Parthenon: Architecture, HPC & AI Frameworks

• Parthenon is a multifaceted term that denotes the ancient Athenian temple known for intricate geometric refinements as well as modern computational frameworks, unified dental benchmarks, and legal-agent systems.
• Its architectural studies blend historical criticism, geometric modeling, and psychophysics to reveal precise, measurable refinements, challenging traditional optical-correction theories.
• In computational science, Parthenon supports adaptive mesh refinement on heterogeneous systems, harmonizes dental AI datasets for multi-task evaluation, and drives self-evolving legal-agent frameworks.

Parthenon denotes, in its primary historical sense, the temple built between 447 and 432 BCE, about $a=30.9\,\mathrm{m}$ wide and $b=69.5\,\mathrm{m}$ long, whose deliberate refinements have long been central to debates in architectural history and perceptual science. In recent research literature, the same name is also used for several distinct technical constructs: a performance portable block-structured adaptive mesh refinement framework for exascale scientific computing, a benchmark unifying ten dental datasets under a common schema, and a self-evolving legal-agent framework. These usages are independent: the architectural Parthenon is studied through historical criticism, geometric modeling, and psychophysics; the computational Parthenon is derived from Athena++ and K-Athena and implemented using Kokkos; the dental benchmark PARTHENON supports tooth detection, caries segmentation, anomaly detection, and dental developmental staging; and the legal-agent framework factors Model, Harness, Agent, Knowledge, Tools, and Skills into auditable surfaces (Goriely, 19 Oct 2025, Grete et al., 2022, Kim et al., 1 Apr 2026, Geng et al., 3 Jun 2026).

1. Monument, geometry, and measured refinements

The Parthenon contains deliberate architectural refinements. The stylobate and entablature curve upward slightly, columns incline inward, shafts have entasis, corner columns are thicker, and corner spacings are contracted. These features are intentional, precise, and repeated, not construction errors. In the recent analytical literature, they are treated as measurable geometric departures from strict rectilinearity rather than as vague aesthetic impressions (Goriely, 19 Oct 2025).

One quantitative model represents the stylobate surface with a Coons patch interpolation,

$$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$

for $x\in[0,a]$, $y\in[0,b]$, with $a=30.9$ m and $b=69.5$ m. Solving $\partial_x f=\partial_y f=0$ gives the crown at about $(x,y)=(13.9,37)$, near the wall between cella and opisthodomos, and the maximum elevation difference is about 6 cm. The result is a physically real curvature, not a conjectural one.

Entasis has likewise been formalized geometrically. A column radius can be modeled as

$r(z)=c_0+c_1 z+c_2 z^2,\qquad z\in[0,h],$

and, for one measured column,

$b=69.5\,\mathrm{m}$0

Compared with a straight taper, the maximum deviation is near mid-height, at $b=69.5\,\mathrm{m}$1 m, with $b=69.5\,\mathrm{m}$2 mm. Doric fluting is modeled separately by

$b=69.5\,\mathrm{m}$3

and the full shaft by

$b=69.5\,\mathrm{m}$4

This treatment places the Parthenon within a quantitatively recoverable design space rather than a purely stylistic one.

2. The optical-correction thesis and its critique

A major contemporary controversy concerns the claim that the Parthenon’s refinements were “optical corrections” designed to cancel visual illusions and make the building appear straight and regular. A 2025 paper argues that there is no good historical or scientific evidence for that thesis. The theory is traced to Vitruvius, writing roughly four centuries after the Parthenon, and its modern authority is linked to nineteenth-century surveys by Hoffer, Pennethorne, and especially Francis Penrose. The claim is that the enduring explanation—curved lines to make them look straight, bulging columns to make them look straight, thickened corners to make them look equal, and enlarged high elements to make them look uniform—is a myth rather than an evidence-based account (Goriely, 19 Oct 2025).

The critique is developed by combining historical criticism, geometric modeling, and perceptual science. For curvature detection, the argument uses the sagitta relation

$b=69.5\,\mathrm{m}$5

where $b=69.5\,\mathrm{m}$6 is viewing distance. Psychophysical studies are reported as suggesting curvature detection thresholds ranging from a few arcseconds up to roughly $b=69.5\,\mathrm{m}$7–$b=69.5\,\mathrm{m}$8 arcsec in more conservative conditions. At $b=69.5\,\mathrm{m}$9 m, this corresponds to detectable sagittae on the order of $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$0–$$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$1 cm. Since the stylobate rises by about 6 cm, the paper concludes that the curvature can in principle be detected from some distances and viewpoints. This is presented as incompatible with the classical correction story: if a line had been curved upward to look straight, it should not itself be visible as curved.

The same style of critique is applied to Hering-, Wundt-, and Zöllner-type explanations of colonnade perception, to entasis, to corner-column thickening, and to size corrections at height. The column-inclination angle is described as about $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$2, implying that the east façade columns would meet at a point about $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$3 km above the stylobate, which is characterized as negligible for inducing curvature. Corner columns are about $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$4 m in diameter at the base, versus about $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$5 m for others, a difference of $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$6 cm, roughly $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$7; the objection is that any supposed irradiation-based correction would work only from very restricted viewing zones. For figures at height, the geometry is summarized by

$$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$8

with $$f(x,y)=10^{-3}\times\Big(1.16078+8.87918 x+8.00577 y-0.288568 x^2-0.105338 y^2 -0.0523071 x y+0.000459584 x^2 y+0.000413477 x y^2\Big),$$9, so maintaining constant visual angle requires

$x\in[0,a]$0

The point is that such corrections are viewpoint-specific and therefore cannot function robustly for buildings seen from many positions.

The paper also explores non-optical accounts. For stylobate curvature, a drainage hypothesis is examined using the Nusselt thin-film relations

$x\in[0,a]$1

with average slopes estimated as about $x\in[0,a]$2 and $x\in[0,a]$3. For entasis, an engineering explanation based on Euler buckling is rejected by noting that the predicted elastic buckling stress is far above the compressive strength of Pentelic marble, so the column would crush before it could buckle elastically. The broader conclusion is not that the refinements are accidental or meaningless, but that their motives are more plausibly sought in empirical craft traditions, aesthetic judgments, inherited rules, or practical considerations than in a scientific program of illusion-cancellation.

3. Parthenon as a performance-portable AMR framework

In computational science, Parthenon is a performance-portable framework for block-structured adaptive mesh refinement aimed at exascale scientific computing. It was developed because traditional AMR infrastructures were built mainly for CPU-era distributed-memory systems and generally do not map well onto modern heterogeneous machines with GPUs, deep memory hierarchies, and multiple layers of parallelism. The framework is derived from Athena++ and K-Athena, but generalized beyond a single astrophysical MHD code. Its central technical choices are block-structured AMR, Kokkos-based on-node portability, device-resident data structures, logical packing of variables and blocks, and one-sided, asynchronous MPI communication (Grete et al., 2022).

Parthenon retains Athena++’s MeshBlock-centered AMR model: fixed-size MeshBlocks arranged in a tree, binary in 1D, quadtree in 2D, and octree in 3D; refinement by splitting one block into $x\in[0,a]$4 children; derefinement by coalescing $x\in[0,a]$5 contiguous fine blocks; neighbor-based communication; Z-ordering for distribution; and prolongation, restriction, and flux correction on multilevel meshes. What is generalized is the application architecture. Variables are named objects with metadata describing location, shape, and flags. Packages register variables, physics routines, tasks, and package-local parameters. MeshBlockData and MeshData expose these abstractions to kernels, while VariablePack and MeshBlockPack collect variables and blocks into packed execution domains indexed by $x\in[0,a]$6.

The framework adopts a device-resident policy because many target methods have roughly $x\in[0,a]$7 floating-point operations per byte moved. Work data are allocated only in device memory; communication buffers are also in device memory; and GPU-aware MPI avoids host staging. On top of Kokkos primitives, Parthenon provides parthenon::par_for and parthenon::par_reduce, plus ParArrayND, an arbitrary-rank array abstraction built on Kokkos::View. The tasking model is hierarchical: a TaskCollection contains one or more TaskRegions, and each region contains one or more TaskLists with explicit dependencies. Driver, EvolutionDriver, and MultiStageDriver supply progressively more specialized driver semantics.

The reference miniapp, Parthenon-hydro, is about 1400 lines of C++ total and solves the compressible Euler equations in 1D/2D/3D on uniform, static multilevel, and adaptive multilevel meshes using two-stage Runge–Kutta integration, piecewise linear reconstruction, and an HLLE Riemann solver. Its reported largest-scale result is about $x\in[0,a]$8 zone-cycles/s on 9,216 Frontier nodes, corresponding to 73,728 logical GPUs, at approximately 92% weak-scaling efficiency relative to one node. The framework is positioned as an open, collaborative project intended to let downstream developers focus on science-specific algorithms rather than on the complexity of massively parallel, device-accelerated AMR.

4. Downstream HPC applications and performance characterization

Parthenon functions not only as a standalone framework but also as the substrate for downstream multiphysics applications. PHOEBUS is described as being built on the PARTHENON performance portable adaptive mesh refinement framework, with the software stack

$x\in[0,a]$9

In that architecture, Parthenon provides block-structured AMR, performance-portable execution across CPUs and GPUs, data structures for mesh-based fields and particles, and the underlying infrastructure that lets PHOEBUS developers focus primarily on physics and numerics. PHOEBUS uses PARTHENON’s swarms particle infrastructure both for Monte Carlo neutrino packets and for tracer particles, and the code demonstrates weak scaling to over 500 H100 GPUs, specifically just below 80% weak scaling efficiency on 512 H100s, reaching a few $y\in[0,b]$0 zone-cycles per second (Barker et al., 2024).

A separate characterization study uses Parthenon-VIBE, a benchmark built on Parthenon that solves the 3D Vector Inviscid Burgers’ Equation, to analyze AMR behavior on heterogeneous CPU-GPU systems. The central result is that smaller mesh blocks, deeper AMR levels, and too few MPI ranks per GPU degrade GPU performance through host-side serial overheads, communication costs, low GPU occupancy, and poor memory-system efficiency. Reducing MeshBlockSize from 32 to 16 increases communicated cells by 2.1× while total cell updates decrease by 5.0×; for a 1 GPU – 1 Rank configuration, total runtime increases from 97.63 s at block size 32 to 257.21 s at block size 16 and to 3023 s at block size 8. At MeshBlockSize $y\in[0,b]$1, 1 H100 GPU is slower than a 96-core Sapphire Rapids CPU, and at MeshBlockSize $y\in[0,b]$2, even 4 GPUs perform worse than the CPU. The best single-GPU performance occurs at about 12 ranks per GPU, but 1 GPU with 12 ranks uses 75.5 GB, near the H100 memory limit (Poptani et al., 24 Sep 2025).

The same study identifies kernel-structure and temporary-memory issues. CalculateFluxes dominates kernel time; weighted-average SM utilization over the top kernels is 23.4% for B32 and 19.1% for B16; weighted-average bandwidth utilization is 18.1% for B32 and 13.2% for B16; and CalculateFluxes uses over 100 registers per thread, limiting active warps per SM to only four. A proposed restructuring from full per-mesh-block 3D temporaries to lower-dimensional thread-block temporaries reduces memory from 8.858 GB before optimization to 0.138 GB after optimization for the Burgers benchmark parameters reported in the paper. The practical implication is that performance portability at the framework level is necessary but not sufficient; AMR configurations that are algorithmically attractive can still be hardware-inefficient on GPUs unless kernel geometry, rank decomposition, communication strategy, and memory footprint are co-optimized.

5. PARTHENON as a unified dental benchmark

In dental AI, PARTHENON is a benchmark unifying ten datasets under a common schema. It aggregates ten dental datasets, consisting of 8 panoramic datasets and 2 periapical datasets, for a total of 15,062 annotated instances. Across those ten sources, the benchmark includes annotations spanning 14 original diagnostic categories, which are merged into task-specific binary labels. Its common task set comprises tooth detection, caries segmentation (CarSeg), anomaly detection (AD), and dental developmental staging (DDS), making it the data substrate for the MATHENA framework rather than merely an evaluation dataset (Kim et al., 1 Apr 2026).

The common annotation types are tooth-level bounding boxes for detection, binary caries segmentation masks for CarSeg, binary anomaly masks or labels for AD, and Demirjian-method dental developmental stage labels $y\in[0,b]$3–$y\in[0,b]$4 for DDS. Because not all source datasets contain all label types, the benchmark uses harmonization procedures. For tooth detection, the authors train RT-DETR-L on D2, D5, D6, D8, D9, and D10 as a teacher model, report 93.7 $y\in[0,b]$5, and use it in semi-supervised pseudo-label generation for the remaining datasets. Predicted boxes are then filtered by confidence threshold, non-maximum suppression, and a Mahalanobis-distance outlier rejection process based on

$y\in[0,b]$6

with predictions whose squared Mahalanobis distance exceeds a $y\in[0,b]$7 threshold at $y\in[0,b]$8 discarded.

PARTHENON is also defined operationally by its crop-extraction protocol. Once tooth boxes are available, cropped image-mask pairs are extracted from the original OPG and corresponding mask, resized to $y\in[0,b]$9, and augmented offline with random rotations and horizontal flips. In the accompanying MATHENA system, MATHE performs full-image tooth detection with a hybrid CNN-SSM backbone and BiFPN fusion, while HENA performs per-tooth analysis with Mamba VSS blocks, a Global Context State Token, and a triple-head architecture for CarSeg, AD, and DDS. On PARTHENON, MATHENA achieves 93.78% $a=30.9$0 in tooth detection, 90.11% Dice for CarSeg, 88.35% for AD, and 72.40% ACC for DDS; with test-time augmentation, the corresponding values are 94.89%, 91.31%, 89.59%, and 74.10%. The benchmark’s scientific role is that it enables these four tasks to be studied together under one harmonized data schema.

6. Parthenon as a self-evolving legal-agent framework

In legal AI, Parthenon is a six-layer self-evolving legal-agent framework proposed to make long-horizon legal LLM systems more reliable, auditable, and continuously improvable without retraining the base model. Its layers are Model, Harness, Agent, Knowledge, Tools, and Skills. The agent layer is itself split into Solver, Evaluator, and Learner; the framework is designed so that the Solver cannot optimize directly on hidden rubric criteria, the Evaluator is isolated from the live drafting loop, and the Learner proposes only task-agnostic edits to external artifacts rather than weight updates (Geng et al., 3 Jun 2026).

The editable harness is formalized as

$a=30.9$1

where $a=30.9$2 is Knowledge, $a=30.9$3 is Tools, $a=30.9$4 is Skills, and $a=30.9$5 is role prompts and audit gates at step $a=30.9$6. A matter is

$a=30.9$7

where $a=30.9$8 is the task brief, $a=30.9$9 the source set, $b=69.5$0 the deliverable specification, and $b=69.5$1 the hidden rubric. The solver, evaluator, and learner interfaces are \begin{equation} \text{Solver:}\quad (\hat y,\tau)=\mathrm{Solve}M(q,X\mid H,S_t,d), \end{equation} \begin{equation} \text{Evaluator:}\quad z=\mathrm{Evaluate}_J(\hat y\mid q,d,C), \end{equation} \begin{equation} \text{Learner:}\quad \widehat{\Delta}_t=\mathrm{Learn}_L(E_t,Z_t,\mathrm{Repo}(S_t)), \end{equation} with harness update \begin{equation} S{t+1}=S_t\oplus\widehat{\Delta}_t. \end{equation} The evaluation metrics are

$b=69.5$2

This formalization is used to distinguish criterion-level accuracy from strict matter completion.

The Knowledge layer stores reusable legal memory as data, not prompt text, in six families totaling over 2,300 entries: statute catalog, window catalog, deliverable catalog, holiday calendars, legal synonyms, and inference rules. The Tools layer contains 14 deterministic, agent-callable tools, including citation_scan, number_scan, date_scan, reconcile_numbers, reconcile_deadlines, audit_all, and build_deliverable. The Skills layer contains 1,251 task-routed procedural skills, each following a seven-part scaffold and constrained by an anti-leakage checklist that forbids task IDs, rubric phrases, client identities, dates, deal amounts, and quotations from the matter that exposed the failure.

Empirically, the framework is evaluated on Harvey LAB, which contains 1,251 matters across 24 practice areas, with median 7 source documents and median 57 criteria per matter. The paper reports 12,510 agent trajectories, corresponding to 10 full-corpus cells × 1,251 matters each. The baseline finding is that stronger models improve pooled criterion accuracy while strict matter completion remains low. Examples include Codex / GPT-5.4-mini at 68.2% criteria accuracy and 1.12% all-pass, Codex / GPT-5.5 at 79.8% and 3.76%, and Claude Code / Sonnet 4.6 at 82.8% and 11.83%. Holding model and workspace harness fixed, Parthenon improves criterion accuracy by +13.8 percentage points on GPT-5.4-mini Codex, +10.2 percentage points on GPT-5.5 Codex, and +7.4 percentage points on Sonnet 4.6 Claude Code. The strongest reported configuration, Parthenon / Claude Code / Sonnet 4.6, reaches 90.2% criterion accuracy. The framework is therefore presented as evidence that, in legal-domain agents, many failures are failures of source coverage, number/date grounding, authority use, deliverable identity, issue closure, and release discipline rather than purely failures of model scale.