# Pass 03 — Contributions and Novelty (Make “What Is New” Unavoidable)

## Purpose

Push the “Novelty as math” score toward 10 by making the contribution boundary crisp:

- what is standard (ingredients)
- what is new (SFT packaging + target correctness + artifact engine)
- what is the flagship claim (engine-level universality with certificates and correct coupled targets)

This document is designed to be pasted into a paper introduction.

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## Standard ingredients (acknowledged)

SFT uses known components:

- degree and winding for circle maps
- equivariant observables under \(S^1\)-actions
- torus translations and equidistribution criteria
- diffusion/advection–diffusion on compact manifolds
- holonomy and gauge invariance in lift/connection frameworks

SFT does not claim these are new.

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## What is new in SFT (core contributions)

- **C1 — Witness-first universality engine**
  - A single meta-witness template (AWT) plus embedded witness tier (ESW) organizes many physical realizations under one mechanism.
  - The key upgrade is not existence, but *structured witness production*.

- **C2 — Target correctness under coupling**
  - SFT enforces a coupled-target principle (CTP): when coupling restricts the image to a coupled subtorus CST, the correct target is CST and the correct baseline is coupled Haar (CHT).
  - This avoids a pervasive technical error: measuring convergence against full torus Haar when support is constrained.

- **C3 — Artifact discipline: certificate or obstruction**
  - SFT is packaged as an artifact-producing engine: given a witness context, output either
    - a Witness Stability Certificate (WSC) with explicit margins, or
    - a Witness Obstruction (WOB) with evidence and recommended next moves.
  - This is the primary “referee-hard” contribution: every universality claim becomes traceable.

- **C4 — Robustness margins as part of the statement**
  - LCM (<\(\pi\)) and HMR (<\(P/2\)) margins are treated as first-class objects (WSC fields), not afterthoughts.
  - “Exists in nature” becomes “exists stably.”

- **C5 — Honest mixing boundary with certificates**
  - SFT distinguishes preservation (transport can preserve witnesses) from mixing (requires NDB/diffusion or explicit RNF conditions).
  - Mixing claims are not rhetoric; they are governed by explicit inequalities (MXC) recorded in the thresholds ledger.

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## Flagship claim (one sentence)

SFT provides a universal mechanism for observable relational form: whenever a cyclic phase observable with nontrivial winding/holonomy occurs on a spatial subsystem, SFT produces a stable finite witness (or a named obstruction), with correct targets under coupling and explicit boundaries for dynamics and mixing.

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## Where this sits relative to the higher aim (RFP)

SFT is not the final “relational form theorem.” It is the PIP scaffold that becomes progressively stronger as certificates, obstructions, moduli, coupling atlases, and dynamics are tightened.

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## Acceptance gates

- The “standard vs new” boundary is explicit.
- The flagship claim is one sentence and reads defensible.
- Contributions explicitly mention certificates, coupling targets, and scope boundaries.
