G-Zero: Exploring Zero-Regime Phenomena

• G-Zero is a term describing several zero-limit regimes characterized by vanishing control parameters in contexts such as microgravity, zero-gap semiconductors, zero-phonon emission, verifier-free machine learning, and constant gravitational solutions.
• In microgravity experiments, G-Zero enables precise control of near weightless dynamics via air-bearing platforms and parabolic flight regimes, achieving stabilization within tight error thresholds.
• In semiconductor and quantum photonics applications, G-Zero governs extreme tuning of g-factor limits, enhanced optical emission, and innovative forward-only optimization in large language model training.

G-Zero is a recurrent research label rather than a single doctrine. In current technical usage it denotes several distinct “zero” regimes: microgravity or “Zero-G” operation in space analogs and parabolic flight experiments, semiconductor regimes associated either with the zero-gap limit or with a Landé $g$-factor tuned toward zero, the zero-phonon line of silicon G centers, verifier-free generation from zero data in large-language-model training, and higher-dimensional cosmological solutions with zero variation of the effective gravitational constant $G$ (Ramezani et al., 2024, Bittermann et al., 2023, Jiang et al., 2023, Chung et al., 2020, Lefaucher et al., 2022, Huang et al., 11 May 2026, Ivashchuk, 2016).

1. Terminological scope

Across the cited literature, “G-Zero” and the closely related “Zero-G” are domain-specific terms tied to different observables. In space systems and airborne experiments, the term refers to operational microgravity: either near-frictionless planar motion on an air-bearing floor or ballistic flight segments in which the net acceleration fluctuates around $0\,g$ (Ramezani et al., 2024, Bittermann et al., 2023). In semiconductor physics, the phrase is attached to two different limits: a zero-gap regime in InAsSb, where multiband Kane physics produces a gigantic effective $g$-factor, and a GaAs two-dimensional electron system tuned by hydrostatic pressure toward $g \simeq 0$ (Jiang et al., 2023, Chung et al., 2020).

In integrated quantum photonics, G-Zero denotes the zero-phonon emission of the silicon G center, specifically the zero-phonon line at about $1278$ nm (Lefaucher et al., 2022). In machine learning, "G-Zero" names a verifier-free co-evolutionary framework for open-ended generation from zero data, while a separate computational usage expands the term into Group-Relative Zeroth-Order Optimization for forward-only LLM fine-tuning (Huang et al., 11 May 2026, Tan et al., 1 Jun 2026). In cosmology and additive combinatorics, the term is tied, respectively, to zero variation of the effective gravitational constant and to zero-sum invariants such as $g(G)$ and $C_0(G)$ (Ivashchuk, 2016, Krishnamoorthy et al., 2020, Fan et al., 2011).

A recurring pattern is the use of “zero” to indicate a vanishing or suppressed control parameter: gravitational acceleration, band gap, Zeeman scale, phonon participation, external supervision, variation of $G$, or total group sum. This suggests that G-Zero functions less as a unified theory than as a family of technically precise zero-limit constructions.

2. Microgravity control and quantum experiments

In the Zero-G Lab at the University of Luxembourg, G-Zero denotes a microgravity analog built around a $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$ facility with an epoxy floor and pressurized air-bearings that create near-frictionless motion. The planar floating platform has three degrees of freedom, $G$0, and is actuated by eight on/off air nozzles capable of up to $G$1 each at $G$2. Six OptiTrack Prime 13W cameras operating at $G$3 measure position and attitude, while the control loop runs at $G$4 and continuous commands are converted to thruster pulses by a PWPF modulator. The dynamics are modeled as

$G$5

with disturbances representing residual floor incline, air currents, imperfect air-bearing behavior, unmodeled couplings, and parameter uncertainty. The controller combines model predictive control with PPO: MPC supplies a $G$6 teacher horizon during training, while the deployed policy is a lightweight PPO feedback controller. The reward penalizes derivative mismatch against the MPC teacher and control effort, plus a terminal stabilization bonus. In experiments with four manual disturbances, PPO-MPC returned the platform to the stabilization condition within the reported thresholds of $G$7 position error and $G$8 rotation, whereas PPO-only showed about $G$9 position error and about $0\,g$0 rotation error (Ramezani et al., 2024).

A second Zero-G usage appears in airborne quantum optics. During parabolic flight, zero-g is operationally realized by ballistic arcs with five segments: steady flight near $0\,g$1, a pull-up into hypergravity of about $0\,g$2–$0\,g$3 and up to approximately $0\,g$4 for about $0\,g$5–$0\,g$6, a transition into the apex, a microgravity interval of about $0\,g$7–$0\,g$8, and a symmetric pull-out. In this setting, a compact entangled-photon source and polarization analysis rack were flown on a modified Airbus A310, and a CHSH Bell test was monitored continuously through hypergravity, transition, and microgravity phases. The reported Bell parameter remained in the interval $0\,g$9, with average $g$0 and average standard deviation $g$1, corresponding to a violation of the local-realistic bound by roughly $g$2 standard deviations on average. Two-sample Kolmogorov-Smirnov tests supported the null hypothesis that the $g$3 values during steady flight, microgravity, hypergravity, and jerk windows were drawn from the same underlying distribution, except for one small-sample case (Bittermann et al., 2023).

These two literatures share an operational view of zero-g. In one case it is a planar air-bearing analog for weakly damped spacecraft dynamics; in the other it is a transient flight regime embedded in repeated $g$4 hyper-g transitions. In both, the central issue is not the literal elimination of gravity but the control or measurement of systems whose dynamics become highly sensitive to small disturbances.

3. Zero-gap and $g$5 regimes in semiconductor physics

One condensed-matter meaning of G-Zero is the zero-gap limit of InAs$g$6Sb$g$7, where strong bowing drives the band gap to very small values and strongly enhances the conduction-band Landé $g$8-factor. In the reported samples, the band-gap bowing parameter is $g$9, and the extracted $g \simeq 0$0 values for $g \simeq 0$1 are $g \simeq 0$2, $g \simeq 0$3, $g \simeq 0$4, $g \simeq 0$5, $g \simeq 0$6, $g \simeq 0$7, and $g \simeq 0$8, respectively. The minimum $g \simeq 0$9 occurs near $1278$0, where the measured lowest-Landau-level $1278$1-factor magnitude at $1278$2 reaches $1278$3, i.e. $1278$4, nearly twice the magnitude of bulk InSb. Near the zero-gap limit, the conventional Roth expression fails because the $1278$5 conduction band and the $1278$6 heavy- and light-hole bands become nearly triply degenerate. In that regime, orbital coupling produces a “relativistic Zeeman effect” with Landau energies dispersing as $1278$7, so that $1278$8; using $1278$9, the model gives $g(G)$0 (Jiang et al., 2023).

A second semiconductor usage moves in the opposite direction, toward a vanishing Zeeman scale. In GaAs two-dimensional electron systems, hydrostatic pressure tunes the bulk $g(G)$1-factor from $g(G)$2 toward zero and even positive values, with $g(G)$3 expected near $g(G)$4. The obstacle is that conventional GaAs/Al$g(G)$5Ga$g(G)$6As heterostructures lose density rapidly with pressure because the charging window $g(G)$7 collapses as donor levels or AlAs cladding states follow the X-band. The reported heterostructure design suppresses this by deriving $g(G)$8 from the confinement energy of a narrow GaAs doping well instead. The demonstrated stack uses a $g(G)$9 main GaAs quantum well, Al$C_0(G)$0Ga$C_0(G)$1As barriers with $C_0(G)$2, spacer thickness $C_0(G)$3, and a $C_0(G)$4 narrow GaAs doping well. Its measured density slope is $C_0(G)$5, compared with $C_0(G)$6 in a reference doping-well structure. At $C_0(G)$7, the sample had $C_0(G)$8 and mobility $C_0(G)$9; extrapolation suggests $G$0 at $G$1, where comparable conventional structures would be depleted (Chung et al., 2020).

These two papers assign G-Zero to different $G$2-factor limits. One concerns giant $G$3 as $G$4; the other concerns direct suppression of $G$5 toward zero at nearly fixed effective mass. This suggests that the label is attached less to the sign or magnitude of $G$6 itself than to a tunable singular regime in band-structure control.

4. G-Zero in integrated quantum photonics

In silicon photonics, G-Zero denotes the zero-phonon emission of the G center, a carbon-related color center formed when two carbon substitutional atoms are bridged by a silicon self-interstitial. Its zero-phonon line lies at about $G$7, in the O-band. The reported silicon-on-insulator platform uses a $G$8 silicon device layer on $G$9 buried oxide. G centers are created by $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$0 carbon implantation at a dose of $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$1, flash annealing at $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$2 for $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$3, and $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$4 proton irradiation at $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$5. The microrings are $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$6 wide, with diameters from $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$7 to $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$8 in $$5\,\mathrm{m} \times 3\,\mathrm{m} \times 2.3\,\mathrm{m}$$9 steps; an external ring improves normal-incidence collection. By tuning the TE$G$00 whispering-gallery mode onto the G-center zero-phonon line, the device reaches $G$01, mode volume $G$02, and measured free spectral range $G$03 (Lefaucher et al., 2022).

The optical consequences are a substantial brightening of the ZPL but only weak lifetime modification. The normalized continuous-wave ZPL intensity is enhanced by $G$04 relative to off-resonant rings, and time-resolved measurements show an approximately $G$05 increase consistent with the continuous-wave data. For an ideally placed and oriented emitter, the textbook Purcell factor

$G$06

gives $G$07. After accounting for spatial averaging over the implanted depth profile, spectral averaging over the inhomogeneously broadened ensemble, and orientation averaging over the three crystallographic dipole families, the ensemble-average enhancement becomes $G$08, with cavity coupling fraction $G$09. The short photoluminescence lifetime component remains $G$10, while a long component $G$11 is attributed to parasitic emitters. Because $G$12 does not measurably decrease on resonance, the radiative yield is estimated to satisfy $G$13.

The limiting factor is not the cavity geometry alone but implantation-induced material degradation. The observed $G$14 is far below the bend-loss-limited and scattering-limited values expected from the geometry, and the paper attributes this gap to absorption by parasitic defects created alongside the G centers. The projected path to deterministic single-photon sources is therefore a materials-and-cavity co-optimization problem: lighter implantation, higher $G$15, smaller $G$16, and deterministic emitter placement. For a high-yield single emitter, the reported projections are a lifetime reduction factor $G$17 and emission probability $G$18 at $G$19, improving to $G$20 and $G$21 at $G$22.

5. Machine-learning uses of G-Zero

In open-ended language-model training, G-Zero is a verifier-free, co-evolutionary framework for autonomous self-improvement from zero data. The central objects are a Generator $G$23, which produces both an unassisted response and a hint-conditioned response, and a Proposer $G$24, which synthesizes query-hint pairs targeting the Generator’s blind spots. The intrinsic reward is Hint-$G$25,

$G$26

a per-token mean log-likelihood difference computed on the Generator’s own unassisted response. The Proposer is optimized by GRPO with reward $G$27, while the Generator is optimized by length-normalized DPO on curated preference pairs in which the hint-assisted response is treated as preferred. The filtering stage retains pairs in the lower half of the round’s empirical $G$28 distribution and removes degeneracies such as length inflation, repetition collapse, prompt echoing, and template leakage. The paper proves a best-iterate suboptimality guarantee for an idealized standard-DPO version under sufficient exploration coverage and low $G$29-certified pseudo-label score noise. Empirically, Qwen3-8B-Base improves from an average of $G$30 to $G$31 by Round 2, with AIME25 increasing from $G$32 to $G$33, while Llama-3.1-8B-Instruct improves from $G$34 to $G$35, with AlpacaEval 2.0 length-controlled win rate increasing from $G$36 to $G$37 (Huang et al., 11 May 2026).

A separate computational usage expands G-Zero into Group-Relative Zeroth-Order Optimization, abbreviated GRZO. Here the objective is memory-efficient forward-only fine-tuning of LLMs without backpropagation. GRZO uses per-example pseudo-independent perturbations constructed from a shared base noise tensor and Flipout-style sign factorization, followed by within-batch group-relative normalization of per-example two-sided loss differences. The estimator

$G$38

is directionally unbiased for the smoothed objective up to $G$39, and its leading variance term shrinks by about $G$40 relative to MeZO. The method preserves inference-level memory because it never mutates base weights in place. On Llama3-8B in fp16 with batch size $G$41, the reported peak memory is $G$42 for GRZO versus $G$43 for MeZO, a $G$44 reduction. Across models and tasks, GRZO improves average accuracy on Llama3-8B by $G$45 over MeZO, and as a drop-in replacement for sparse, low-rank, and quantized ZO variants it yields a reported average lift of $G$46 (Tan et al., 1 Jun 2026).

A shared computational theme is the replacement of external evaluators or stored gradients by internally generated training signals. In G-Zero self-play, the supervision comes from the model’s own distributional shift under hints; in GRZO, the update direction comes from self-normalized two-sided perturbation probes. In both cases, “zero” marks the removal of a conventional dependency: external labeled data in one case, full first-order differentiation in the other.

6. Formal uses: zero variation and zero-sum structure

In Einstein-Gauss-Bonnet cosmology, G-Zero denotes solutions with zero variation of the effective four-dimensional gravitational constant. The model uses the action

$G$47

with diagonal cosmological metrics and two constant Hubble-like parameters $G$48 and $G$49. If the observed three-dimensional space sits inside the $G$50-dimensional expanding sector, the internal volume satisfies

$G$51

so the G-Zero condition is

$G$52

The paper finds explicit exponential solutions with $G$53, nonzero $G$54, and $G$55, and proves their stability in the class of diagonal cosmological solutions. The stability criteria are $G$56 and $G$57, where $G$58 (Ivashchuk, 2016).

In additive combinatorics, one zero-labeled invariant is

$G$59

For $G$60, the paper proves that a subset $G$61 of cardinality $G$62 contains a zero-sum subset of size $G$63 whenever one row contains all $G$64 points or at least $G$65 points. As an application, it proves $G$66, settling the Gao-Thangadurai conjecture for the case $G$67 (Krishnamoorthy et al., 2020).

A related sequence-based literature studies short zero-sum subsequences inside zero-sum sequences. There, $G$68 is the least length forcing a zero-sum subsequence of length in $G$69, and

$G$70

For rank-two groups $G$71 with $G$72, the paper proves $G$73. It also identifies exact endpoint sets for several special families, including $G$74 and $G$75 for the listed 2-group regimes (Fan et al., 2011).

Taken together, these mathematical and cosmological usages show the widest semantic separation under the G-Zero label. In one setting, zero refers to exact cancellation in abelian groups; in the other, it refers to exact constancy of an effective coupling in higher-dimensional gravity. The commonality is structural: a nontrivial system is engineered or constrained so that a nominally varying quantity is forced to vanish.