> Full-text translation from Chinese. The original remains authoritative for its research claims; this translation is not independent mathematical verification.

# WSFC Round 28
## Independent Verification Pack: From Internal Closure to an Externally Falsifiable Reviewer Protocol

**English Title:** *Independent Verification Pack: Turning Internal Closure into Falsifiable External Review*  
**Document ID:** `WSFC-R28-v0.1`  
**Version:** v0.1  
**Date:** 2026-09-24  
**Author:** Neo.K  
**AI Research Collaborator:** Aletheia / OpenAI GPT-5.6 Sol  
**Series:** Worm Sequence Freedom Closure  
**Prerequisite:** `WSFC-R27-v0.1`  
**Status:** `INDEPENDENT REVIEW PACK / BLIND-FIRST / NO AUTHORITY UPGRADE`  
**Canonical Source:** UTF-8 Markdown

---

# Abstract

Round 27 reclassified the authority of the seven 2007 conjectures into:

$$
\boxed{
2\text{ classical-source closures}
+
5\text{ WSFC provisional research closures}.
}
$$

Round 28 introduces no further theorem.

The goal instead becomes:

$$
\boxed{
\textbf{Make it as easy as possible for the reviewer to refute us.}
}
$$

Accordingly, this round separates WSFC's five genuinely new core claims into five independently separable verification packets:

```text
Packet A — G0 finite-stage exactness
Packet B — strict breadth monotonicity
Packet C — finite-stage uniqueness / symmetry
Packet D — full-domain coverage / convergence
Packet E — endpoint strictness / interval certificate
```

Each packet provides a fixed set of items:

```text
00 Theorem Statement
01 Minimal Assumptions
02 Proof Skeleton
03 Attack Checklist
04 Dependency Manifest
05 Reviewer Prompt
evidence/
```

But the reviewer must follow:

$$
\boxed{
\text{Blind Attack Before Proof Exposure}.
}
$$

On the first pass, read only:

- the theorem statement;
- the minimal assumptions;
- the attack checklist.

Do not read the proof skeleton first.

Only after completing the first counterexample search should the proof and machine evidence be opened.

---

# 1. Why Blind-First Is Needed

Once reviewers see the original proof, they may merely follow its path looking for typos, overlooking:

- whether the theorem statement itself is false;
- whether the assumptions are too strong;
- whether there is an entirely different counterexample;
- whether the quantifier order is wrong;
- whether a boundary class has been omitted altogether.

Thus the reviewer's first pass must answer without proof bias: “How would I refute this theorem?” The original wording of that prompt is retained verbatim below.

```text
我會怎麼把這個 theorem 打死？
```

---

# 2. Packet A — G0

Goal:

$$
\operatorname{Argmax}(\mathcal F_n)
\subseteq
\mathcal T_n
$$

up to lower-stage normalization.

This is the most crucial dependency of the entire finite-stage structural program.

Prioritize attacks on:

- a slack support edge;
- an endpoint shortcut that loses hull-support responsibility;
- a plateau / q=0;
- the support-order boundary;
- exact-n versus at-most-n semantics.

---

# 3. Packet B — Strict Breadth

Goal:

$$
t_{n+1}>t_n.
$$

This depends on Packet A's G0-lite, not the full reduced formula.

Core attack:

> Does tangent-bisector insertion really remain feasible in every other width direction?

---

# 4. Packet C — Uniqueness / Symmetry

Goal:

$$
\operatorname{Argmax}(\mathcal F_n)
/\operatorname{Isom}(\mathbb R^2)
$$

to be a singleton, yielding the even / odd symmetry classification.

Prioritize attacks on:

- whether a fixed allocation has a second global minimum;
- the equality case of integer balancing;
- the Schur-complement profile;
- the odd mirror convention;
- whether support reconstruction is injective.

---

# 5. Packet D — Full-Domain Coverage

Goal:

$$
r_n^H
\le
\frac1{2\lfloor n/2\rfloor}
$$

and uniform convergence of normalized optimizers.

This packet deliberately depends very little on G0 and is the best suited to genuine independent verification.

Prioritize attacks on:

- the local tent Hausdorff bound;
- exact unit length;
- odd exact-n accounting;
- breadth Lipschitz continuity;
- Arzelà–Ascoli / the length limit;
- simple versus general polygonal semantics.

---

# 6. Packet E — Endpoint Strictness

Goal:

$$
b_{n+1}<b_n.
$$

This packet poses the greatest authority risk, because the decisive step is an interval certificate for:

$$
\boxed{
\mathcal K>0
}
$$

.

The reviewer should prioritize:

1. replaying with a second interval backend;
2. attacking stationarity pruning;
3. attacking the $d$-domain enclosure;
4. attacking continuous support-count interpolation;
5. redoing the finite base cases.

---

# 7. Dependency Cut

The five packets have the dependencies:

$$
\boxed{
A
\rightarrow
B
\rightarrow
C
}
$$

$$
\boxed{
D
}
$$

is almost independent.

And:

$$
\boxed{
E
\leftarrow
A,C,D.
}
$$

Thus the review priority should not simply follow A onward.

A better order is:

```text
D first
A second
B third
C fourth
E last
```

D tests whether the reviewer can genuinely reproduce a low-dependency claim independently.

E should come last because it includes the most upstream assumptions and computer-assisted evidence.

---

# 8. Authority Rule

Round 28 fixes:

$$
\boxed{
\text{Claim authority}
\le
\min
(
\text{indispensable dependency authorities}
).
}
$$

Even if the Packet E interval replay succeeds completely, if G0 still has only research-proof authority:

$$
E
$$

still cannot be promoted to a formal theorem.

---

# 9. Evidence Integrity

Each packet's:

```text
04_Dependency_Manifest.json
```

stores:

- the source path;
- the packet-copy path;
- the byte count;
- SHA-256.

The reviewer's first step must be to verify hashes.

This prevents the following mistake: the reviewer replays a different version of the script (the original description is retained verbatim below),

```text
reviewer重播了不同版本的 script
```

yet mistakenly believes the same certificate was verified.

---

# 10. Required Verdicts

Round 28 prohibits vague verdicts such as:

```text
looks correct
probably true
seems convincing
```

Only the following are permitted:

```text
REFUTED
GAP_FOUND
SURVIVES_CURRENT_AUDIT
INDEPENDENTLY_REPRODUCED
FORMALLY_VERIFIED
```

---

# 11. Reviewer Score

It also defines an authority score from $0$–$5$:

```text
0 refuted
1 major gap
2 unresolved indispensable dependency
3 survives analytic audit
4 independently reproduced
5 formally verified
```

And:

$$
\boxed{
\text{overall score}
=
\min
\text{ indispensable layers}.
}
$$

Averaging is not allowed.

---

# 12. What Round 28 Does Not Do

This round does not:

- add a conjecture;
- upgrade theorem status;
- claim that independent review is complete;
- claim novelty;
- claim formal verification.

This round establishes only:

$$
\boxed{
\text{an externally attackable verification interface}.
}
$$

---

# 13. Next Steps

A reasonable Round 29 should not have us continue expanding the proofs ourselves.

There are two directions:

### A — Internal Blind Red-Team Simulation

Give a new verifier context only Packet D or A, without the earlier conversation, and actually run the protocol.

### B — Formalization Queue

In dependency order:

```text
D coverage lemma
A support-width saturation
B tangent split
C strict convexity
E interval bridge
```

send the items to Lean / Coq one at a time.

For maximum information gain, I would begin with:

$$
\boxed{
\textbf{Packet D blind independent replay}.
}
$$

It has the fewest dependencies, and if the reviewer cannot reproduce it, that immediately exposes a problem in our verification protocol itself.

---

# Conclusion

Round 28 moves WSFC from:

$$
\boxed{
\text{internal research closure}
}
$$

to:

$$
\boxed{
\text{falsifiable independent-review packaging}.
}
$$

The genuinely valuable question is no longer:

> Can we prove one more statement?

Instead it is:

> Can someone who does not believe us at all refute it after receiving only the minimum information?

This is the starting point for authority elevation in the next stage.

===END===