Freeze — Absolute-Scale Theory · M13 Three-Gate Hypothesis · \(R\) Residual
Geometry \(\to\) spectrum · \(R\) sets scale · stop minting \(m_e\) · no promote
CPT Framework — absolute scale Date: 2026-08-16 Status: THEORY FREEZE ·PASS_M13_THREE_GATE_FREEZE · local \(m_e\) mint CLOSED-NULL / PARK
Parents: Scale wall · Lemma L1 · GS stance · Mach M7–M16 · SC4 · GE-C · P3 · MCL consideration
Census: scripts/investigations/s3_geometry/m13_three_gate_hypothesis_census.py · data/m13_three_gate_hypothesis_census.json
Tags: [E process] · [E honesty] · [Programme] · [M packaging] · [O residual] · [P prediction]
0. One-line
*Absolute scale is frozen as a theory of the cosmic radius \(R\) (Mach / Sciama / mixed-mass closure), not as a local electron factory: geometry supplies dimensionless structure and mass ratios; M13 is a falsifiable three-gate hypothesis (Hubble invert, independent-\(H_0\) contact, \(R\)-ontology); theoretical effort concentrates on what \(R\) is and how it does or does not move, not on reproducing \(511\,\mathrm{keV}\); GE linear kernel and Compton-pixel stacks stay parked; no promote.
1. Why this freeze now
| Banked fact | Consequence | |-------------|-------------| | L1 / scale wall | Local \(1/a\) cannot mint \(a_\) or \(m_e\) | | GE-0…5 / GE-C | Linear Sciama / ZM / self-energy informative negative | | MCL-1 | Compton cell \(4\pi\bar\lambda_e^{2}\) circular | | P3 | SOFT_SCALE_OK; HARD_SCALE_PASS false | | SC4 / M13–M14 | Soft absolute relation already exists; \(H_0\) is the live prediction | | M12 | Naive expanding \(R\) FIRE vs LLR |
Continuing to invent local \(m_e\) theorems repeats a closed-null. The remaining theory is the ontology and dynamics of \(R\).
2. Absolute-scale theory (frozen)
\[ \boxed{ \begin{aligned} &\text{geometry on }S^3(R)\text{ acts on the spectrum (modes, }C_i\text{, ratios);}\\ &\text{the cosmic radius }R\text{ (Mach/Sciama state) sets the absolute scale;}\\ &m=\hbar/(a c)\text{ is a reading after a scale-break, not a local mint.} \end{aligned} } \]
| Layer | Does | Does not | |-------|------|----------| | Hopf / Clifford / \(T(p,q)\) / DN | Ratios, \(n=2\) class, form | SI \(m_e\) | | Mach closure \(p=2\), \(k_1=3/8\), \(k_2=1\) | Why \(\alpha_G\sim 10^{-40}\) | Unique \((R,m)\) without an anchor | | M13 mixed-mass + α double-copy | Percent-class relation among \(\{G,H_0,\alpha,m_e,m_p\}\) | Free α; free local \(m_e\) | | Soft \(\mathcal{P}_{\mathrm{EMC}}\) | Join \(m\leftrightarrow a\) | Hard join / hold closed |
Effort rule: do not spend WPs on reproducing \(m_e\). Allowed theory WPs attack \(R\): static vs quantized vs present-epoch; what Hubble expansion is if \(R\) is not \(\dot R/R=H_0\); whether \(\sqrt{6}\) is a law for \(R\) or a brick. Parked as \(m_e\) factories: GE linear kernel; Robin \(f\); F1 \(\alpha^3/2\); MCL Compton pixel; CODATA invert (NS-S1).3. M13 as a three-gate hypothesis
Statement (M13). Packing length = electron Compton; Mach gravitational seat = proton; α double-copy [M]: \[ G = \frac{3\alpha}{8\sqrt{6}} \frac{\hbar^{2} H_0}{c\, m_e^{2}\, m_p}. \] Equivalent invert (M14 / SC4 dual). α is INPUT + [M] placement, not a derived theorem. \(\sqrt{6}\) is [M]. Hypothesis status: [M/P], not HARD_SCALE_PASS.Census invert (lab \(G,\alpha,m_e,m_p\)): \(H_0^{\mathrm{M13}}=68.97\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\).
Convention condition (R-XCHECK / R-XCHECK-D). This invert is of the published book (Green3/8 used in the raw \(GNm/R\) slot, plus mixed-mass and \(\sqrt{6}\)). Sol showed that 3/8 is \(K_{\mathrm{Green}}\) only at \(\Omega x^2=1\), and that the same-book raw coefficient \(3\pi/4\) moves the invert to \(\sim10.98\). The contact is therefore convention-conditional [P], not a one-convention derivation. It is not retired: G-H0 / G-EXT stay OPEN on the published book until a single-functional rederivation exists. Do not patch 3/8 after seeing \(H_0\). Do not promote \(\Omega=1/6\) or \(\Omega=\alpha/(12\pi)\) as the repair.
Gate G-H0 — Hubble invert [P]
| Field | Freeze | |-------|--------| | Prediction | \(H_0=69.0\,\mathrm{km\,s^{-1}\,Mpc^{-1}}\) (census \(68.97\)) | | Lives in | Planck \(67.4\) – SH0ES \(73.0\) | | Falsify if | A tension-resolved consensus \(H_0\) lies outside \([66,73]\), or excludes \(69.0\) at the hypothesis’s claimed percent class | | Now | OPEN | | Honesty | Using only \(H_0=69\) recycled from this invert is circular (B-circ). This gate waits on external Hubble resolution. The invert itself is of the published (spliced) coefficient book — convention-conditional, not withdrawn |
Gate G-EXT — independent \(H_0\) contact
| Field | Freeze | |-------|--------| | Test | Insert external \(H_0\) (Planck or SH0ES), predict \(G\) or \(m_e\); do not recycle \(69\) | | Census | Planck: \(\delta G/G\approx-2.3\%\); SH0ES: \(\delta G/G\approx+5.8\%\) (linear in \(H_0\)); \(m_e\) errors are the cube-root (SC4: \(\sim-0.8\%\) / \(\sim+1.9\%\)) | | Falsify if | Planck-class independent \(H_0\) gives \(|\delta G/G|>5\%\) or \(|\delta m_e/m_e|>3\%\), or both Planck and SH0ES give \(|\delta G/G|>8\%\), with no new named brick | | Now | OPEN · percent-class · SH0ES \(+5.8\%\) on \(G\) is the Hubble tension, not an extra fail |
Gate G-R — ontology / dynamics of \(R\) ★ theory residual
If \(R(t)=\sqrt{6}\,c/H(t)\) tracks an expanding 3-sphere and M13 is an eternal law with fixed masses, \[ \frac{\dot G}{G}=-H_0 \sim 7\times 10^{-11}\,\mathrm{yr}^{-1} \sim 700\times\text{ LLR}. \] Naive expanding \(R\): already FIRE (M12). Census \(\approx 716\times\).
M13-as-law survives only if one of:
| Ontology | Meaning | |----------|---------| | R-static | Cosmic \(S^3\) radius is not the Hubble flow; expansion is something else | | R-locked | \(R\) is quantized / discrete and sits in a ground state (\(\dot R=0\)) | | R-epoch | M13 is a present-epoch constraint, not a differential-in-time law |
This is the licensed theory residual. A proposed \(R\)-ontology is itself falsifiable once stated (e.g. “expanding \(R\) + constant \(G\)” is already dead). Corollary (not a fourth M13 algebra gate): M16 — Mach sum is baryonic only; adding \(\Omega_m/\Omega_b\) destroys percent contact. Separate [P].4. What theoretical work is for
| Do | Do not | |----|--------| | Say what \(R\) is (static / locked / epoch) | Another local \(511\,\mathrm{keV}\) formula | | Say what Hubble expansion is if \(\dot R\neq H_0 R\) | GE-6 compare; Robin; F1; MCL-1 pixel | | Possibly derive \(\sqrt{6}\) as a law for \(R\) | Invert \(c_\varepsilon^{2}\to\alpha\) | | Keep M13’s three gates honest | Recycle \(H_0=69\) as a cosmology theorem | | GE-J only if a design computes \(\sigma\) | Treat GE-J as an \(m_e\) mint |
R-ONT-0…2: DONE · lock underived · \(\sqrt{6}\) [M]. R-EFF: DONE · ontology unnamed ·a_geom_r_eff_ontology_honesty_freeze.md.
R-XCHECK / R-XCHECK-D: DONE · splice held · directional chips restored.
R-MCR: DONE · PASS_R_MCR_NO_SOLUTION · no one-convention PRIMARY Hubble hit.
R-MCR-2: DONE · PASS_R_MCR2_FAIL_DERIVE_K · remainder \(k\) ruled out as a derivation · one-convention Sciama+\(\alpha\) is \(H_0\sim11\) · published book stays convention-conditional [P].
5. Integrity gates
| Gate | Status | |------|--------| | PASS_THEORY_NAMED | PASS | | PASS_THREE_GATES_NAMED | PASS | | PASS_H0_IN_BAND | PASS (\(68.97\in[66,73]\)) | | PASS_EXT_PLANCK_CLASS | PASS | | PASS_NAIVE_R_FIRE | PASS (M12 held) | | PASS_NO_ME_MINT | PASS | | PASS_GE_LINEAR_STILL_PARK | PASS | | PASS_NO_PROMOTE | PASS | | PASS_INTEGRITY | PASS |
Status:PASS_M13_THREE_GATE_FREEZE
6. Kill board
| ID | Kill | |----|------| | K-AST-1 | M13 sold as free local \(m_e\) theorem | | K-AST-2 | \(H_0=69\) recycled as the only “confirmation” | | K-AST-3 | Expanding \(R=\sqrt{6}\,c/H(t)\) + constant \(G\) | | K-AST-4 | New Compton-pixel / Green-self-energy \(m_e\) factory | | K-AST-5 | Free α from M13 double-copy slogan | | K-AST-6 | Close hold / TOE from this freeze | | K-SC4- / K-GE- | Held |
7. Handoff
| Option | Note | |--------|------| | R-ONT-0 | DONE · spin-2 coherence length | | R-ONT-1 | DONE · lock not derived from C3 · a_geom_r_ont1_lock_results.md | | R-ONT-2 | DONE · \(\sqrt{6}\) stays [M] · a_geom_r_ont2_sqrt6_brick_results.md | | Observe G-H0 / G-EXT | Wait on Hubble resolution; do not retune bricks | | R-MCR-2 remainder \(k\) | DONE · FAIL_DERIVE · coefficient line closed | | GE-J | Still gated (compute \(\sigma\)); not an \(m_e\) programme | | Stop \(m_e\) minting | Default |
8. One-line
§AST: scale from unnamed \(R_{\mathrm{eff}}\); M13 three-gate; remainder k ruled out; \(H_0\simeq69\) convention-conditional [P]; √6 brick; stop naming \(R\); stop minting \(m_e\); no promote.