# Results — R-ONT-2: Honest \(\sqrt{6}\) Brick Card

### No upgrade · lock extra law · brick not retired · R-ONT derivation path **CLOSED** · no promote

**CPT Framework — absolute-scale \(R\) ontology · WP R-ONT-2**  
**Date:** 2026-08-16  
**Status:** **BANKED** · `PASS_R_ONT2_BRICK` · \(\sqrt{6}\) **[M]** · `PASS_LOCK` **false**  
**Parents:** R-ONT-0 · R-ONT-1 · AST / M13 three-gate · SC4 B-√6  
**Census:** `scripts/investigations/s3_geometry/r_ont2_sqrt6_brick_census.py` · `data/r_ont2_sqrt6_brick_census.json`

Tags: **[E honesty]** · **[Programme]** · **[M packaging]** · **[O residual]**

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## 0. One-line

> **R-ONT-2 freezes the \(\sqrt{6}\) ledger after R-ONT-1: the \(L=2\) eigenvalue \(\omega_2=\sqrt{6}\,c/R\) stays **[E]**; the lock \(\omega_2=H_0\) stays an **OPEN extra law** (not derived, not falsified); therefore \(R=\sqrt{6}\,c/H_0\) is **not upgraded** and **not retired** — it remains the SC4/M13 **[M]** brick; the R-ONT *derivation* path for that brick is **CLOSED** pending a new slaving/clock principle; no \(m_e\) mint; no promote.**

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## 1. Integrity (held)

| Rule | Held |
|------|:----:|
| No silent theorem upgrade | **Yes** |
| No silent brick retirement | **Yes** |
| FAIL_DERIVE \(\neq\) \(\omega_2\neq H_0\) | **Yes** |
| FLRW \(\Omega_k=-1/6\) still rejected | **Yes** |
| No \(m_e\) mint | **Yes** |
| No promote | **Yes** |

---

## 2. Two layers (do not collapse)

| Layer | Statement | Tag after R-ONT-1 |
|-------|-----------|-------------------|
| **Eigenvalue** | \(\omega_2=\sqrt{6}\,c/R\) | **[E]** (S7a/S7d; \(L(L+2)-2=6\)) |
| **Lock** | \(\omega_2=H_0\) | **OPEN extra law** |
| **Mach anchor** | \(R=R_{\mathrm{spin2}}=\sqrt{6}\,c/H_0\) | **[M]** = eigenvalue **+** lock |

R-ONT-0’s *candidate* reading (tensor coherence length, not FLRW curvature) is **not** a present identification.  
**R-EFF:** the framework does not know what \(R\) is; \(R_{\mathrm{eff}}\) is the Mach-inferred length; \(\sqrt{6}\,c/H_0\) is the M13 dual.

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## 3. Brick card (live)

| Field | Freeze |
|-------|--------|
| Symbol | \(\sqrt{6}\) in \(R=\sqrt{6}\,c/H_0\) |
| SC4 / M13 role | Cosmic-radius anchor (B-√6) |
| Status | **[M]** |
| Upgrade to **[E]** | **Denied** (R-ONT-1) |
| Retire | **Denied** (lock not falsified as a law) |
| Derivation path | **BLOCKED** until a new named lock principle |
| \(H_0=69\) | Still M14-class / circular if recycled |

M13 three-gate **unchanged:** G-H0 and G-EXT stay observational; G-R still forbids naive expanding \(R\).

---

## 4. What is closed vs what may reopen

| Closed without a new principle | May reopen only with |
|--------------------------------|----------------------|
| C3 \(\Rightarrow\omega_2=H_0\) | Named slaving / matter-clock / non-imported friction law |
| S7d Hubble-class \(\Rightarrow\) Mach \(\sqrt{6}\) | Same |
| \(3H\dot q\) paste as lock | A *derived* damping, not an EH import |
| R-ONT-3+ on this skeleton | New principle, new WP name |

**Default after this card:** stop the lock-derivation spine. Theory effort may still discuss \(R_{\mathrm{spin2}}\) as ontology, but must not treat \(\sqrt{6}\) as derived.

---

## 5. Gates

| Gate | Status |
|------|--------|
| PASS_NO_UPGRADE | **PASS** |
| PASS_EIGENVALUE_STILL_E | **PASS** |
| PASS_LOCK_STILL_OPEN | **PASS** |
| PASS_BRICK_STILL_M | **PASS** |
| PASS_BRICK_NOT_RETIRED | **PASS** |
| PASS_NOT_THEOREM | **PASS** |
| PASS_NO_ME_MINT | **PASS** |
| PASS_NO_EH_PASTE | **PASS** |
| PASS_NO_PROMOTE | **PASS** |
| PASS_INTEGRITY | **PASS** |

**Status:** `PASS_R_ONT2_BRICK`

---

## 6. Kill board (R-ONT-2 additions)

| ID | Kill |
|----|------|
| **K-RONT2-1** | \(R=\sqrt{6}\,c/H_0\) sold as **[E]** after this card |
| **K-RONT2-2** | Brick dropped because “R-ONT-1 failed” (that was FAIL_DERIVE, not FAIL_LAW) |
| **K-RONT2-3** | New C3 re-arrange sold as R-ONT-3 |
| **K-RONT-1…6** / **K-RONT1-*** | Held |

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## 7. Next

| Option | Action |
|--------|--------|
| **Default** | **Stop** lock-derivation; \(\sqrt{6}\) **[M]**; M13 gates stand |
| Later | New lock principle only |
| Not | \(m_e\) mint; \(\Omega_k=-1/6\); EH; GE-6 |

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## 8. One-line

> **§R-ONT-2: √6 brick stays [M]; lock extra law; no upgrade; no retire; derivation path CLOSED; no promote.**