarantee to become possible?
The current repository freezes the initial semantic foundation:
- foundational purpose
- Σ-Core v1.0
- layered architecture
- repository bootstrap plan
- core grammar
- minimal AST schema
- normal form
- golden tests and canonical fixtures
- electroweak/Higgs canonical example
- first core fixture pack
These artifacts are meant to constrain implementation. Parser, normalizer, and linter behavior should answer to these documents and fixtures.
SigmaLanguage is not yet a full compiler, runtime, policy engine, proof system, or LSP-backed IDE language.
The current implementation target is deliberately small:
- parse top-level Σ-Core declarations
- normalize canonical
.sigmatext - lint structural closure rules
- run golden comparisons
The minimal reference implementation currently supports:
- top-level Σ-Core parsing
- canonical normalization of core and example fixtures
- structural linting for selected closure errors
- AST JSON serialization for valid fixtures
- golden-test comparison across core and example fixtures
It is intentionally small and should be treated as a reference skeleton, not a complete language implementation.
Higher layers such as time, scope, measure, types, policy, governance, modules, templates, trust, and tooling are documented as architecture, not yet as stable implementation.
docs/
00-foundation/ foundational language boards
01-core/ Σ-Core canonical documents
grammar/
ebnf/ implementation-facing EBNF grammar
specs/
core/ machine-oriented core spec artifacts
examples/ canonical domain examples
tests/
fixtures/ source inputs
golden/ frozen expected outputs
sigma_ref/ minimal Python reference implementation
The core documents live under docs/:
docs/00-foundation/foundational-board.mddocs/00-foundation/layered-architecture.mddocs/00-foundation/canonical-bootstrap.mddocs/00-foundation/repository-bootstrap-plan.mddocs/01-core/sigma-core-v1.0.mddocs/01-core/grammar-core.mddocs/01-core/ast-minimal.mddocs/01-core/normal-form.mddocs/01-core/golden-tests-and-fixtures.md
The first scientific example lives at:
specs/examples/physics/electroweak-higgs-core.md
- Physics: electroweak/Higgs regime shift
- Operations: logistics dispatch under disruption
Golden tests protect the identity of the language while the implementation is still immature.
The first frozen fixture pack lives under:
tests/fixtures/core/
tests/golden/core/
The first required properties are:
- valid core specs parse and lint cleanly
- invalid core specs produce deterministic diagnostics
- equivalent specs normalize to the same canonical output
- normal form stays byte-stable
Run the golden suite:
python -m sigma_ref testNormalize a fixture:
python -m sigma_ref normalize tests/fixtures/core/core.minimal.valid.sigmaLint an invalid fixture:
python -m sigma_ref lint tests/fixtures/core/core.missing_lambda.invalid.sigmaEmit AST JSON:
python -m sigma_ref ast tests/fixtures/examples/example.logistics_dispatch.valid.sigmaCurrent local validation:
- 2 canonical domains represented
- scientific example: electroweak/Higgs
- operational example: logistics dispatch
- minimal parser, normalizer, linter, AST serializer, and golden runner working
- 12 golden tests passing locally
Run:
python -m sigma_ref test- Push the first public repository state.
- Freeze an internal
v0.1.0-alphabaseline. - Tighten the AST contract for all core fixtures, not only examples.
- Add more invalid fixtures for structural linter coverage.
- Add a third canonical domain, likely AI governance or clinical triage.
- Keep canonical documents and golden fixtures synchronized.
SigmaLanguage is in the canonicalization and reference-bootstrap phase.
The project is intentionally optimizing for semantic stability before broad language surface area.
Project author ORCID:
TBD