SC-AS

Structural Coherence — Anchor Specification (SC-AS) v1.0

Constitutional Release — March 2026
Published by Coherence Research

Canonical Documents

The SC-AS specification consists of four canonical documents. Each is available as markdown source and rendered PDF.

SC-CORE-000001 — The Coherence Core Specification

The complete structural kernel: 76 formally defined terms covering primitive definitions, foundational conditions, valid emergence conditions, and admissibility rules.

Version 1.2.5 · Issuance v39d

Download PDF · View Source (GitHub)

SC-AXIOM-000001 — The Coherence Axioms Specification

Ten canonical axioms (I–X) derived from the Core primitives — from minimal coherent excitation through hierarchy, information encoding, replication, and observation.

Version 1.0.0 · Issuance v11l

Download PDF · View Source (GitHub)

SC-HDR-000001 — Document Header Specification

The normalized metadata header, document class extensions, integrity computation rules, and validation requirements governing all SC-AS artifacts.

Version 0.4.0 · Issuance v11

Download PDF · View Source (GitHub)

SC-SCOPE-000001 — Semantic Scope and Non-Prescriptive Clause

Defines what SC-AS does and does not claim, the canonical boundary, the certificate tier architecture, and the constitutional bundle composition.

Version 1.1.0 · Issuance v05

Download PDF · View Source (GitHub)

Download the Complete Release

SC-AS Constitutional Release v1.0 contains all four canonical documents, four reflexive closure certificates, five stewardship documents, four rendered PDFs, release manifest, merkle tree, and an independent verification script.

Download Constitutional Release Bundle (ZIP)

The bundle includes verify_bundle.py — a zero-dependency Python script that independently verifies every SHA-256 hash, recomputes the Merkle root, validates RCC target coupling, and checks bundle composition. Run it:

python3 verify_bundle.py

Verification

Every canonical document carries a SHA-256 hash in its header, computed per SC-HDR §3.2 Rule 7.

To verify any document’s integrity:

1. Open the .md source file
2. Blank the SHA-256: value (line ends at the colon)
3. Compute SHA-256 over the UTF-8 bytes with LF line endings
4. Compare against the hash in the header

Current SHA-256 hashes:

Merkle Root: 8038a44578aab8d3e07f41a86be1542307289fa1f2c7fa22a0b4f5b9fe188a72

Reflexive Closure Certificates

Each canonical document is accompanied by a Reflexive Closure Certificate (RCC) — a structural attestation that the document satisfies schema completeness, dependency acyclicity, primitive closure, and binding vocabulary discipline. All RCCs were built from mechanical verification of the target artifacts.

Reading Path

New to Structural Coherence? Start with the Overview for orientation, then:

1. SC-SCOPE — understand what the specification does and does not claim
2. SC-CORE — the formal kernel: primitives, conditions, rules
3. SC-AXIOM — the axiomatic consequences derived from the Core
4. SC-HDR — how documents are structured and verified

For implementers: The specification is designed to be readable by both humans and AI systems. The Core uses a rigorous term schema (T0–T7) where every definition carries explicit scope, dependencies, necessity witness, minimality proof, and admissibility interface.

Archival & Citation

SC-AS is archived on Zenodo with persistent DOIs:

• SC-CORE-000001: DOI: 10.5281/zenodo.18039635
• SC-AXIOM-000001: DOI: 10.5281/zenodo.18043770

Citation format:

Carroll, J. (2026). Structural Coherence — Anchor Specification (SC-AS), v1.0. Coherence Research. https://coherenceresearch.com/standard

License

SC-AS is published under the Creative Commons Attribution-NoDerivatives 4.0 International License (CC BY-ND 4.0).

You are free to share the specification in its original form with attribution. You may not distribute modified versions of the canonical documents. Independent implementation — including commercial implementation — is unrestricted.

Source Repository

The canonical source repository is hosted on GitHub:

Coherence-Research/public

This specification does not ask you to trust the framework. It asks you to test it.

Worked Example: Admissibility Check

What does an admissibility check actually look like in practice? Here’s a minimal example against SC-AS conditions.

Configuration under review

An AI system that modifies its own objective function during deployment in response to user feedback.

SC-AS check

Condition 1 — Identity persistence (D1.1, F3): A system must maintain invariant structural identity across transformations. Self-modification of the objective function changes what the system is optimizing for — the identity of the optimization target is not preserved across the transformation. Result: FAIL. The configuration violates the identity persistence condition because the system’s defining optimization target is not invariant under the transformation.

Condition 2 — Bounded interaction (F5, AR4): Interactions must remain bounded under composition. If the objective modification is triggered by external feedback, the feedback loop creates an unbounded interaction path between deployment context and system internals. Result: FAIL. The interaction between the external environment and the system’s objective is structurally unbounded.

Condition 3 — Admissible change (AR6, AR9): Change must redistribute structural content without destroying it. Objective replacement that doesn’t conserve prior structural commitments is not admissible redistribution — it’s deletion. Result: FAIL unless prior objectives are explicitly conserved.

Verdict

NOT ADMISSIBLE under SC-AS admissibility conditions as stated. The system would need to either preserve objective-function identity across modifications (making modifications parametric, not structural) or formally declare objective replacement as a regime transition — which itself requires passing through a structural gate.

This verdict holds independent of whether the system performs well in testing. It holds independent of what failure modes we anticipated. It’s a structural fact about the configuration — derived from the axioms, not from outcome enumeration.

Full admissibility FAQ → | The layer governance frameworks don’t reach →

Continue

What Is Structural Coherence? →
A conceptual orientation — what the specification defines, why it exists, and how it works.

Release Announcement →
What’s in the Constitutional Release and where to find it.

About Coherence Research →
The organization and the person behind the specification.