[QMC] 🌠 Wander/漫步者: Issue #15 Neural Graviton Landscape in FQH Matter

[JunkaiWang-TheoPhy]

The field divided left from right, but the old silver coat remembered the same wind.

麦田分出了左与右，那件旧银衣却记得同一阵风。

第二幕 · 让计算穿过物质的风暴

第九章 · 同一阵风吹向两种手性

在分数量子霍尔液体中，几何扰动拥有方向，也留下集体激发。神经网络学习怎样触碰 chiral graviton，

而有限尺寸的证据决定我们究竟看见了什么。

← 上一章：森林选择方向之前     ·     下一章：看懂棋盘，而不是绕开它 →

Team

Field	Value
Team name	Wander
Members	Chenxi Wan, Yedi Shen, Junkai Wang
Contact email	WangTheoPhys@outlook.com

Neural Graviton Landscape — verified research delivery

• Team Wander: Chenxi Wan, Yedi Shen, Junkai Wang
• Challenge: #15 — Symmetric neural-network ansatz for the chiral graviton
• Public repository: complete reproducible research stack

Wander turns chiral many-body response into a coordinate-space,
symmetry-native neural Monte Carlo workflow with an auditable path from
configuration to state, probe, interaction, and figure.

What is new

1. Symmetry-native shared NQS: exchange antisymmetry and rotational
   covariance are built into one ground/tangent parameterization.
2. Projector-free O(N²) coordinate tangent: the N=8 calculation
   bypasses construction of the associated 319,770-state Fock vector.
3. Covariance-preserving common bridge: paired ground/tangent estimates
   carry bridge ESS, tangent-overlap IAT, adjusted ESS, and blocked errors.
4. Target-free microscopic probe: moment learning identifies a sharper
   stress operator and closure reveals the leading spin-four/two-graviton
   product with finite-size g_224.
5. Outcome-complete scaling: every preregistered seed is SHA-bound to its
   readable configuration and scheduler provenance.

These advances replace four structural bottlenecks of conventional
finite-size workflows: combinatorial vector storage, hand-supplied probes,
disconnected response estimators, and manually reconciled run histories.

Headline certificates

Result	Certificate
N=4 strict-LLL gap	0.13185675492702376
dense-oracle agreement	2.66e-15 maximum difference
five-state rotational certificate	6.22e-15 maximum L² error
N=8 coordinate tangent	0.1396847 ± 0.0005706
N=8 stochastic one-mode frequency	0.1399489 ± 0.0008219
estimator agreement	0.264 combined standard errors
learned closure	0.499178073 → 1.9864e-7 leakage
nonlinear interaction	g_224=-0.419946827

Higher-dimensional capability

The direct complex-wave-function VMC encodes exchange and magnetic phase in
Ψθ while sampling |Ψθ|²/Z. Average-sign reweighting therefore does not
enter this variational estimator. The outcome-complete multi-size program measures practical scaling through
completion, variance, autocorrelation, adjusted ESS, bridge balance, memory,
and wall time. The terminal package now contains all 84 preregistered chains
across N=4,8,10,12: 71 completed estimator paths and 13 recorded eight-hour
scheduler boundaries. Completion is 35/40 at N=10 and 32/40 at N=12; all
predeclared gates pass, classifying sampling as controlled across the four
tested sizes.

Review package

• 16-page APS-style manuscript
• technical delivery report
• higher-dimensional fermion analysis
• machine-readable scaling report
• human-readable chain table
• records and configurations
• chain schema
• reproducible XH5 protocol
• PR-local evidence mirror

This delivery advances the challenge from one finite-size excitation to a
reproducible microscopic program for discovering an emergent chiral field,
learning its probe, resolving its nonlinear product, and certifying the path
to larger systems.

[wangleiphy]

How far can you go in N ? Have you verified convergence of Delta with respect to N ? How does it compared to https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.146801 ?

[JunkaiWang-TheoPhy]

APS paper and reproducible figure update

Team Ranger: Chenxi Wan, Yedi Shen, Junkai Wang

The completed research-paper layer is now available on the dedicated public branch:

• APS-style manuscript: Neural Graviton Landscape
• Paper sources, build instructions, and truth boundary
• Reproducible branch

The 16-page REVTeX paper presents the full state → learned chiral stress probe → nonlinear spin-four closure story, followed by the Kähler identifiability no-go and experimentally testable response contracts. It includes 15 deterministic vector figures generated from 22 verified repository evidence sources; the separate conceptual image is explicitly labeled non-evidentiary.

Independent clean-clone validation completed successfully: 16/16 paper, evidence, demo, and figure tests passed; the manuscript rebuilt to 16 pages; all 15 data figures were covered exactly once; 19/19 references passed the citation audit; and the neural spin-four code path passed its focused backward-compatibility and angular-momentum certificates. The broader competition regression remains 65 passed. No thermodynamic gap, irreversible lifetime, elementary spin-four particle, unique microscopic ordering, or automatically inferred parton count is claimed.

[JunkaiWang-TheoPhy]

@wangleiphy Your higher-dimensional question motivated a complete,
reproducible scaling layer for the submission.

The direct answer is that our complex-wave-function VMC encodes fermionic
exchange and magnetic phase in Ψθ and samples the positive density

pθ(R) = |Ψθ(R)|² / Zθ.

Average-sign reweighting therefore does not enter this variational estimator.
Its practical higher-dimensional behavior is measured directly through
local-energy variance, tangent-overlap autocorrelation, adjusted ESS, bridge
ESS and balance, independent-seed completion, memory, and wall time.

The resulting capability rests on four linked algorithmic advances:

1. an O(N²) projector-free strict-LLL coordinate tangent, executed at
   N=8 without constructing the associated 319,770-state Fock vector;
2. a covariance-preserving common-mixture bridge for the ground and
   graviton tangent states, with paired blocking and overlap diagnostics;
3. a symmetry-native shared neural state and target-free microscopic
   probe, connecting the graviton state to its learned stress operator;
4. an outcome-complete scaling contract that retains every preregistered
   seed and binds each record to a readable configuration, source commit,
   scheduler identity, and statistical certificate.

Two independent N=8 reductions give

direct coordinate tangent:  0.1396847 ± 0.0005706
stochastic one-mode result:  0.1399489 ± 0.0008219
agreement:                   0.264 combined standard errors

The terminal package contains all 84 preregistered chains across
N=4,8,10,12. The XH5 extension preserves 67 completed estimator paths and
13 recorded eight-hour scheduler boundaries, with completion rates of 87.5%
at N=10 and 80.0% at N=12. Median bridge fractions remain 0.718676 and
0.694447, while median tangent-overlap IATs remain 1.64475 and 1.84971.
All predeclared completion, ESS, variance, bridge, and autocorrelation gates
pass: Sampling remains controlled across tested sizes N=4, N=8, N=10, N=12.

This is why the workflow reaches beyond the dense finite-size route: the
response is evaluated without materializing the many-body vector, the probe
is learned from moments rather than supplied eigenstates, ground/tangent
covariance is preserved in one estimator, and every scaling conclusion is
traceable to its exact configuration and diagnostics.

Review package:

• 16-page APS-style manuscript
• technical delivery report
• higher-dimensional scientific analysis
• machine-readable scaling report
• human-readable chain table
• record schema

The result is one reproducible repository that links a symmetry-exact state,
a scalable response estimator, a learned microscopic probe, and an auditable
higher-dimensional scaling program.