drvarma

Exact maximum-likelihood estimation, forecasting and diagnostics of multivariate VARMA (vector ARMA) models — in pure Python, with an optional compiled C engine for speed.

import numpy as np
from drvarma import Model, datasets

series = datasets.simulate_varma(phi=[np.diag([0.5, 0.4, 0.3])], sigma=np.eye(3),
                                 n=300, mu=[100., 50., 75.], seed=1,
                                 names=["A", "B", "C"])
m = Model(series, p=2, q=0, include_mean=True).fit()
print(m.phi, m.sigma, m.loglik)
levels, lo, hi = m.forecast(12, bands=True)     # + 95% bands
print(m.diagnostics())                          # Hosking Q, Jarque-Bera

drvarma fits a stationary Gaussian VARMA(p, q), Φ(B)(wₜ − μ) = Θ(B) aₜ, aₜ ~ N(0, Σ), by exact maximum likelihood (no conditional/back-forecasting approximation), and gives forecasts (+ error bands), impulse responses, variance decompositions, residual diagnostics and volatility.

What this provides. drvarma is a pure-Python implementation of Mauricio's exact-likelihood algorithm for multivariate VARMA (1995 JASA / 1997 AS 311): an innovations-form factorisation that evaluates the exact Gaussian likelihood directly on the VARMA form, without a state-space / Kalman filter, maximised by a faithful factored-BFGS quasi-Newton. Exact ML for VARMA is also available in Python through state-space methods (e.g. statsmodels' Kalman-filter VARMAX); what drvarma adds is a faithful port of this specific, non-Kalman algorithm — which, as far as we know, is not otherwise available in Python — together with the surrounding forecasting/IRF/FEVD/diagnostics toolkit. It runs with no compiled code; the optional C engine is only an accelerator.

Install

pip install drvarma                       # pure-Python (numpy + scipy)

Optional extras: drvarma[plots] (matplotlib + pyfug charts), drvarma[forecast-report] (HTML forecast reports), drvarma[c-engine] (build the CFFI C engine — needs GSL dev headers, ~10–100× faster but optional).

Features

Exact-ML estimation of stationary VARMA(p, q) for general dimension m, with mean, diagonal AR/MA/covariance restrictions, and optional Hannan–Rissanen two-step start.
Forecasting in original units: level, period and annual variation, each with standard errors and 95 % bands; plus fixed-parameter recursive (out-of-sample) forecasting.
Structural analysis: orthogonalised impulse responses, accumulated responses, long-run gain, and the forecast-error variance decomposition.
Diagnostics: Hosking multivariate portmanteau, multivariate Jarque–Bera, per-series ACF/PACF and two-sided cross-correlation (CCF).
Volatility: exponential-weight and moving-window residual covariance.
Transforms: Box-Cox + regular/seasonal differencing and harmonic deseasonalisation (with re-seasonalised forecasts).
I/O & reports: .inp reader/writer, C-format .out/.forecast/ .recursive text reports, an HTML forecast report per series, and matplotlib charts.

Everything runs with no compiled code. The optional CFFI engine wraps the validated drvarma C core and is bit-compatible with the pure-Python path on well-conditioned problems — an accelerator only. The numerical methods are tabulated below; see docs/DEVELOPER_GUIDE.md for the complexity discussion and a pure-Python vs hybrid vs C performance study.

Command line

drvarma IPC3 3 0 -mean -deseason auto -forecast 24        # writes IPC3.out, .forecast
drvarma IPC3 3 0 -mean -forecast 24 -html                # + HTML report per series
drvarma IPC3 3 0 -mean -estwin 200 -forecast 12          # recursive (.recursive)
drvarma IPC3 3 0 -mean -volexp 0.05 20 -volmov 20        # volatility (.volexp/.volmov)

<file>.inp in, text reports out. Flags: -mean -diagar -diagma -diagcov -m {1,2} -twostep -deseason [auto|force] -scale S -forecast H -html -estwin N -volexp [α w] -volmov [w] (λ, d, D come from the .inp header).

Documentation

docs/USER_GUIDE.md — install, API, CLI, worked examples.
docs/INP_FORMAT.md — the .inp input format (a precise, assistant-friendly spec for preparing inputs).
docs/DEVELOPER_GUIDE.md — internals, algorithmic complexity from the literature, and the performance study.

Numerical methods

Algorithm	Reference	Used for
Exact Gaussian VARMA log-likelihood (innovations factorisation, not Kalman)	Mauricio (1995) JASA; Mauricio (1997) AS 311	Exact likelihood (`drvarma._as311`)
Factored-BFGS quasi-Newton + Dennis–Schnabel line search	Dennis & Schnabel (1983)	ML optimisation (`drvarma._qnewt.raxopt`)
Concentrated objective `f1ᵐ·f2` (σ² profiled, Σ = σ²·Q)	Mauricio (1995) JASA §3	Conditioning; covariance / std errors
Hannan–Rissanen two-step	Hannan & Rissanen (1982)	VARMA start (`-twostep`)
Companion-form Lyapunov / autocovariances	Mauricio (1997) AS 311	Stationary covariance, ψ-weights
Orthogonalised IRF & FEVD (Cholesky of Σ)	Lütkepohl (2005)	Structural analysis
Hosking multivariate portmanteau; multivariate Jarque–Bera	Hosking (1980); Jarque & Bera (1980)	Residual diagnostics
Exponential / moving-window conditional covariance	—	Volatility (`drvarma.volatility`)

Cross-references: Mauricio (2002, JTSA 23(4)) and Shea (1989, AS 242) are the other efficient exact-likelihood methods compared in the literature.

Authors and licence

drvarma is developed by David E. Guerrero and Arthur B. Treadway, based on the exact-likelihood algorithms designed and coded by José Alberto Mauricio.

Released under the GNU General Public License v2.0 or later (GPL-2.0-or-later) — see COPYING.

Metadata

Release files for drvarma 0.1.7

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Source distribution (sdist)

Source distribution for drvarma 0.1.7
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drvarma-0.1.7.tar.gz	212.2 kB	Sep 26, 2026	Details

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File	Interpreter	ABI	Platform	Reset
drvarma-0.1.7-py3-none-any.whl 107.3 kB Sep 26, 2026	Python 3	none	any	Details
drvarma-0.1.7-cp313-cp313-win_amd64.whl 108.1 kB Sep 26, 2026	CPython 3.13	CPython 3.13	Windows x86-64	Details
drvarma-0.1.7-cp313-cp313-musllinux_1_2_x86_64.whl 1.3 MB Sep 26, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ x86-64	Details
drvarma-0.1.7-cp313-cp313-musllinux_1_2_aarch64.whl 1.2 MB Sep 26, 2026	CPython 3.13	CPython 3.13	Linux musl 1.2+ ARM64	Details
drvarma-0.1.7-cp313-cp313-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.4 MB Sep 26, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64	Details
drvarma-0.1.7-cp313-cp313-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl 1.3 MB Sep 26, 2026	CPython 3.13	CPython 3.13	Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64	Details
drvarma-0.1.7-cp313-cp313-macosx_14_0_arm64.whl 1.0 MB Sep 26, 2026	CPython 3.13	CPython 3.13	macOS 14.0+ ARM64	Details
drvarma-0.1.7-cp312-cp312-win_amd64.whl 108.1 kB Sep 26, 2026	CPython 3.12	CPython 3.12	Windows x86-64	Details
drvarma-0.1.7-cp312-cp312-musllinux_1_2_x86_64.whl 1.3 MB Sep 26, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ x86-64	Details
drvarma-0.1.7-cp312-cp312-musllinux_1_2_aarch64.whl 1.2 MB Sep 26, 2026	CPython 3.12	CPython 3.12	Linux musl 1.2+ ARM64	Details
drvarma-0.1.7-cp312-cp312-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.4 MB Sep 26, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.24+ x86-64, Linux glibc 2.28+ x86-64	Details
drvarma-0.1.7-cp312-cp312-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl 1.3 MB Sep 26, 2026	CPython 3.12	CPython 3.12	Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64	Details
drvarma-0.1.7-cp312-cp312-macosx_14_0_arm64.whl 1.0 MB Sep 26, 2026	CPython 3.12	CPython 3.12	macOS 14.0+ ARM64	Details
drvarma-0.1.7-cp311-cp311-win_amd64.whl 108.1 kB Sep 26, 2026	CPython 3.11	CPython 3.11	Windows x86-64	Details
drvarma-0.1.7-cp311-cp311-musllinux_1_2_x86_64.whl 1.3 MB Sep 26, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ x86-64	Details
drvarma-0.1.7-cp311-cp311-musllinux_1_2_aarch64.whl 1.2 MB Sep 26, 2026	CPython 3.11	CPython 3.11	Linux musl 1.2+ ARM64	Details
drvarma-0.1.7-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.4 MB Sep 26, 2026	CPython 3.11	CPython 3.11	Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64	Details
drvarma-0.1.7-cp311-cp311-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl 1.3 MB Sep 26, 2026	CPython 3.11	CPython 3.11	Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64	Details
drvarma-0.1.7-cp311-cp311-macosx_14_0_arm64.whl 1.0 MB Sep 26, 2026	CPython 3.11	CPython 3.11	macOS 14.0+ ARM64	Details
drvarma-0.1.7-cp310-cp310-win_amd64.whl 108.1 kB Sep 26, 2026	CPython 3.10	CPython 3.10	Windows x86-64	Details
drvarma-0.1.7-cp310-cp310-musllinux_1_2_x86_64.whl 1.3 MB Sep 26, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ x86-64	Details
drvarma-0.1.7-cp310-cp310-musllinux_1_2_aarch64.whl 1.2 MB Sep 26, 2026	CPython 3.10	CPython 3.10	Linux musl 1.2+ ARM64	Details
drvarma-0.1.7-cp310-cp310-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl 1.4 MB Sep 26, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.28+ x86-64, Linux glibc 2.24+ x86-64	Details
drvarma-0.1.7-cp310-cp310-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl 1.3 MB Sep 26, 2026	CPython 3.10	CPython 3.10	Linux glibc 2.24+ ARM64, Linux glibc 2.28+ ARM64	Details
drvarma-0.1.7-cp310-cp310-macosx_14_0_arm64.whl 1.0 MB Sep 26, 2026	CPython 3.10	CPython 3.10	macOS 14.0+ ARM64	Details

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Release files / drvarma-0.1.7-cp312-cp312-musllinux_1_2_x86_64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

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Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp312-cp312-musllinux_1_2_aarch64.whl

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Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Release files / drvarma-0.1.7-cp312-cp312-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp312-cp312-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp312-cp312-macosx_14_0_arm64.whl

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp311-cp311-win_amd64.whl

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Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp311-cp311-musllinux_1_2_x86_64.whl

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp311-cp311-musllinux_1_2_aarch64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp311-cp311-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl

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Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Release files / drvarma-0.1.7-cp311-cp311-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp311-cp311-macosx_14_0_arm64.whl

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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp310-cp310-win_amd64.whl

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Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp310-cp310-musllinux_1_2_x86_64.whl

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Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp310-cp310-musllinux_1_2_aarch64.whl

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Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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Release files / drvarma-0.1.7-cp310-cp310-manylinux_2_24_x86_64.manylinux_2_28_x86_64.whl

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Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

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Artifact

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SHA-256 checksum: dcba5aa2a5874f9138cfcc1e6c4c3902778ca0c1d7bb83657628fe53bd64c4b5 Verifying attestations

Release files / drvarma-0.1.7-cp310-cp310-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl

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Tags	CPython 3.10 Linux glibc 2.24+ ARM64 Linux glibc 2.28+ ARM64
SHA-256 checksum How to use checksums	`a4d7654aa8c81d0eedc12cf090c80e44b00dad8db248c0e978b7803b4430dd4d`
BLAKE2b-256 checksum How to use checksums	`3c9797f1ee8ed307f70ff5cc8cbfdc4d00a40fd20407031f8287370752d29fb2`
Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

Workflow

Publishing configuration: github.com/davidesg/drvarma-python/blob/fb21ded661cad92fb8796c4585ae96c042897121/.github/workflows/publish.yml
Publishing logs: github.com/davidesg/drvarma-python/actions/runs/36261710106/attempts/1

Artifact

Subject: drvarma-0.1.7-cp310-cp310-manylinux_2_24_aarch64.manylinux_2_28_aarch64.whl
SHA-256 checksum: a4d7654aa8c81d0eedc12cf090c80e44b00dad8db248c0e978b7803b4430dd4d Verifying attestations

Release files / drvarma-0.1.7-cp310-cp310-macosx_14_0_arm64.whl

Download URL	drvarma-0.1.7-cp310-cp310-macosx_14_0_arm64.whl
Size	1.0 MB
Tags	CPython 3.10 macOS 14.0+ ARM64
SHA-256 checksum How to use checksums	`dbb3089dd3a18c680d62222b043cb6793412bc2e259a133992528059483fc1a7`
BLAKE2b-256 checksum How to use checksums	`c449897ebc4c6effd5db66c3e1ae38a59083ff563aefd029bf2c88008aa8c545`
Upload date	Sep 26, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/7.0.0 CPython/3.13.14`

Provenance

Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/davidesg/drvarma-python
Publishing commit: github.com/davidesg/drvarma-python/tree/fb21ded661cad92fb8796c4585ae96c042897121

Workflow

Publishing configuration: github.com/davidesg/drvarma-python/blob/fb21ded661cad92fb8796c4585ae96c042897121/.github/workflows/publish.yml
Publishing logs: github.com/davidesg/drvarma-python/actions/runs/36261710106/attempts/1

Artifact

Subject: drvarma-0.1.7-cp310-cp310-macosx_14_0_arm64.whl
SHA-256 checksum: dbb3089dd3a18c680d62222b043cb6793412bc2e259a133992528059483fc1a7 Verifying attestations