Freeze — \(R_{\mathrm{eff}}\) Is an Unnamed Mach Length
Ontology unresolved · \(\sqrt{6}\,c/H_0\) is M13 dual, not a derivation · stop premature naming · no promote
CPT Framework — absolute-scale \(R\) honesty Date: 2026-08-16 Status: THEORY FREEZE ·PASS_R_EFF_HONESTY · supersedes R-ONT-0 default name \(R_{\mathrm{spin2}}\) as “what \(R\) is”
Parents: R-ONT-0…2 · AST / M13 three-gate · SC4 B-√6 · Mach M12–M14
Census: scripts/investigations/s3_geometry/r_eff_ontology_honesty_census.py · data/r_eff_ontology_honesty_census.json
Tags: [E honesty] · [Programme] · [M packaging] · [O residual]
0. One-line
The framework does not presently know what physical object \(R\) is. Mixed-mass Mach closure plus laboratory \(\{G,\alpha,m_e,m_p\}\) infers an effective length \(R_{\mathrm{eff}}\approx 3.28\times 10^{26}\,\mathrm{m}\) under the published coefficient book (\(k_1=3/8\) as \(K_{\mathrm{Green}}\) at \(\Omega x^2=1\)); writing \(R_{\mathrm{eff}}\approx\sqrt{6}\,c/H_0\) is the same M13/M14 relation (\(H_0\approx 68.97\)), not an independent derivation and convention-conditional; FLRW curvature, expanding \(S^3\), theorem-grade spin-2 coherence, and horizons are all not licensed names; \(\sqrt{6}\) stays a brick; stop naming \(R\) until a proposal explains both stationarity and the \(\sim\sqrt{6}\) Hubble match.
1. Integrity (held)
| Rule | Held | |------|:----:| | Ontology left unnamed | Yes | | \(\sqrt{6}\,c/H_0\) not sold as derived \(R\) | Yes | | R-ONT-1 FAIL_DERIVE not forgotten | Yes | | \(\Omega_k=-1/6\) still rejected | Yes | | M12 expanding-\(R\) still FIRE | Yes | | No \(m_e\) mint | Yes | | No promote | Yes |
This freeze does not retire \(R_{\mathrm{spin2}}\) as a candidate. It denies it as the present answer.
2. What is actually known
Before the \(\sqrt{6}\) Hubble anchor, mixed-mass closure with \(k_1=3/8\) is \[ G = \frac{\alpha\,k_1\,\hbar^{2}}{R\,m_e^{2}m_p}, \qquad k_1=\frac38. \] Laboratory constants therefore infer \[ \boxed{ R_{\mathrm{eff}} = \frac{\alpha\,(3/8)\,\hbar^{2}}{G\,m_e^{2}m_p} \approx 3.285\times 10^{26}\,\mathrm{m} } \] (\(\approx 10.65\,\mathrm{Gpc}\approx 34.7\,\mathrm{Gly}\)).
Census: inverting \(R_{\mathrm{eff}}=\sqrt{6}\,c/H_0\) returns \(H_0\approx 68.97\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\) — exactly the M13/M14 invert. So \[ R_{\mathrm{eff}}\approx\sqrt{6}\,\frac{c}{H_0} \] is an empirical dual of that prediction, not a second derivation of \(R\). After R-XCHECK the dual is convention-conditional: the same algebra with the raw-book coefficient \(3\pi/4\) moves \(R_{\mathrm{eff}}\) by \(2\pi\) and \(H_0\) to \(\sim10.98\). The published number remains the length the published closure requires. 3/8 stays [E] in the named Green book; it is not a radius-independent constant.
3. What it cannot currently be called
| Name | Why not | |------|---------| | FLRW curvature radius | Implies \(\Omega_k=-1/6\) (R-ONT-0 REJECT) | | Expanding \(S^3\) scale factor | M12 \(\dot G/G\sim H_0\) FIRE | | Spin-2 coherence length as a theorem | Lock \(\omega_2=H_0\) FAIL_DERIVE (R-ONT-1) | | Particle or event horizon | No identification banked |
The \(L=2\) eigenvalue \(\omega_2=\sqrt{6}\,c/R\) remains [E]. That does not identify the Mach \(R_{\mathrm{eff}}\) with a coherence length until the lock is a theorem.
4. Correct next posture
| Do | Do not | |----|--------| | Leave \(R=R_{\mathrm{eff}}\) as an independently inferred Mach length | Prematurely name it | | Treat \(\sqrt{6}\) as a brick (R-ONT-2 held) | Call \(\sqrt{6}\,c/H_0\) the answer | | Demand any new proposal explain stationarity and the \(\sim\sqrt{6}\) Hubble match | Reopen C3 as if it locked | | Keep M13 three-gate observational (convention-conditional invert) | Recycle \(H_0=69\) as confirmation of a name, or retire G-H0 because the coefficient is spliced |
R-ONT-0 default label \(R_{\mathrm{spin2}}\) is hereby demoted from “what \(R\) is” to one candidate among unnamed options, consistent with R-ONT-2 (brick [M], lock extra law).5. Gates
| Gate | Status | |------|--------| | PASS_R_EFF_FROM_LAB | PASS | | PASS_SQRT6_IS_M13_DUAL | PASS | | PASS_ONTOLOGY_UNNAMED | PASS | | PASS_SPIN2_NOT_THEOREM | PASS | | PASS_FLRW_STILL_REJECTED | PASS | | PASS_NO_PREMATURE_NAME | PASS | | PASS_NO_ME_MINT | PASS | | PASS_NO_PROMOTE | PASS | | PASS_INTEGRITY | PASS |
Status:PASS_R_EFF_HONESTY
6. Kill board
| ID | Kill | |----|------| | K-REFF-1 | “The framework knows \(R\) is the spin-2 coherence length” | | K-REFF-2 | \(\sqrt{6}\,c/H_0\) sold as independent of M13/M14 | | K-REFF-3 | \(R_{\mathrm{eff}}\) sold as FLRW \(R_k\) or horizon | | K-RONT- / K-AST- | Held |
7. Next
| Option | Note | |--------|------| | Default | Live with unnamed \(R_{\mathrm{eff}}\) (published-book length); observe M13 gates | | R-MCR / R-MCR-2 | DONE · no one-convention PRIMARY hit · remainder \(k\) FAIL_DERIVE · coefficient line closed | | New proposal | Must do stationarity + \(\sim\sqrt{6}\) to \(H_0\) together, without shopping \(k\) | | Not | Another name; another \(m_e\) mint |
8. One-line
§R-EFF: framework does not know what \(R\) is; \(R_{\mathrm{eff}}\) from published Mach+lab; \(\sqrt{6}\) brick = convention-conditional M13 dual; stop naming; no promote.