Appendices

Appendix V: The Prediction Registry

V.1 The Falsification Contract

To ensure scientific integrity and prevent the retroactive fitting of data, Geometric Consciousness Theory (GCT) formally registers the following physical predictions. This contract defines the exact parameters and thresholds required to falsify the theory's various Tiers.

Table V.1: Candidate Falsification Metrics

Prediction ID	Type	Description	Predicted Value	Falsification Threshold	Timeframe	Tier	Distinguishability Protocol
P.1	Postdiction	Muon Mass	$105.656$ MeV	Outside 100 ppm of the geometric fit; ~21 ppm residual is conditional on SM-equivalent radiative-correction discipline	Immediate	Tier 2 mechanism + Tier 3 integer/residual	Harmonic-ladder mechanism vs fitted parameter
P.2	Postdiction	Proton Mass	$938.417$ MeV	Lattice QCD confirms value outside 500 ppm of $m_e\phi^{15+\phi^{-1}}$ ; current $\sim0.015\%$ residual is Tier 2 mechanism + Tier 3 sheet/exponent handle pending AKN-action closure, with ppm display suppressed for this offset-fitted handle	Long-term	Tier 2 mechanism + Tier 3 handle	Topological winding vs QCD dynamics
P.3	Conditional protocol design	Protocol C XRISM 3.55 keV conditional preregistration; centroid is separate postdiction-status context, not the operative falsifier	$E_c=3.548\pm0.005$ keV context; forward test is Gamma/exposure sensitivity + $W_{\rm int}$ + morphology, where $W_{\rm int}$ is the deconvolved intrinsic line-width residual after instrument and registered kinematic/turbulence deconvolution	Protocol C XRISM 3.55 keV (conditional preregistration design): Decision rule: GCT FALSIFIED at decisive sensitivity if any registered branch holds: (a) NO 3.55 keV line detected at the terminal Bulbul-level empirical-derived floor $\Gamma\lesssim2.0\times10^{-28}\ {\rm s^{-1}}$ in $\geq94$ Ms equivalent stacked exposure, derived from the XRISM 3.75 Ms ten-cluster limit $\Gamma\lesssim1.0\times10^{-27}\ {\rm s^{-1}}$ scaled by $\sqrt{3.75/94}$ , OR (b) detected line has $W_{\rm int}>20$ eV FWHM after instrument and registered kinematic/turbulence deconvolution, OR (c) detected line morphology does NOT follow the stress-gated $\rho_{\rm above\,\sigma_{crit}}^2$ template by $\Delta\chi^2\geq9$ versus both smooth $\rho$ and smooth $\rho^2$ templates. The 26 Ms / $\Gamma\lesssim3.8\times10^{-28}\ {\rm s^{-1}}$ stack remains a morphology-linewidth milestone, not a terminal no-line falsifier of a Bulbul-normalized signal. The background-limited theoretical floor $F_{3\sigma}\approx1.1\times10^{-8}\ {\rm ph\,cm^{-2}\,s^{-1}}$ ( $\Gamma\lesssim1.2\times10^{-30}\ {\rm s^{-1}}$ ) is a non-operative ceiling unless real-stack penalties are controlled; the preregistration must include a per-cell ARF/RMF/background/effective-mass exposure table proving terminal-floor sensitivity after real response, masking, continuum, and stacking losses before the no-line branch is executable as a decisive falsifier. Aperture: mass-weighted stress-gated regions with pre-line $P_{\rm proxy}\ge\sigma_{\rm crit}=0.53\ {\rm keV\,cm^{-3}}$ , where $\sigma_{\rm crit}=\sqrt{(0.07)(4.0)}\ {\rm keV\,cm^{-3}}$ from the Perseus-core / Bullet-shock pressure bracket. Frozen target cells: Bullet bow-shock/Mach shell, Coma merger or radio-relic shells, A2142 cold-front/merger shell, A3667/A2256/A2319 shock or merger shells, and only off-core Perseus/A2029/A1795 annuli whose pre-line maps pass the same cut; relaxed cool cores are sub-threshold calibrators unless their pre-line maps exceed the cut. Low-shear dSph branch separately falsifies stress-gating on a $>3\sigma$ 3.548±0.005 keV line in a registered dSph with $\sigma_v<15$ km/s at the same terminal decay-rate-normalized sensitivity, $W_{\rm int}\le5$ eV, and S1-S6 controls passed. Morphology power at 26 Ms: $B\approx343$ and $3\sqrt{B}\approx55.6$ counts power $\Delta\chi^2\ge9$ for one registered morphology degree of freedom when the pre-line stress template is separated from both smooth templates.	Sensitivity-limited until per-cell table frozen	Tier 2 linewidth/morphology mechanism; centroid context is Tier 3 postdiction	K-XVIII discriminant; shear-map morphology; dSph low-shear null branch
P.4	Prediction	Neutrino Floor	$\Sigma m_\nu=0.0853\pm0.0003$ eV	Canonical registered band (Fork A): $\Sigma m_\nu<0.075$ eV at definitive precision or $\Sigma m_\nu>0.15$ eV; operational survival gate: $\Sigma m_\nu>0.10$ eV at $3\sigma$ over Planck+DESI+CMB lensing keeps biogenic-DE active, while a definitive value in $[0.05,0.10)$ eV is a registered tension/exclusion-zone outcome handled by App NS. The lower gate is set above the normal-hierarchy oscillation floor near $0.059$ eV; the GCT-native $w(z)$ likelihood path is expected to return $\approx0.064$ eV rather than $0.0853$ eV because the registered dark-energy amplitude is too small to import the generic CPL relaxation. DESI 2024 $\Lambda$ CDM $\Sigma m_\nu<0.072$ eV and DESI DR2 $\Lambda$ CDM $\Sigma m_\nu<0.064$ eV are TENSION, not final falsification, pending that native likelihood	DESI DR2 + Euclid DR1	Tier 2 mechanism + Tier 3 conditional remapping	Strict equality vs model-dependent cosmological bound
P.5	Tension	Muon g-2 (HVP arbitration channel)	$\Delta a_\mu\approx250.65\times10^{-11}$	Tier 3 revival path requires a reopened $>3\sigma$ experiment-theory gap near the GCT correction scale under R-ratio/lattice arbitration. A consolidated high-HVP lattice-dominant WP2025-class baseline and CMD-2/CMD-family R-ratio reanalysis context reduce the anomaly and are adverse evidence, not a survival path; current WP2025 baseline registers as adverse evidence because the GCT correction overshoots the consolidated gap by $\sim3.4\sigma$ .	Long-term HVP-synthesis arbitration	Tier 3 fitted/equal-weight $1/5$ coefficient + A3 on top of a geometric mechanism class; tension under WP2025	HVP-synthesis arbitration
P.5b	Consistency Check	Electron g-2 kinematic-threshold null	$\Delta a_e^{\rm lattice}=0$	PENDING-α-RESOLUTION: detection requires resolution of α-input ambiguity between Cs-α and Rb-α determinations; future $	\Delta a_e^{\rm anom}	>10^{-12} $at$ >3\sigma$ robustly across α-input choices falsifies the null	Immediate (α-input contingent)
P.5c	Long-horizon theoretical extrapolation / consistency check	Tau anomalous magnetic moment	$\Delta a_\tau\approx2.50655\times10^{-9}$	Operationally unfalsifiable at current and FCC-ee-target sensitivities; form-factor universality remains O.26-dependent, so this row is not an operative falsifiable prediction until a plausible discriminator exists	Long-horizon	Tier 2 mechanism + Tier 3 universality assumption	FCC-ee tau-g-2 program
P.6	Diagnostic / conditional prediction	Dark-energy phantom direction — ACTIVE TENSION (DES-Dovekie recalibrated DESI registered-menu CLOSURE-FAILS); Euclid/Roman reserved for robustness	$w(z)\le -1$ for the biogenic channel; registered multi-channel shape-proxy menu CLOSURE-FAILS at best diagnostic score ≈4.861 against the DES-Dovekie recalibrated target	DESI + Euclid/Roman produce a 3σ+ CPL detection of $w_0>-1$ and $w_a<0$ with no biogenic-channel fingerprint. This falsifies the registered five-channel state-level shape-proxy menu, not a physical likelihood-weighted multi-fluid prediction and not a no-go theorem over all possible GCT dark-energy channels; a physical prediction requires continuity-evolved $\rho_c(z)$ and the DESI covariance treatment.	DESI + Euclid/Roman	Tier 3 registered-menu caveat	Ch14 §14.6.3 shape-proxy partition; O.13 C1/C2/C3 closure paths
P.6b	Consistency Check	Frozen dark-energy baseline	$w=-1$ baseline	Phason mass extraction differs from $1.7\times10^{-5}$ eV geometrically; specific value conditional on O.1 closure	2030+	Tier 2 mechanism + Tier 3 specific value	Frozen phason mass-gap extraction
P.7	Prediction	PTA $l=6$ anisotropy	$\Delta\Gamma_{\max}\approx1.73\times10^{-4}=\phi^{-18}$	SKA-PTA null at the registered $\hat C_6$ amplitude; confident detection requires template-stacked SKA-era precision	SKA-PTA precision window	Tier 2 mechanism + Tier 3 amplitude pending O.15(b)	Icosahedral harmonic template fit
P.8	Prediction	Anti-Zeno crossover frequency	Branch A $112\pm10$ MHz; Branch B $42\pm10$ MHz	F1 = four-conjunct joint null: no peak in Branch A, no peak in Branch B across the full required 32-200 MHz scan band, no 150 MHz anti-Zeno sign, and no chirality contrast, all after S0-S7 acceptance. Authoritative scan statistic: $M=201{,}600$ trials, $\alpha_{\rm local}\approx1.34\times10^{-8}$ , $N_{T_2,\rm scan}\approx5.1\times10^3$ shots per frequency/bin cell, and $\approx1.03\times10^9$ total shots across the six-cell scan. A single-branch null does not falsify. Frozen NV ensemble: $N_{\rm caps}=50$ caps with $N_{\rm NV}=20$ implanted NV centers per cap, giving $1000$ NV-center observations and shot-noise scaling $1/\sqrt{N_{\rm caps}N_{\rm NV}}$ . CISS floor: pre-unblinding per-cap CD/VCD plus spin-polarimetry is required using $\mu$ SR rotation of injected polarized muons or two-terminal magnetoresistance with a reference unpolarized contact at 4 K; CD/VCD is necessary but not sufficient. Clean F1 requires $r_{\rm transfer}P_{\rm CISS}^{net}\ge0.1$ at $\ge5\sigma$ after cap-to-NV transfer. $0.025\le r_{\rm transfer}P_{\rm CISS}^{net}<0.1$ is Sensitivity-Limited Pending Re-Powering with $N_{\rm shots}\propto1/(r_{\rm transfer}P_{\rm CISS}^{net})^2$ ; below $0.025$ is sensitivity-limited, NOT falsification.	2-5 years; executable after preregistration verifier/package freeze	Tier 2 mechanism + Tier 3 specific branch values (Branch A 112 MHz, Branch B 42 MHz)	Chiral NV-centre + h-BN A-Prime scan
P.8b	Prediction	Coherent THz shadow pulse	$\nu_{\rm leak}\approx380\pm20$ GHz	Direct-detection gate is not reachable at current detector noise floor; modulation-differential falsifier requires absence of anaesthetic-cycle-correlated 360-400 GHz modulation at $>3\sigma$ over $N_{\rm shots}\gtrsim10^5$ cycles	Multi-month modulation-differential; cryogenic upgrade for direct detection	Tier 3	Active vs anaesthetized neural tissue
P.8c	Prediction	Protocol A-Tertius LGI gate	$K_3(\nu_c)>1$ , $K_3(150{\rm MHz})\le1$ , deuterated-Trp suppression	Blinded $K_3(\nu_c)\le1$ at $3\sigma$ after Holm correction across the registered branch window, 150 MHz, and isotope contrasts	Execution conditional on benchmarking	Tier 2 sign pattern + Tier 3 branch value	LGI radical-pair parity readout
P.9	Prediction	Shapley biogenic dipole	$\delta w/w\sim[0.6,1.5]\times10^{-4}$ aligned within $\pm30^\circ$ of Shapley	Post-Roman spatial- $w(z)$ mapping finds no aligned dipole amplitude in the registered $[0.6,1.5]\times10^{-4}$ band at $>3\sigma$	Post-Roman	Tier 3	Biogenic strain orientation
P.10	Alias / implementation row	NV-centre chiral surrogate test (Protocol A-Prime implementation of P.8)	Same Branch A/B + 150 MHz + chirality-contrast decision rule as P.8	Alias row only: see P.8 for the authoritative Protocol A-Prime thresholds, scan statistic, sample-size budget, S0-S7 acceptance, measured per-cap CISS and post-transfer retention floors, 50 caps × 20 NV ensemble, and single-branch-null discipline; readiness and verifier/package-freeze status are identical to P.8.	2-5 years; same readiness as P.8	Tier 2 mechanism + Tier 3 amplitude readout	Alias to P.8 / substrate chirality dependence
P.11	Prediction	CMB $\phi$ -birefringence	6-fold azimuthal birefringence; operational threshold $\beta_{\rm birefringence}>0.1^\circ$ at 3σ	Estimator: TB+EB cross-correlation; falsifying statistic: $\beta_{\rm birefringence}\le0.1^\circ$ at 3σ after Bonferroni correction over 6 azimuthal bins under the Planck PR4 70% galactic mask + foreground residual model; gray zone $0.05^\circ<\beta\le0.1^\circ$ sensitivity-limited; systematic budget: instrument polarization-angle uncertainty $\le0.05^\circ$ ; estimator, mask, bins, foreground model, synthetic-data budget, and OSF/Zenodo package frozen before unblinding	Immediate	Tier 2 prediction + Tier 3 statistical-floor	Planck PR4 TB+EB cross-correlation
P.12	Prediction	FRB azimuthal birefringence	6-fold azimuthal correlation amplitude $>0.05\ {\rm rad}^2$	Estimator: rotation-measure dispersion vs frequency; falsifying statistic: six-fold amplitude $\le0.05\ {\rm rad}^2$ in the CHIME/FRB 1000-burst sample + SKA-Mid 1-year sample after Galactic Faraday residual $\le5\ {\rm rad/m^2}$ control; gray zone $0.025<A_6\le0.05\ {\rm rad}^2$ sensitivity-limited; frozen l=6 sky-angle estimator; sky-angle labels, RM cleaning, estimator code, synthetic-data budget, and OSF/Zenodo package frozen before unblinding	CHIME/FRB + SKA window	Tier 2 prediction + Tier 3 statistical-floor	FRB RM dispersion vs sky angle
P.13	Pilot/Systematics	Anaesthetic-threshold isotope shift	Central $0$ under $n_{rp}=0$ pending O.21; sensitivity branch $\Delta C_{50}/C_{50}\in[-0.20\%,-0.10\%]$ under $n_{rp}=1$	Not an operative falsifier under §16.3.4 systematic budget; quantitative gate deferred until systematics-validated	Protocol D LORR pilot window	Tier 2 mechanism + Tier 4 no-gate systematics study	$^{17}$ O LORR assay
P.13c	Prediction	NMR polarity gate for Protocol D	Active-state $\Delta T_2=T_2(^{17}{\rm O})-T_2(^{16}{\rm O})$	Decision rule (sign-aware): (a) 99% bootstrap CI of $\Delta T_2 = T_2(\mathrm{H}_2{}^{17}\mathrm{O}) - T_2(\mathrm{H}_2{}^{16}\mathrm{O})$ excludes zero, AND (b) $\lvert\Delta T_2\rvert > 3 \cdot \sigma_{\rm measurement}$ , AND (c) $\mathrm{sign}(\Delta T_2)=+1$ ( $T_2$ in ${}^{17}$ O is longer than in ${}^{16}$ O, per the GCT Tier-3 calibration prediction). GCT CONFIRMED on (a)+(b)+(c) jointly only if pilot variance is at or below the verifier-returned 80%-power sigma ceiling for the 5% target. GCT FALSIFIED if (a)+(b) hold but (c) fails. A sign-positive significant effect below 5% is positive-sensitivity / effect-size revision, not confirmation or failure. Operational preregistration: minimum $n=24$ independent biological preparations per isotope condition, three repeated NMR acquisitions per preparation, two-sided $\alpha=0.01$ , $\beta=0.20$ , power target for a 5% active-state polarity reversal, pilot variance gate, dominant $^{17}$ O quadrupolar-relaxation systematic bounded to $\sigma<0.2$ ppm under the frozen relaxation model, S1-S8 systematics required, preregistration package/code/synthetic-data budget frozen before unblinding, and first decisive run targeted for 12-18 months after protocol freeze and isotope-logistics validation.	Protocol D NMR polarity window	Tier 2 mechanism + Tier 3 active-state $\Delta T_2$ calibration anchor pending O.21/O.33	Blinded isotope NMR with S1-S8 systematics
P.17	Postdiction	Higgs VEV scale	$v=m_e\phi^{11}(1+5\alpha+\phi^8\alpha^2)1440\phi$ ; residual ~181 ppm	O.20/O.5/O.14/O.15 closure stack fails to derive the 1440 saturation handle and second-order term; without $\phi^8\alpha^2$ residual is ~2588 ppm	Immediate	Tier 2 mechanism + Tier 3 calibrated handle	App R P.17 / Parameter Ledger VEV
P.36	Consistency Check	Wavefunction-overlap suppression	$(\ell_P/\xi)^3\sim10^{-80}$	200,000 ppm cross-route convention band; row is a consistency check pending a single declared Bohr-Compton/ $\xi$ convention, not a hard biological-overlap falsifier	current	Tier 2 wavefunction-overlap mechanism	App FM P.36 / App R
P.37	Consistency Check	$f_{\rm bound}$ conservative geometry	Central $0$ under $n_{rp}=0$ pending O.21; sensitivity branch $[1.0,2.0]\times10^{-3}$ under $n_{rp}=1$ local Trp21 branch	Outside O.21/O.33 conservative band after assembled-MT geometry + hydration-shell validation	Protocol A-Prime	Tier 3 biological substrate value	ARITHMETIC-CONSISTENT; biology pending O.21+O.33
P.47	Consistency Check	Polaron Unity trefoil/operator bridge	Trefoil-case unity conditional on Y.6.3 closure stack	Failure of O.18 fixed-slice reduction, finite-quotient meridian trace, Anderson-Putnam-to-knot-complement extension, O.35 trivial-amenable-radical, O.36 primary representation hypothesis, O.32 KO-dimension sign verification, or direct-product/operator-factor non-factorization	Current trefoil; long-horizon general-prime extension	Tier 3 conditional	App Y §Y.6.3 / O.18 / O.35 / O.36 / O.32

Note on P.3: Status: Sensitivity-limited (terminal no-line branch pending per-cell table). XRISM has stacked 3.75 Ms across 10 clusters and did not resolve the 3.55 keV line. The upper limit on the decay rate ( $\Gamma \lesssim 1.0 \times 10^{-27}\ \mathrm{s}^{-1}$ ) is 5× weaker than the Bulbul et al. XMM-Newton detection. Naive exposure scaling gives a 26 Ms morphology-linewidth milestone $\Gamma \lesssim 3.8 \times 10^{-28}\ \mathrm{s}^{-1}$ and a terminal Bulbul-level no-line floor $\Gamma \lesssim 2.0 \times 10^{-28}\ \mathrm{s}^{-1}$ at 94 Ms equivalent; the background-limited $\Gamma \lesssim 1.2 \times 10^{-30}\ \mathrm{s}^{-1}$ calculation is a theoretical ceiling, not the decisive gate. Until the per-cell ARF/RMF/background/effective-mass exposure table is frozen, the terminal no-line branch is preregistered but not executable as a decisive falsifier. The current package supports sensitivity-limited constraints plus morphology/linewidth milestones; deeper observations are needed.

[!WARNING] K-XVIII Contamination Flag (3.514 keV) [Tier 2 Conditional]: The formal centroid-context window is $E_c = 3.548 \pm 0.005$ keV; the broader "3.5 keV line complex" language is only an informal search-band shorthand. This lies perilously close to the Potassium K-XVIII atomic transition line at 3.514 keV. While pristine microcalorimeter spectral resolution (XRISM Resolve $\sim 5$ eV FWHM at 3.55 keV per Ishisaki et al. 2022, Proc. SPIE 12181:121811S (DOI 10.1117/12.2630654); Athena X-IFU $\sim 2.5$ eV) can in principle resolve the separation (ΔE ≈ 36 eV), thermal broadening in hot clusters (T > 5 keV) can blend these lines. Ruling: Any future detection of a line complex near 3.5 keV must explicitly fit and subtract the K-XVIII flux model before the residual can be claimed as the GCT 3.55 keV topological signal.

Note on P.5: The physical parameter depends on the HVP synthesis. The row becomes a live survival test only if R-ratio/lattice arbitration reopens a material experiment-theory gap. It fails as load-bearing evidence if consolidated HVP synthesis definitively matches the WP2025-class high-HVP baseline and no dispersive/lattice arbitration gap remains. Note on P.6: The operative principled V7' Class-2 envelope is $|\Delta w_{\rm bio}(z{=}0.28)| \in [2,5]\times10^{-5}$ , with clean Roman/DESI distinguishability only at the joint low- $z$ precision floor. The broad empirical logistic ansatz threshold $|w(z)+1| > 10^{-3}$ is retained only as a disfavored comparison branch, not the registered P.6 falsification amplitude. The underlying $w(z)$ asymptotes to $-1$ from below without crossing the $w=-1$ boundary (see Ch14 §14.6.3). The $w = -1$ baseline (P.6b) is a Tier 2 frozen-phason-vacuum mechanism; the specific $m_{\rm phason}$ value is Tier 3 conditional on O.1 closure. Note on P.7: the $l=6$ harmonic form is Tier 2, while the specific $\Delta\Gamma_{\max} \approx \phi^{-18} \approx 1.73 \times 10^{-4}$ amplitude is Tier 3 pending O.15(b). The amplitude sits below the current NANOGrav 15yr sensitivity floor of $\sim 10^{-3}$ ; theoretical template stands but matched-filter detection awaits SKA-PTA-era precision. Falsification of the $C_6/C_0$ form requires $|\hat C_6/C_0| < 2.9 \times 10^{-8}$ at SKA-PTA precision.

Scope note on P.9 (Shapley biogenic dipole amplitude): The dipole amplitude $\delta w/w \sim [0.6,1.5]\times10^{-4}$ is the self-consistent value implied by the V7' Class-2 envelope of Ch14 §14.6.3 (cosmic-mean $|\Delta w(z{=}0.28)| \in [2, 5] \times 10^{-5}$ ) scaled by the realistic biogenic overdensity factor $\delta_{bio} \in [1, 3]$ at Shapley scale (Local Sheet to Laniakea filament density). Amplitudes above this band would require $\delta_{bio}$ outside the realistic-overdensity ceiling that governs the framework's $w(z)$ predictions throughout V2 Ch14. The Shapley amplitude sits below DESI spatial-mapping sensitivity on the registered 2030 horizon; positive falsification requires a post-Roman successor mission with sub- $10^{-4}$ all-sky $w(z)$ -map precision. The prediction therefore functions as a post-Roman successor amplitude target rather than a near-term gate; the qualitative dipole-orientation prediction (toward Shapley / Great Attractor) remains the operative near-term observable in Ch14 §14.4.1.

Muon g-2 HVP Condition: The GCT icosahedral vertex correction ( $\Delta a_\mu \approx 250.65 \times 10^{-11}$ , using $\alpha_{\rm CODATA}$ as A3 and the Tier 3 equal-weight $1/5$ coefficient) is not robust confirmation under the current world-average synthesis. A consolidated high-HVP lattice-dominant WP2025-class baseline and CMD-2/CMD-family R-ratio reanalysis context reduce the anomaly and are adverse evidence, not a survival path. The channel re-enters decisive-test status only if R-ratio/lattice arbitration reopens a $>3\sigma$ experiment-theory gap compatible with the GCT offset. Current WP2025 baseline registers as adverse evidence because the GCT correction overshoots the consolidated gap by $\sim3.4\sigma$ .

V.2 Formal Pre-registration Registry

V.2.1 PTA l=6 Performance Package

Prediction ID: P.I.PTA Datasets: NANOGrav 15yr + PPTA DR3 + EPTA DR2 Target Signal: $l=6$ anisotropy with $\Delta\Gamma_{\max} \approx 1.73 \times 10^{-4}$ ( $\phi^{-18}$ ) at the icosahedral characteristic angles; equivalent linear projection $\hat C_6 \approx 1.67 \times 10^{-4}$ and squared ratio $C_6/C_0 \approx 2.90 \times 10^{-8}$ — see Ch21 §21.7 for normalization. Decision Criterion: Combined Bayesian Ĉ₆ / σ(Ĉ₆) ≥ 3.0. Blinding: Pipeline deposited on arXiv before data inspection; arXiv timestamp = registration date. Falsification Bond: |Ĉ₆| < 10⁻⁴ at 3σ falsifies the icosahedral vacuum claim (§21.7).

V.3 Epistemic Governance

Hard Falsification (Tier 2)

Hard Falsification — per-row gates:

The GCT core architecture is hard-falsified if ANY of the following per-row tolerances is exceeded by $\geq 1$ independent precision measurement:

Muon mass $m_\mu$ outside 100 ppm of $m_e \cdot \phi^{11} \cdot (1 + 5\alpha + \phi^8\alpha^2)$ (registry P.1; verify_muon_mass.py).
Proton mass $m_p$ outside 500 ppm of $m_e \cdot \phi^{15 + \phi^{-1}}$ (registry P.2; verify_proton_mass.py).
Bare fine-structure $\alpha^{-1}$ outside 5000 ppm of $\alpha^{-1}=137.035\ldots$ times the geometric correction depending on $D=18$ stiffness plus the $1/(2N)$ bilayer term; see App M §M.7.1 for the bare derivation and registry P.13b for the explicit gate.
Bilayer-corrected $\alpha^{-1}$ outside 100 ppm of the corrected formula (registry P.1d).
Tau mass $m_\tau$ outside 55 ppm of $m_e \cdot \phi^{17} \cdot (1 - 3.6\alpha)$ (registry P.1b; tri-state: 0-50 PASS, 50-55 AT-GATE TENSION, $\geq55$ FAIL).

There is no single aggregate "precision window" — each gate is row-specific.

Soft Falsification (Tier 3)

Soft Falsification: a null Isotope-Shift result is operationally inconclusive (Protocol D LORR is no-gate per Ch16 §16.4); a null is interpretable as either (a) the biophysical model is wrong OR (b) the protocol systematic budget exceeded the predicted signal. Definitive falsification requires Protocol A-Prime + NMR polarity gate (Protocol D §16.5). Biogenic Dark Energy remains governed by the P.6/P.4 joint gates above.

V.4 Consensus Requirement

The GCT Golden Master delivers a structurally complete mass spectrum: every observed fundamental mass is identified with a specific topological/spectral object in the framework. Mass-sector OPEN ITEMS that prevent calling this a "closed" theory: (1) down-quark R=2 baseline 197,216 ppm tension vs PDG (pending O.5 + AKN-action); (2) charm mass + higher CKM angles $s_{13}$ , $s_{23}$ remain Tier 3 calibrated ansätze (pending O.5); (3) P.4 neutrino-sum $\Sigma m_\nu$ in tension with Planck+DESI bounds (pending GCT-native CMB+BAO+LSS likelihood); (4) P.47 general-prime Polaron Unity is Tier 3 conditional pending O.35/O.36 closure. Structural-completeness is not closed-theory; see App H for the operative open-problem inventory. Revisions to the Tier 2 registry require independent verification by the international physics community.