================================================================================ ANTIPARTICLE PRECISION MEASUREMENTS — SPIN-FOCUSED COMPENDIUM ================================================================================ Compiled: 2026-03-18 Purpose: Comprehensive numerical data on antiparticle spin properties, CPT tests in the spin sector, and anomalies relevant to TLT dimensional boundary predictions. ALL data from published experiments (CERN, Fermilab, PDG). Focus: anything spin-related showing even hints of CPT deviation. Sources: PDG 2025, Nature, Nature Physics, Phys Rev Lett, CERN Courier, Fermilab, BASE/ALPHA/ASACUSA/ALPHA-g collaborations, J-PET. ================================================================================ 1. BASE EXPERIMENT — PROTON vs ANTIPROTON (CERN Antiproton Decelerator) ================================================================================ 1A. CHARGE-TO-MASS RATIO (not directly spin, but foundational CPT test) Best measurement (2022, Nature): (q/m)_pbar / (q/m)_p = 1.000 000 000 003 (16) Fractional uncertainty: 16 parts per trillion (ppt) Previous best: 69 ppt (2015) Improvement factor: 4.3× CPT energy scale probed: 1.96 × 10^-27 GeV (CL 0.68) Result: CONSISTENT WITH CPT. No deviation detected. 1B. MAGNETIC MOMENT (SPIN-DEPENDENT — key measurement) Antiproton magnetic moment (2017/2022, Nature): μ_pbar = −2.792 847 3441 (42) μ_N Fractional precision: 1.5 parts per billion (ppb) at 68% CL Improvement over previous: 350× Proton magnetic moment (comparison value): μ_p = +2.792 847 350 (9) μ_N Fractional precision: 0.3 ppb RATIO (CPT test — should be exactly −1): μ_pbar / μ_p = −1.000 000 (uncertainty at ~1.5 ppb level) RESULT: CONSISTENT WITH CPT INVARIANCE. CPT constraint from magnetic moment comparison: |δμ| < 1.8 × 10^-24 GeV (CPT-violating energy scale bound) Possible CPT-odd dimension-5 splitting: < 6 × 10^-12 Bohr magnetons NOTE ON SPIN CONTENT: The magnetic moment is DIRECTLY a spin observable. It measures the coupling between the particle's spin angular momentum and an external magnetic field. The measurement involves detecting individual spin-flip transitions (Larmor frequency) in a Penning trap. 1C. ANTIPROTON QUBIT — COHERENT SPIN SPECTROSCOPY (2025, Nature) Breakthrough: First antimatter quantum bit demonstrated. - Coherent spin oscillations of a single antiproton maintained for 50 seconds - Previous methods: incoherent spin-flip detection (disturbed by decoherence) - New method: "coherent spin quantum transition spectroscopy" - Technique: suppressed magnetic field fluctuations and measurement interference - Comparison: many matter qubits struggle for milliseconds without error correction Significance for future CPT tests: - Enables 10× to 100× improved precision on antiproton magnetic moment - BASE-STEP upgrade could achieve spin coherence 10× longer (500+ seconds) - Will push CPT tests in the spin sector to sub-ppb level IMPORTANT FOR TLT: This is the most sensitive spin probe of antimatter. If spin geometry is modified near a dimensional boundary, this is where a signal would first appear as the precision improves. ================================================================================ 2. ALPHA EXPERIMENT — ANTIHYDROGEN SPECTROSCOPY (CERN) ================================================================================ 2A. GROUND-STATE HYPERFINE SPLITTING (spin-dependent) Hydrogen HFS (established value): ν_HFS(H) = 1,420,405,751.768 (1) Hz (The famous 21-cm line; precision: ~1 part in 10^12) Antihydrogen HFS (ALPHA, 2017, Nature): ν_HFS(H-bar) = 1,420.4 ± 0.5 MHz = 1,420,400,000 ± 500,000 Hz Relative precision: ~3.6 × 10^-4 (360 ppm) Based on: 194 detected antihydrogen atoms RESULT: CONSISTENT WITH HYDROGEN within 360 ppm uncertainty. WHAT HYPERFINE SPLITTING MEASURES: The interaction between the NUCLEAR SPIN (antiproton) and the ELECTRON SPIN (positron) in antihydrogen. This is a PURE SPIN observable — it depends on both particle spins and their coupling. Any modification of spin geometry would directly alter this frequency. CURRENT PRECISION GAP: 360 ppm (antihydrogen) vs ~10^-12 (hydrogen) → Room for improvement: factor of ~10^8 before matching hydrogen precision → This gap is where TLT predicts potential signal could hide 2B. 1S-2S TRANSITION — HYPERFINE COMPONENTS (2024/2025, Nature Physics) New result: Simultaneous observation of BOTH accessible hyperfine components of the 1S-2S transition in trapped antihydrogen. Key advance: - Previous: could only characterize one hyperfine component at a time - Now: both components measured in a single 1-day run (70× faster) - Determined the 2S hyperfine splitting in antihydrogen - Used results to constrain CPT-violating coefficients in the Standard Model Extension (SME) framework Specific CPT constraints: Constrained SME coefficients for the antiproton and positron sectors. (Exact numerical bounds are in the Nature Physics supplementary data.) SIGNIFICANCE: This is the first measurement of the 2S hyperfine structure of antihydrogen, providing NEW spin-dependent observables for CPT tests. 2C. ASACUSA EXPERIMENT — IN-BEAM HYPERFINE SPECTROSCOPY Hydrogen beam measurement (proof of concept): ν_HFS(H, beam) = 1,420,405,748.4 (3.4)(1.6) Hz Relative precision: 2.7 × 10^-9 (2.7 ppb) Method: Rabi-type spectroscopy of antihydrogen beam (not trapped) Antihydrogen beam measurement: NOT YET ACHIEVED. Status: Apparatus validated with hydrogen to ppb level. Next: Apply same technique to antihydrogen beam. Advantage over ALPHA: beam method potentially allows different systematics. TARGET: Ground-state HFS of antihydrogen at ppb level using beam method. ================================================================================ 3. ELECTRON/POSITRON g-2 — ANOMALOUS MAGNETIC MOMENT ================================================================================ 3A. ELECTRON g-2 (most precise particle property ever measured) Latest measurement (2023, Gabrielse group, Northwestern, PRL): a_e = (g-2)/2 = 0.001 159 652 180 59 (13) Absolute uncertainty: ±1.3 × 10^-13 Fractional precision: 0.13 ppt (parts per trillion) Improvement: 2.2× over previous 14-year-old record (also by Gabrielse) QED prediction (using independent α): Agrees to better than 1 part in 10^12 → Most precisely verified prediction in all of physics Fine structure constant derived: α^-1 = 137.035 999 166 (15) [0.11 ppb] 3B. POSITRON g-2 (the CPT partner) Best measurement (Dehmelt & VanDyck, 1987): The electron/positron g-factor comparison: (g_e+ − g_e−) / g_avg = (−0.11 ± 0.12) × 10^-8 → Consistent with zero: NO CPT violation detected at 10^-8 level CRITICAL GAP: The positron g-2 is known to ~10^-8 relative precision, while the electron g-2 is known to ~10^-13. This is a factor of 100,000 difference in precision. Future plans (Gabrielse group): - New Penning trap built for BOTH electron and positron measurements - Goal: improve positron magnetic moment by factor of 150 - Goal: improve electron magnetic moment by factor of 10 - Same apparatus → direct CPT comparison → most precise lepton CPT test - Expected precision: ~10^-11 or better for the difference WHAT g-2 MEASURES (spin interpretation): The anomalous magnetic moment measures how a particle's SPIN precesses in a magnetic field relative to its orbital motion. Specifically: - A Dirac particle with g=2 has spin precession = cyclotron frequency - The anomalous part (g-2) arises from quantum loop corrections - Virtual particles in the vacuum modify how the spin couples to B fields - This is fundamentally a SPIN PRECESSION measurement TLT RELEVANCE: The 10^5 precision gap between electron and positron g-2 is the single largest unexplored window for CPT violation in the spin sector of leptons. The upcoming Gabrielse experiment will close this gap. ================================================================================ 4. MUON g-2 — THE (FORMER?) ANOMALY ================================================================================ 4A. EXPERIMENTAL RESULT (Final — Fermilab, June 2025) Combined Runs 1-6 (final result): a_μ(exp) = 116 592 070.5 (11.4)(9.1)(2.1) × 10^-11 Statistical uncertainty: ±11.4 × 10^-11 Systematic uncertainty: ±9.1 × 10^-11 External uncertainty: ±2.1 × 10^-11 Total uncertainty: ±14.7 × 10^-11 (combined in quadrature) Fractional precision: 127 ppb (surpassed design goal of 140 ppb) Dataset: ~100 billion muon decay events (2018-2023) World average (BNL + Fermilab combined): a_μ(world avg) = 116 592 071 (25) × 10^-11 [approximate] 4B. THEORETICAL PREDICTIONS — THE SPLIT 2020 Theory Initiative White Paper (data-driven HVP): a_μ(SM, 2020) = 116 591 810 (43) × 10^-11 → Deviation from experiment: 5.1σ (this was the "anomaly") 2025 Theory Initiative Update (lattice QCD HVP): a_μ(SM, 2025) = 116 592 033 (62) × 10^-11 → Deviation from experiment: (70705 - 92033)/√(147² + 620²) ≈ 0.6σ → THE ANOMALY EFFECTIVELY DISAPPEARS with lattice QCD prediction. BMW Lattice calculation (2021, pioneering): a_μ(BMW) was the first lattice result suggesting higher HVP → less tension Subsequent lattice groups (RBC/UKQCD, Mainz, ETMC) confirmed BMW's direction The 2025 Theory Initiative formally adopted lattice QCD as the primary method CMD-3 complication: A new e+e- → π+π- cross-section measurement from CMD-3 (Novosibirsk) is INCONSISTENT with previous data-driven approaches at ~5σ level. This tension between data-driven evaluations makes the old approach unreliable, further motivating the shift to lattice QCD. 4C. CURRENT STATUS Experiment vs. lattice QCD theory: ~0.6σ → NO SIGNIFICANT ANOMALY Experiment vs. old data-driven theory: ~5.1σ → APPEARS ANOMALOUS The community consensus is shifting toward "resolved by improved theory" but NOT yet definitive. The theoretical uncertainty (530 ppb) exceeds the experimental uncertainty (127 ppb) by a factor of ~4. UNRESOLVED QUESTION: The data-driven and lattice QCD approaches give incompatible results for the HVP contribution. Understanding WHY they disagree is itself a major open problem. 4D. SPIN INTERPRETATION OF MUON g-2 The experiment measures the anomalous spin precession frequency ω_a: ω_a = (a_μ × e × B) / (m_μ × c) Procedure: 1. Polarized muons (spin aligned with momentum) injected into storage ring 2. 1.45 T uniform dipole magnetic field bends orbits 3. Spin precesses faster than momentum by the anomalous amount a_μ 4. Muon decays: e± emitted preferentially along spin direction 5. Calorimeters detect high-energy positrons vs. time 6. Oscillation frequency of detection rate = ω_a The entire measurement is fundamentally about HOW SPIN RESPONDS TO A MAGNETIC FIELD. Any modification to spin geometry (such as a 4D contribution near a dimensional boundary) would directly alter ω_a. ================================================================================ 5. ANTIHYDROGEN GRAVITY — ALPHA-g ================================================================================ 5A. FIRST MEASUREMENT (2023, Nature) Result: a_g(H-bar) = [0.75 ± 0.13(stat+syst) ± 0.16(sim)] × g Combined uncertainty: ~20% of g (not 75% — see note below) g = 9.81 m/s² (local) CORRECTION ON "75%": The measured value is 0.75g, but this does NOT mean "75% precision." The measurement is CONSISTENT with 1g within ~1.3σ. The precision (uncertainty/value) is approximately 25-30%. Key conclusions: - Antimatter falls DOWN (rules out repulsive gravity at >100σ) - Magnitude consistent with |a_g| = g (General Relativity prediction) - Cannot yet distinguish a_g = 0.75g from a_g = 1.0g at high significance 5B. IMPROVED MEASUREMENTS (2024-2025) Status: - Laser cooling of antihydrogen implemented in ALPHA-g (2024) - Over 2 million antihydrogen atoms produced in 2023-24 runs - Previous: ~100 atoms per experimental cycle Near-term precision target: 1% (a_g to ±0.01g) Method: laser-cooled antihydrogen in quantum superposition states Timeline: expected within 2-3 years Long-term precision target: beyond 1% Method: anti-atomic fountains, anti-atom interferometry Future experiment: HAICU at TRIUMF (Vancouver) 5C. TLT RELEVANCE The framework predicts gravity IS the dimensional mechanism. If 4D structure influences 3D physics, antimatter gravity is a prime detection channel because: 1. Antimatter (spin-reversed in 4D interpretation) couples to gravity 2. The Weak Equivalence Principle (WEP) for antimatter is untested at high precision 3. Any WEP violation for antimatter would be a direct signal of non-standard spin-gravity coupling 4. Current precision (~20%) leaves enormous room for small deviations PREDICTION WINDOW: A deviation at the 1% level or below would be invisible in current data but detectable in the next-generation experiments. ================================================================================ 6. POSITRONIUM — SPIN STATES AND CPT TESTS ================================================================================ 6A. POSITRONIUM SPIN STATES Para-positronium (p-Ps): spin singlet (S=0, antisymmetric) Decay: 2γ Lifetime: 125 ps = 0.125 ns QED prediction: 124.4 ps (O(α²) corrections included) Ortho-positronium (o-Ps): spin triplet (S=1, symmetric) Decay: 3γ (charge conjugation symmetry forbids 2γ) Lifetime: 142.05 ± 0.02 ns QED prediction: 7.0401 (11) μs^-1 decay rate → 142.0 ns Experimental decay rate: 7.0401 (11) μs^-1 AGREEMENT: Theory and experiment match at ~100 ppm level. HISTORICAL "o-Ps LIFETIME PUZZLE" (1990s): Earlier measurements showed a persistent ~0.1% discrepancy with QED. RESOLVED: The discrepancy was traced to unthermalised positronium in the experimental setup, not to new physics. Current status: NO anomaly in positronium lifetimes. 6B. CPT TESTS WITH POSITRONIUM (J-PET, 2021-2025) J-PET detector (Jagiellonian-PET, Krakow): Tests CPT using angular correlations of o-Ps → 3γ decay photons. The CPT-sensitive observable involves positronium SPIN direction correlated with decay photon momenta. Best result (2025, Phys Rev D): CPT-violating asymmetry amplitude: −0.000 29 ± 0.000 22 (stat) → CONSISTENT WITH ZERO (CPT conserved) Precision: 2.2 × 10^-4 Improvement: 4× over previous best measurement Dataset: 356 days of data, 47.8 million o-Ps → 3γ events Earlier result (2024, Nature Communications): Discrete symmetries tested at 10^-4 precision using LINEAR POLARIZATION of photons from positronium annihilations. → All consistent with exact CPT symmetry. SPIN CONTENT: The J-PET measurement directly involves the positronium SPIN POLARIZATION axis. The experiment determines spin direction without an external magnetic field, using the positronium emission geometry. ================================================================================ 7. SPIN-STATISTICS AND ANTIPARTICLES ================================================================================ 7A. DO ANTIPARTICLES OBEY THE SPIN-STATISTICS THEOREM? Theoretical status: YES, rigorously. The CPT theorem and the spin-statistics theorem are deeply linked in relativistic quantum field theory. Both follow from: 1. Lorentz invariance 2. Locality (causality) 3. Positive-definite energy (stable vacuum) If antiparticles exist (required by CPT), they MUST obey the same spin-statistics connection as their particle counterparts. Experimental status: No violations detected. Best test (2010, Berkeley Lab): 100 billion to one confidence level that spin-statistics is obeyed. However, this test was primarily for matter particles (bosons vs fermions), not specifically for antiparticle spin-statistics. DIRECT TESTS FOR ANTI-FERMIONS: No dedicated high-precision test exists specifically for whether anti-fermions are spin-1/2. The evidence is INDIRECT: 1. Positron behaves as spin-1/2 in all g-2 measurements 2. Antiproton spin-flip transitions in Penning traps are consistent with spin-1/2 behavior 3. Antihydrogen spectroscopy (hyperfine splitting) is consistent with spin-1/2 constituents 4. Pair production (e+e- → γγ) angular distributions confirm spin-1/2 GAP: There is no experiment that has DIRECTLY measured the spin of an antiparticle to the same precision as the spin-statistics theorem tests for matter. This is an untested assumption at the highest precision. ================================================================================ 8. CURRENT ANOMALIES/TENSIONS AND THEIR SPIN CONTENT ================================================================================ 8A. MUON g-2 → SPIN OBSERVABLE: YES (directly) Status: LARGELY RESOLVED by lattice QCD (see Section 4) Residual: 0.6σ (theory uncertainty dominates) Spin content: Entirely spin-dependent (spin precession measurement) 8B. W BOSON MASS → SPIN OBSERVABLE: INDIRECT CDF (2022): M_W = 80,433.5 ± 9.4 MeV (7σ above SM) ATLAS (2023): M_W = 80,366.5 ± 15.9 MeV (consistent with SM) CMS (2024): M_W = 80,360.2 ± 9.9 MeV (consistent with SM) SM prediction: M_W = 80,357 ± 6 MeV Status: CDF is the OUTLIER. ATLAS + CMS agree with SM. Spin content: The W boson is spin-1. Its mass is not a direct spin observable, but spin-1 propagator structure affects mass renormalization. The anomaly appears to be an experimental systematic in CDF, not new physics. 8C. B-MESON ANOMALIES → SPIN OBSERVABLE: YES (angular distributions) R(K) ratio (electrons vs muons in B decays): Previous: ~3σ deviation from lepton universality Updated (2023): RESOLVED — additional backgrounds found in electron channel Current: Consistent with SM within improved analysis R(K*), angular observables: Still show 2.2-2.5σ tensions in some bins These involve ANGULAR DISTRIBUTIONS of decay products, which are sensitive to spin correlations and polarization effects Status: MOSTLY RESOLVED, some residual tensions at ~2σ (not significant) 8D. PROTON RADIUS PUZZLE → SPIN OBSERVABLE: NO (charge radius) Muonic hydrogen: r_p = 0.84087 ± 0.00039 fm Electronic hydrogen (recent): converging toward muonic value PDG 2022 consensus: r_p = 0.8408 ± 0.0004 fm Previous tension: ~7σ between muonic and electronic measurements Current status: LARGELY RESOLVED by improved electronic measurements Spin content: The proton radius is a CHARGE distribution observable, not a spin observable. However, the muonic hydrogen involves the muon spin-orbit coupling, and any spin-dependent correction would appear here. 8E. SUMMARY: WHICH ANOMALIES ARE SPIN-RELATED? DIRECTLY spin-related: ✓ Muon g-2 (spin precession) → resolving ✓ B-meson angular observables (spin correlations) → mostly resolved ✓ Antiproton magnetic moment (spin-flip) → consistent with CPT INDIRECTLY spin-related: ~ W boson mass (spin-1 particle mass) → likely CDF systematic ~ Proton radius (spin-orbit corrections) → resolving NOT spin-related: ✗ Neutrino masses (mass, not spin) — but see below ✗ Dark matter (unknown spin) — no direct connection yet NEUTRINO NOTE: Neutrino oscillations prove neutrinos have mass, which is NOT predicted by the minimal SM. The Dirac vs Majorana nature of neutrinos IS a spin question (is the neutrino its own antiparticle?). Neutrinoless double beta decay experiments (LEGEND, nEXO, KamLAND-Zen) are searching for this. NO positive signal yet. ================================================================================ 9. CPT VIOLATION SEARCHES — COMPREHENSIVE SPIN-SECTOR BOUNDS ================================================================================ 9A. STANDARD MODEL EXTENSION (SME) FRAMEWORK The SME parameterizes ALL possible Lorentz/CPT violations as additional terms in the Standard Model Lagrangian. CPT-violating terms necessarily also violate Lorentz symmetry. Spin-dependent CPT-violating operators in the SME: - b_μ coefficients: couple to fermion spin (axial-vector) - d_μν coefficients: spin-momentum coupling - H_μν coefficients: spin-spin coupling modifications Current bounds on b_μ (spin-coupled CPT violation): Electron sector: |b_e| < 10^-31 GeV (from torsion balance experiments) Proton sector: |b_p| < 10^-27 GeV (from hydrogen maser comparisons) Neutron sector: |b_n| < 10^-33 GeV (from co-magnetometer experiments) Antiproton: |b_pbar| < 1.8 × 10^-24 GeV (from BASE magnetic moment) NOTE: The antiproton bound is 3-9 ORDERS OF MAGNITUDE weaker than the best matter-sector bounds. This is the precision frontier for antimatter spin-sector CPT tests. 9B. PENNING TRAP g-FACTOR COMPARISONS Proton vs antiproton g-factor: g_p = 5.585 694 6893 (16) [0.3 ppb] g_pbar = 5.585 694 713 (84) [~15 ppb based on best μ measurement] Ratio: consistent with 1 at ppb level Electron vs positron g-factor: (g_e+ − g_e−) / g_avg = (−0.11 ± 0.12) × 10^-8 → |Δg/g| < 2 × 10^-9 (95% CL) → Next generation (Gabrielse): expected |Δg/g| < 10^-11 9C. MATTER-ANTIMATTER MASS COMPARISONS (complementary to spin) Proton vs antiproton mass: identical to 16 ppt (BASE, 2022) Electron vs positron mass: identical to < 8 × 10^-9 (PDG) Kaon vs anti-kaon mass: |Δm/m| < 8 × 10^-19 (CPLEAR) → This is the MOST precise CPT test by mass, but in the meson sector 9D. "UNEXPLAINED RESIDUALS" — DO ANY EXIST? After exhaustive search of published data: NO STATISTICALLY SIGNIFICANT CPT violations have been found in ANY spin observable for ANY antiparticle system. However, there are PRECISION GAPS where violations could hide: 1. Positron g-2 vs electron g-2: gap of 10^5 in precision Current: |Δg/g| < 2 × 10^-9 Electron precision: 1.3 × 10^-13 → Violations between 10^-9 and 10^-13 would be INVISIBLE 2. Antihydrogen HFS vs hydrogen HFS: gap of 10^8 in precision Current: 360 ppm vs ~10^-12 → Violations between 10^-4 and 10^-12 would be INVISIBLE 3. Antiproton magnetic moment vs proton: gap of ~5× in precision Current: 1.5 ppb vs 0.3 ppb → Closing rapidly with coherent spectroscopy (2025 breakthrough) 4. Antimatter gravity: gap of 10^2 from current 20% to target 1% → WEP violations at the percent level would be INVISIBLE ================================================================================ 10. SUMMARY TABLE — KEY NUMBERS FOR TLT FRAMEWORK ================================================================================ MEASUREMENT VALUE PRECISION CPT STATUS ───────────────────────────────────────────────────────────────────────────────────────────── Antiproton/proton (q/m) 1.000 000 000 003 (16) 16 ppt ✓ CPT OK Antiproton magnetic moment −2.792 847 3441 (42) μ_N 1.5 ppb ✓ CPT OK Antiproton spin coherence 50 seconds (qubit demo) — NEW 2025 Electron g-2 0.001 159 652 180 59 (13) 0.13 ppt — Positron g-2 comparison |Δg/g| < 2 × 10^-9 2 ppb ✓ CPT OK Antihydrogen HFS 1,420.4 ± 0.5 MHz 360 ppm ✓ CPT OK Antihydrogen 2S HFS measured (2024) improving ✓ CPT OK Muon g-2 (experiment) 116 592 070.5 (14.7) × 10^-11 127 ppb — Muon g-2 (lattice SM theory) 116 592 033 (62) × 10^-11 530 ppb ~0.6σ Muon g-2 (old data-driven theory) 116 591 810 (43) × 10^-11 370 ppb ~5.1σ Antimatter gravity (a_g/g) 0.75 ± 0.13 ± 0.16 ~20% ✓ consistent o-Ps decay rate 7.0401 (11) μs^-1 100 ppm ✓ CPT OK o-Ps CPT asymmetry (J-PET) −0.00029 ± 0.00022 2.2 × 10^-4 ✓ CPT OK W boson mass (CMS, 2024) 80,360.2 ± 9.9 MeV 120 ppm SM OK W boson mass (CDF, 2022) 80,433.5 ± 9.4 MeV 120 ppm 7σ OUTLIER ═══════════════════════════════════════════════════════════════════════════════════════════════ BOTTOM LINE FOR TLT: 1. NO CPT violation has been detected in any spin observable — but the precision frontier for ANTIMATTER spin measurements lags matter by 10^3 to 10^8 depending on the system. 2. The muon g-2 "anomaly" is largely resolved by lattice QCD, removing what was the most prominent spin-related tension in particle physics. 3. The THREE MOST PROMISING WINDOWS for detecting spin-geometry effects: a) Positron g-2 (factor 10^5 precision gap vs electron) b) Antihydrogen hyperfine splitting (factor 10^8 gap vs hydrogen) c) Antimatter gravity (currently 20%, target 1%) 4. The 2025 antiproton qubit breakthrough (BASE) is a game-changer: coherent spin spectroscopy will push antiproton magnetic moment precision by 10-100×, directly probing the spin sector. 5. If TLT predicts that spin geometry is modified near a dimensional boundary, the signal would most likely appear as: a) A tiny CPT violation in antiproton or positron magnetic moments b) A deviation in antihydrogen hyperfine splitting c) An anomalous component in antimatter gravitational acceleration All three are being actively measured with rapidly improving precision. ================================================================================