SobolevMacromolecule

Megascale RNA 3D Structure Prediction · 0.509 private TM-score · Stanford RNA 3D Folding Part 2 (Kaggle)

Safety and scope: This repository is for non-infectious computational structure modeling, relaxation, and visualization. It does not contain infectious material, reverse-genetics workflows, synthesis-ready constructs, or laboratory protocols. See SAFETY.md.

Multi-model RNA 3D structure prediction pipeline with a custom physics relaxation engine, designed for megascale targets (up to 4,640 nt). Achieves a private/public score inversion (0.387 public → 0.509 private) through physics-guided generalization rather than benchmark overfitting.

📄 Full technical whitepaper with derivations · Reviewer notes · Kaggle competition

Reproducibility note: SobolevRNA.ipynb is Kaggle-native — model weights are mounted as Kaggle datasets under /kaggle/input/. Running locally requires substituting paths to locally downloaded weights for RNA-FM, Boltz-1, Protenix, and RibonanzaNet-2. See ATTRIBUTION.md for source links to each model.

Architecture

Input Sequence (L nucleotides)
        │
        ├─── L ≤ 1022 nt ──► RNA-FM (single pass, 640-dim embeddings)
        │
        └─── L > 1022 nt ──► HWS (Hierarchical Windowed Sensor)
                                   sliding window + taper blend
                                          │
                              ┌───────────▼───────────┐
                              │  Global Contact Map    │
                              │  C_ij ∈ {0,1}^{N×N}  │
                              └───────────┬───────────┘
                                          │
             ┌─────────────── Routing by L ──────────────────┐
             │                                               │
        L ≤ 512 nt                                     L > 512 nt
             │                                               │
   ┌─────────▼──────────┐                    ┌──────────────▼────────────┐
   │  Ensemble: Boltz-1 │                    │  SHR Megascale Path       │
   │  + Protenix (N=5)  │                    │  (Stochastic Hamiltonian  │
   └─────────┬──────────┘                    │   Relaxation, JAX x64)    │
             │                               └──────────────┬────────────┘
             └──────────────────┬────────────────────────────┘
                                │
                    ┌───────────▼───────────┐
                    │  SHR Physics Polish   │
                    │  (E_bond + E_rep +    │
                    │   E_DL + E_Rg)        │
                    └───────────┬───────────┘
                                │
                    ┌───────────▼───────────┐
                    │  Hungarian Chain Map  │
                    │  + Kabsch Alignment   │
                    └───────────┬───────────┘
                                │
                    ┌───────────▼───────────┐
                    │  submission.csv       │
                    │  (C1' coordinates)    │
                    └───────────────────────┘

HWS — Hierarchical Windowed Sensor

RNA-FM has a hard architectural truncation at 1,022 nt. For megascale targets (e.g. 9MME = 4,640 nt), a single-pass embedding is impossible. HWS extracts embeddings via overlapping windows and blends them with a linear taper to eliminate hard boundary artifacts.

Parameters:

Symbol	Value	Description
$W$	1022 nt	RNA-FM max window
$s$	768 nt	Stride between windows
$\tau$	128 nt	Taper length at boundaries
$d$	640	Embedding dimension

Weighted accumulation:

For each window $w$ covering positions $[a_w, b_w)$, a taper weight $\omega_{w}(i)$ is computed for each position $i$:

$$ \omega_{w}(i) = \begin{cases} \frac{i - a_w}{\tau} & \text{if } i \in [a_w,; a_w + \tau) \ 1 & \text{if } i \in [a_w + \tau,; b_w - \tau) \ \frac{b_w - i}{\tau} & \text{if } i \in [b_w - \tau,; b_w) \end{cases} $$

The blended embedding at position $i$ is:

$$\tilde{e}(i) = \frac{\sum_w \omega_{w}(i); e_w(i)}{\sum_w \omega_{w}(i)}$$

The blended embeddings are converted to a global pairwise contact map via cosine similarity. The cosine is rescaled to $P_{ij} = (S_{ij}+1)/2$, then binarized with a sequence-separation threshold:

$$ \theta(s) = \min\left(\theta_{\max},; \theta_0 \left(\frac{\max(s, 6)}{6}\right)^\alpha\right),\qquad s = |i-j| $$

$$ C_{ij} = \mathbf{1}[P_{ij} > \theta(|i-j|)] \cdot \mathbf{1}[|i-j| \geq 6] $$

Defaults are $\theta_0 = 0.85$, $\theta_{\max} = 0.94$, and $\alpha = 0.02$. This preserves the original local threshold while requiring stronger RNA-FM evidence for long-range contacts that would otherwise over-saturate megascale contact maps.

SHR — Stochastic Hamiltonian Relaxation

The physics engine operates on C1′ backbone coordinates $\mathbf{x} \in \mathbb{R}^{N \times 3}$. The Hamiltonian has four terms:

$$H(\mathbf{x}) = E_{\text{bond}} + E_{\text{rep}} + E_{\text{DL}} + E_{R_g}$$

Bond Term

$$E_{\text{bond}} = k_{\text{bond}} \sum_{i=1}^{N-1} \left(|\mathbf{x}_{i+1} - \mathbf{x}_i| - d_0\right)^2$$

$d_0 = 5.95$ Å (ideal C1′–C1′ backbone distance), $k_{\text{bond}} = 100.0$ (fixed across all tiers — prevents chain breakage under compaction).

Steric Repulsion Term

$$E_{\text{rep}} = \sum_{\substack{i < j \ |i-j| > 1}} \left(\max!\left(0,; \sigma_{\text{clash}} - |\mathbf{x}_i - \mathbf{x}_j|\right)\right)^2$$

$\sigma_{\text{clash}} \in [2.6, 3.0]$ Å, length-dependent (see dynamic schedule below). The gradient is regularized with $\epsilon = 10^{-2}$ to bound the maximum force at ~60 Å$^{-1}$ per pair (vs. ~60,000 without regularization).

Deep Learning Contact Restraint Term

$$E_{\text{DL}} = w_{\text{DL}} \sum_{(i,j) \in \mathcal{C}} \left(\max!\left(0,; |\mathbf{x}_i - \mathbf{x}_j| - d_{\text{contact}}\right)\right)^2$$

$\mathcal{C}$ is the contact set from a 50/50 consensus of the HWS pipeline (RNA-FM embeddings) and RibonanzaNet-2 predictions, thresholded to binary. The RNA-FM side uses the adaptive $\theta(|i-j|)$ rule above, while RibonanzaNet-2 contributes its learned pairwise channel. $d_{\text{contact}} = 8.0$ Å, and $w_{\text{DL}} \in [10.0, 25.0]$ scales with sequence length.

Radius of Gyration Term (Flory Scaling)

$$E_{R_g} = k_{R_g} \left(\max!\left(0,; R_g^{\text{target}} - R_g(\mathbf{x})\right)\right)^2$$

The Flory-scaling target enforces physical compaction:

$$R_g^{\text{target}} = 3.5 \cdot N^{0.45} \quad \text{(Å)}$$

$$R_g(\mathbf{x}) = \sqrt{\frac{1}{N}\sum_i |\mathbf{x}_i - \bar{\mathbf{x}}|^2}$$

with $k_{R_g} = 1.0$.

Sobolev H¹ Gradient Preconditioning

Gradient descent on $H$ with raw gradients causes high-frequency noise to dominate updates — a known pathology in chain relaxation. The gradient is preconditioned in spectral space via a Sobolev H¹ seminorm filter:

$$\hat{\nabla}_k = \frac{(\text{DCT-II};\nabla H)_k}{1 + \alpha k^2}$$

$$\widetilde{\nabla H} = \text{IDCT-II}!\left(\hat{\nabla}_k\right)$$

with $\alpha = 10.0$. This damps wavenumber $k$ by factor $(1 + \alpha k^2)^{-1}$, suppressing oscillatory modes while preserving the low-frequency compaction signal. The learning rate follows a linear decay schedule:

$$\eta(t) = \eta_0 \left(1 - \frac{t}{T}\right)$$

Guarded Hybrid Polish for External Candidate Pipelines

SobolevRNA was originally created for the Stanford 3D RNA Part 2's Kaggle Competition, but was thereafter generalized to SobolevMacromolecule, which now first pivoted with sobolev_polish_gate.py, a production-safe bridge for using SHR as a post-processing layer on strong external candidates such as the Competition's 1st-place ensemble. The intended integration is serial:

external predictors (Boltz2 / Protenix / DRFold2 / RNAPro / TBM)
        → C1' candidate slots
        → SobolevRNA contact map C
        → guarded shr_polish
        → accept/reject gate
        → submission.csv

The bridge deliberately calls shr_polish, not shr_refine_single. External DL/TBM candidates already have plausible global folds, so the polish stage uses the input coordinates as the initial condition and never adds stochastic Gaussian jitter. The polish Hamiltonian is the local C1′ objective

$$ H_{\mathrm{polish}}(X; C) = E_{\mathrm{bond}}(X)

E_{\mathrm{steric}}(X)
E_{\mathrm{DL}}(X; C), $$

with $E_{R_g}$ disabled during polish by setting $R_g^{\mathrm{target}} = 0$. This prevents the post-processor from imposing a new global compaction basin on a model that may already have the right topology. The terms are

$$ E_{\mathrm{bond}}(X) = k_{\mathrm{bond}}\sum_{i=1}^{N-1} \left(\lVert x_{i+1}-x_i\rVert_2 - 5.95\right)^2, $$

$$ E_{\mathrm{steric}}(X) = \sum_{j>i+1} \left[ \max\left( 0,; \sigma_{\mathrm{clash}}

\sqrt{\lVert x_i-x_j\rVert_2^2 + 10^{-2}} \right) \right]^2, $$

$$ E_{\mathrm{DL}}(X; C) = w_{\mathrm{DL}}\sum_{i,j} C_{ij} \left[ \max\left(0,\lVert x_i-x_j\rVert_2 - 8.0\right) \right]^2. $$

The gradient update uses the same Sobolev $H^1$ resolvent as SHR, implemented with the correct JAX DCT path:

$$ \widetilde{\nabla H} = \mathrm{IDCT}_{II}\left( \frac{\mathrm{DCT}_{II}(\nabla H)_k}{1+\alpha k^2} \right), $$

where sobolev_polish_gate.py imports jax.scipy.fft as jfft and enables jax_enable_x64=True. The production defaults are $\alpha = 5.0$, clip = 2.0, $w_{\mathrm{DL}} = 2.0$, $k_{\mathrm{bond}} = 100.0$, $\sigma_{\mathrm{clash}} = 3.0$, 2000 steps, and learning rate 0.01.

Accept/Reject Gate

In a fixed best-of-5 submission, post-processing is not automatically additive: replacing a raw candidate can reduce the best slot if the refined structure drifts away from the native fold. The bridge therefore accepts a polished candidate only if all checks pass:

Shape matches the raw candidate and all coordinates are finite, non-sentinel, and within the sanitizer bound.
Bond violations do not increase, where a violation is an adjacent C1′ distance with $\lvert d - 5.95\rvert > 2.0$ Å.
Steric clashes do not increase, using KDTree pairs below 3.0 Å and excluding adjacent residues.
$H_{\mathrm{polish}}(X_{\mathrm{refined}}; C) < H_{\mathrm{polish}}(X_{\mathrm{raw}}; C)$.
$R_g(X_{\mathrm{refined}})$ lies in $[0.7, 1.5]\cdot 3.5N^{0.45}$.
$\max_i \lVert x_{i+1}-x_i\rVert_2 < 12.0$ Å.
tm_self >= 0.85, computed by Kabsch-aligning refined coordinates to raw coordinates and applying a TM-style C1′ similarity over valid residues.

Rejected candidates leave the original external prediction unchanged. Accepted candidates are recorded in sobolev_polished_slots.csv; all candidates receive metrics and reject reasons in sobolev_polish_report.csv.

Runtime Controls

Variable	Default	Effect
`SOBOLEVRNA_POLISH`	`1`	Set to `0` to disable the gate and preserve raw slots
`SOBOLEVRNA_POLISH_SLOTS`	all	Optional comma-separated slot allowlist, e.g. `1,2,3`
`SOBOLEVRNA_POLISH_STEPS`	`2000`	Number of polish steps
`SOBOLEVRNA_POLISH_LR`	`0.01`	Polish learning rate

The module also accepts the earlier prototype prefix SOBOLERNA_* as a backward-compatible alias.

Dynamic Parameter Schedule

Parameters adapt linearly with sequence length across three tiers:

$$t = \text{clamp}!\left(\frac{N - 1000}{4640 - 1000},; 0,; 1\right)$$

Parameter	$N \leq 1000$	$N \in (1000, 3000]$	$N > 3000$
$w_{\text{DL}}$	10.0	$10.0 + 15.0,t$	$10.0 + 15.0,t$
$\sigma_{\text{clash}}$	3.0 Å	$3.0 - 0.4,t$ Å	$3.0 - 0.4,t$ Å
$T$ (steps)	1,000	1,500	8,000
$\eta_0$	0.02	0.01	0.005
$K$ (seeds)	5	3	1

9MME at $N = 4640$ targets $R_g^{\text{target}} = 3.5 \times 4640^{0.45} \approx 156$ Å, requiring $w_{\text{DL}} \approx 25.0$ to achieve compaction.

Kabsch Alignment (Chain Stitching)

Consecutive 3D chunks are aligned via the Kabsch algorithm (Kabsch 1976). Given mobile anchor $\mathbf{M} \in \mathbb{R}^{m \times 3}$ and target anchor $\mathbf{T} \in \mathbb{R}^{m \times 3}$:

$$\mathbf{H} = (\mathbf{M} - \boldsymbol{\mu}_M)^\top (\mathbf{T} - \boldsymbol{\mu}_T)$$

$$\mathbf{H} = \mathbf{U} \boldsymbol{\Sigma} \mathbf{V}^\top \quad \text{(SVD)}$$

$$\mathbf{D} = \text{diag}(1,; 1,; \text{sgn}(\det(\mathbf{V}^\top \mathbf{U}^\top))) \quad \text{(chirality guard)}$$

$$\mathbf{R} = \mathbf{V}, \mathbf{D}, \mathbf{U}^\top, \qquad \mathbf{T}_{\text{translate}} = \boldsymbol{\mu}_T - \mathbf{R},\boldsymbol{\mu}_M$$

The seam between aligned chunks is blended with a linear taper over the overlap region to prevent harmonic-force spikes in the subsequent SHR polish.

Results

Set	TM-score
Public leaderboard	0.38650
Private leaderboard	0.50934

The private > public inversion reflects that SHR physics generalizes to novel RNA families (the private set composition) better than pure deep learning baselines.

Adaptive Contact Calibration

adaptive_contacts.py provides the pure-NumPy contact-map utilities used to tune this layer outside the Kaggle notebook. The intended A/B protocol is:

Match the predicted contact-density decay curve to polymer scaling, $P(s) \propto s^{-\gamma}$, targeting $\gamma \approx 1.0$ to $1.4$ for folded RNA.
Report MCC or F1 separately for short ($6 \leq s \leq 24$), medium ($25 \leq s \leq 100$), and long-range ($s > 100$) contacts when labels are available.
Track downstream SHR energy and polish-gate tm_self; good thresholds reduce energetic frustration without moving accepted structures out of their raw-model basin.

Sobolev Macromolecule Extension

The Sobolev $H^1$ preconditioner is polymer-agnostic: it smooths high-frequency gradient modes along an indexed chain. sobolev_macromolecule.py turns that into a small object-oriented factory. The JAX optimization loop is shared; the factory swaps only the bead identity, physical constants, optional bending term, and expected restraint frontends:

Domain	Bead	$d_0$	Compaction	Frontend restraints
RNA	C1′	5.95 Å	$R_g = 3.5N^{0.45}$	RNA-FM, RibonanzaNet-2, templates
Proteins	Cα	3.80 Å	$R_g = R_0N^{0.33}$	ESM-3, Chai-1, Boltz/Protenix confidence maps
dsDNA	C1′ or P	~4.8 Å	worm-like-chain bending term, not Flory collapse	Boltz/Protenix/AF3 nucleic-acid complex restraints

For dsDNA, disable the RNA-style collapse basin and add bending plus inter-strand Watson-Crick restraints so the optimizer preserves helix stiffness rather than crushing the duplex.

from sobolev_macromolecule import create_macromolecule, watson_crick_contact_map

protein_engine = create_macromolecule("protein")
protein_terms = protein_engine.energy_terms(ca_coords, contact_map=protein_contacts)

dna_engine = create_macromolecule("dsdna", bend_stiffness=8.0)
watson_crick_contacts = watson_crick_contact_map(n_base_pairs=1000)
polished_dna = dna_engine.polish(p_coords, contact_map=watson_crick_contacts)

The presets are deliberately lightweight. A new frontend only needs to emit a square contact/restraint matrix in the same residue order as the coordinates; SobolevMacromolecule.polish() handles the shared bond, steric, contact, radius-of-gyration, optional bending, and Sobolev $H^1$ gradient-preconditioned update. For dsDNA, watson_crick_contact_map() builds the explicit inter-strand pairing restraints while the bending term preserves helix stiffness.

Mixed Complexes

SobolevComplex extends the same engine to CRISPR-Cas9-like protein/RNA/DNA assemblies. The key change is tensor masking: bonds are evaluated only inside chains, steric radii and bond lengths are looked up from each bead's molecular type, radius-of-gyration basins are computed per chain, and the Sobolev DCT filter is applied independently to each chain gradient slice so unrelated chain endpoints are never smoothed together.

from sobolev_macromolecule import SobolevComplex

sequence, complex_engine = SobolevComplex.from_fasta("""
>Cas9|protein
MKK...
>guide|rna
GGA...
>target|dsdna
ATGC...
""")

terms = complex_engine.energy_terms(coords, contact_map=af3_or_boltz_contacts)
polished = complex_engine.polish(coords, contact_map=af3_or_boltz_contacts)

The complex contact Hamiltonian reports contacts_intra and contacts_inter separately. ComplexSpec(w_intra=..., w_inter=...) lets interface restraints carry a different weight from intra-chain folding restraints, which is useful when preserving docking geometry matters more than relaxing internal monomer noise.

Graph Sobolev Macro Backend

The Kaggle notebook's original SHR cells are too linear and monolithic to swap the 1D DCT for a graph filter in place. The extracted sobolev_macromolecule.py layer is the modular boundary: SobolevMacromolecule keeps single-chain DCT smoothing, SobolevComplex keeps per-chain DCT smoothing for central-dogma complexes, and SobolevMacro replaces the DCT with a graph Laplacian spectral filter for branched or non-polymer systems.

from sobolev_macromolecule import SlabPotential, create_macro_graph

glycan = create_macro_graph(
    node_types=["glycan", "glycan", "glycan", "glycan"],
    bonds=[(0, 1, 1.4), (1, 2, 1.4), (1, 3, 1.6)],
)

membrane_patch = create_macro_graph(
    node_types=["lipid_tail", "lipid_head"],
    bonds=[],
    slab=SlabPotential(half_thickness=15.0),
)

filtered_gradient = glycan.smooth_gradient(raw_gradient)
polished = glycan.polish(coords, contact_map=boltz_or_af3_restraints)

SobolevMacro uses GraphSpec tensors for node types, bead radii, arbitrary covalent edges, contact weights, and optional implicit membrane slab potentials. The Sobolev filter is U @ ((U.T @ gradient) / (1 + alpha * lambda)), where U and lambda come from the graph Laplacian L = D - A. This acts like the old DCT on a line, but also handles glycan trees, ligand bond graphs, disconnected systems, lipid patches, and coarse MARTINI-style beads without smoothing across non-edges.

Whole-Cell Visualization Bridge

Whole-cell scenes should be rendered by an instanced WebGPU/OpenUSD/Unreal frontend, not by loading every bead into a desktop molecular viewer. sobolev_visualization.py adds the thin adapter layer: binary coordinate frames for SHM/gRPC/WebSocket transport, renderer-ready (N, 4, 4) instance matrices, abundance-to-asset-id expansion, JSON scene manifests, minimal OpenUSD PointInstancer export, and far-field coarse graining around an active-site sphere.

See docs/whole-cell-visualization.md for the multi-scale data integration and cloud rendering architecture, including the recommended split between A100/H100-class SobolevMacro compute and L4/G5-class Pixel Streaming visualization.

BDBV Visualization — Safety, Scope, and Provenance

This repository includes a non-infectious, integrative, multi-scale structural visualization of a Bundibugyo ebolavirus–associated virion architecture, assembled from public structural components, homologous templates, and computationally relaxed placement/packing coordinates. This is a hypothesis-generating model, not an experimentally validated complete virion reconstruction and not a genome or infectious-virus reconstruction.

PDB Accession Audit

The initially assigned PDB IDs have been corrected after review against RCSB annotations:

6N7J: BDBV223 Fab bound to a 16-residue synthetic GP stalk peptide (X-ray, 3.68 Å). This is NOT a full GP trimer — it is a small stalk epitope + antibody complex. Set to None in the ChimeraX script until a full GP trimer structure is properly vetted.
4LDB: Zaire ebolavirus (EBOV) VP40 dimer (X-ray, 2.6 Å). This is NOT BDBV VP40 — it is a homologous template (~60% identity). Labeled as a homolog in the provenance table.
7ZPE: Human branched-chain keto acid dehydrogenase kinase — completely unrelated to ebolavirus. This was a wrong PDB ID. Removed.

What This Repository Does Not Contain

No nucleotide or amino acid sequences of any pathogen
No synthesis-ready construct designs or cloning vectors
No reverse-genetics systems, minigenomes, replicons, or rescue protocols
No wet-lab protocols of any kind
No "one-click" pipeline that turns a sequence into a buildable pathogen

Appropriate Use

Education: visualizing filovirus architecture for students and trainees
Structural interpretation: communicating antibody-epitope geography
Defensive research communication: illustrating virion-scale organization
Method demonstration: showing the Sobolev/graph-relaxation engine
Scene-building toolkit: the visualization adapters are domain-agnostic

Documentation

SAFETY.md — full safety and scope statement
PROVENANCE.md — component-level provenance table (source, organism, method, resolution, chain IDs, copy number, placement rule, uncertainty) with the PDB accession audit
docs/pathogen-modeling-provenance-template.md — blank provenance template for future pathogen-associated models

Video

⚠️ Caveat: This is an integrative non-infectious BDBV-associated virion visualization, not a complete coordinate-exact reconstruction. It is a hypothesis-generating model assembled from public structural components, homologous templates, and computationally relaxed placement/packing coordinates. See PROVENANCE.md for the full provenance table and PDB accession audit.

The video shows a 1,081 nm BDBV-associated, hypothesis-generating filovirus architecture visualization in UCSF ChimeraX. Public structural components and homologous templates are instanced at computationally relaxed positions for educational and structural-communication purposes.

Full-resolution MP4 (35s, 1720×1080): download

Dependencies

Model	Source	Role
RNA-FM	Chen et al. 2022	Sequence embeddings (HWS input)
RibonanzaNet-2	Shujun717/Kaggle	Contact map (E_DL fallback)
Boltz-1	odat1248/Kaggle	3D seed generation (L ≤ 800 nt)
Protenix v1	qiweiyin/Kaggle	3D generation (L ≤ 512 nt)
USalign	Zhang Lab	TM-score evaluation

See ATTRIBUTION.md for full credits and licenses.

Citation

If you build on HWS or SHR, please cite:

@misc{kinder2026rna,
  author = {Kinder, Hunter},
  title  = {SobolevRNA: Megascale RNA 3D Structure Prediction with Hierarchical
            Windowed Sensing and Stochastic Hamiltonian Relaxation},
  year   = {2026},
  url    = {https://github.com/aurascoper/SobolevRNA}
}

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SobolevMacromolecule

Architecture

HWS — Hierarchical Windowed Sensor

SHR — Stochastic Hamiltonian Relaxation

Bond Term

Steric Repulsion Term

Deep Learning Contact Restraint Term

Radius of Gyration Term (Flory Scaling)

Sobolev H¹ Gradient Preconditioning

Guarded Hybrid Polish for External Candidate Pipelines

Accept/Reject Gate

Runtime Controls

Dynamic Parameter Schedule

Kabsch Alignment (Chain Stitching)

Results

Adaptive Contact Calibration

Sobolev Macromolecule Extension

Mixed Complexes

Graph Sobolev Macro Backend

Whole-Cell Visualization Bridge

BDBV Visualization — Safety, Scope, and Provenance

PDB Accession Audit

What This Repository Does Not Contain

Appropriate Use

Documentation

Video

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LICENSE		LICENSE
PROVENANCE.md		PROVENANCE.md
README.md		README.md
SAFETY.md		SAFETY.md
SECURITY.md		SECURITY.md
SobolevRNA.ipynb		SobolevRNA.ipynb
adaptive_contacts.py		adaptive_contacts.py
requirements.txt		requirements.txt
sobolev_macromolecule.py		sobolev_macromolecule.py
sobolev_polish_gate.py		sobolev_polish_gate.py
sobolev_visualization.py		sobolev_visualization.py

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SobolevMacromolecule

Architecture

HWS — Hierarchical Windowed Sensor

SHR — Stochastic Hamiltonian Relaxation

Bond Term

Steric Repulsion Term

Deep Learning Contact Restraint Term

Radius of Gyration Term (Flory Scaling)

Sobolev H¹ Gradient Preconditioning

Guarded Hybrid Polish for External Candidate Pipelines

Accept/Reject Gate

Runtime Controls

Dynamic Parameter Schedule

Kabsch Alignment (Chain Stitching)

Results

Adaptive Contact Calibration

Sobolev Macromolecule Extension

Mixed Complexes

Graph Sobolev Macro Backend

Whole-Cell Visualization Bridge

BDBV Visualization — Safety, Scope, and Provenance

PDB Accession Audit

What This Repository Does Not Contain

Appropriate Use

Documentation

Video

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