DFT Theorem and Lemma Map

Public Boundary

This page presents the current theorem architecture of Digital Fabrica Theory as an authorial formalization roadmap. It distinguishes established mathematical references from DFT-specific formalization targets.

Note: This is not a claim of completed external proof or a formal verification result unless explicitly linked to actual proof artifacts.

External Reference Graph

Core Theorem Stack

Layer	Theorem / Lemma	Role	Status
Well-foundedness	Ordinal stabilization lemma	Prevents runaway recursive process	Formalization target
Graph theory	Spectral expansion lemma	Supports robust routing model	Established reference applied as architecture
Fractal geometry	Bounded-growth / Hausdorff constraint lemma	Supports scalable subnet model	Formalization target
Knot theory	Policy-invariance lemma	Supports governance equivalence model	Established reference adapted to DFT
Computation	Invocation-depth gate lemma	Bounds recursive execution	Implementation candidate
Governance	Ethics Kernel consistency lemma	Maps policy checks to runtime gates	Formalization target
Economics	Zeta-indexed issuance lemma	Economic design concept	Research extension
Architecture	DFDF→FNS→IDFF→SIDS composition theorem	Connects data, topology, execution, services	Architecture model

DFT Master Theorem Candidate

Digital Fabrica Theory proposes that a digital network can remain source-routed, governance-bounded, evidence-preserving, and scalable if its data, topology, execution, and service layers each preserve explicit invariants and expose reviewable proof/evidence routes.

Review Path

Define symbols.
State assumptions.
Formalize lemmas.
Produce mechanized proof skeletons.
Simulate adversarial cases.
Submit externally for mathematical, cryptographic, legal, and systems review.

Validation Discipline

Review Pathway

Digital Fabrica Theory follows a structured validation pathway before claims are considered externally established.

Source Binding

Each public claim is connected to a source document, media item, or implementation artifact.

Claim Boundary

Claims are classified as authorial framework, formalization target, applied architecture, implementation candidate, or external review needed.

Formalization

Mathematical claims are translated into explicit assumptions, definitions, lemmas, and proof obligations.

Simulation

Systems claims are tested through simulation, adversarial modeling, and runtime evidence.

External Review

Independent mathematical, cryptographic, legal, and systems reviewers evaluate the claims.

Proof Discipline

Formalization Targets Behind This Page

These targets show how DFT claims are decomposed into assumptions, dependencies, and proof obligations before they can be treated as formal results.

Mechanization targetlogic

Infinite Stabilisation Formula — Ordinal Stabilization Target

A recursively specified DFT process should either terminate or stabilize when its transitions are governed by a well-founded ordinal ranking.

Assumptions

Each process state has an assigned ordinal rank.
Every non-terminal transition strictly decreases or stabilizes the relevant rank.
The transition relation is well-founded.
Fixed points are defined modulo accepted policy equivalence.

Proof Obligations

Define state space and transition relation.
Define ordinal rank function.
Prove monotonic descent or stabilization.
Prove absence of infinite descending chains.

Boundary: Formalization target. Public description must not be treated as completed proof until mechanized and externally reviewed.

Lemma map draftedsystems-architecture

DFDF → FNS → IDFF → SIDS Composition Theorem Candidate

The DFT architecture composes data schemas, network topology, deterministic execution, and service/governance logic into a source-routed fabric stack.

Assumptions

Each layer exposes explicit interfaces.
Each layer preserves required invariants.
Cross-layer transitions are logged and reviewable.
Failure behavior is defined at each boundary.

Proof Obligations

Define layer interfaces.
Prove invariant preservation across layer transitions.
Define failure and rollback semantics.
Specify audit trail semantics.

Boundary: Architecture model and theorem candidate. Requires implementation evidence and formal interface definitions.