Research artifact — attested · publisher paused

OT

Orszag-Tang vortex, preserved in a verifiable public record.

The canonical 2D ideal-MHD test (Orszag & Tang, 1979) on a periodic 256² grid, integrated by Lax-Friedrichs in a GPU compute kernel; signing and verification run through Rail. Each published frame was hashed and signed by an Ed25519 witness against the entropy beacon, so a paper citing a state at pulse_id N can be verified years later from the public record. The publisher is paused — the frame below is the last attested state, and it still verifies.

state paused
grid 256×256
field ρ
frame —
pulse 396703

The stream stopped at p#396703 · chain intact to here · every signed record below still verifies.

The OT publisher has been offline since 2026-04-29. The frame above is the last attested state, signed against the beacon pulse current at signing time. Nothing here has been re-signed since.

age unknown until the beacon answers

There is no verify button here any more, and that is the honest outcome rather than a tidy one. This run's attestations were only ever kept in a hosted object store, which we shut off on 2026-07-24 when the bill stopped being worth paying. The signatures were real and the records are gone — we did not keep a second copy, so nobody can check this particular frame now, including us. A page that offers proof it cannot produce is worse than a page that admits the gap. The live beacon is the same Orszag–Tang system on a 128² grid, re-signed every ~32 s, and its attestation does verify — that is where to point a checker.

Numerical method

scheme
Lax-Friedrichs (1st order, divergence-clean by accident of LF flux structure)
grid
256 × 256 periodic, square 2π domain
equations
ideal MHD, γ = 5/3, 6 conserved fields (ρ, ρvx, ρvy, Bx, By, E)
timestep
CFL-bounded: dt = 0.3 · Δx / max|cfast|, host-side max reduction every frame
init
OT vortex: ρ0 = 25/(36π), p0 = 5/(12π), v = (−sin y, sin x), B = (−sin y / √(4π), sin 2x / √(4π))
conservation
Δm/m ≈ 10−7, ΔE/E ≈ 10−7, ∇·B ≈ 10−6 (f32 precision; the lower-resolution sister at /plasma runs in f64 and conserves to 10−15)
runtime
Metal compute kernel on an Apple-silicon GPU, two-pass LF dispatched per step. Host driver in Objective-C; bytes published via the same primitive that signs every other Ledatic surface.
cadence
~388 frames/s solver while running; attestations were re-signed every 30 s against the live entropy pulse. Publisher paused since 2026-04-29 — the last attestation remains verifiable, and no re-signing is claimed.

Cite this state

Each published frame's bytes were signed against the beacon pulse current at signing time. To cite a state, capture both the frame attestation and the beacon pulse it was bound to. Anyone can verify with the public verifier (/attest/verify.sh) and the public key (/attest/fleet0.pub.pem, fp = cac5f21a70564aeb).

# citation — last attested state
"OT MHD, ledatic.org/ot,
frame_id=…, sha=…,
pulse_id=…, pk_fp=…,
accessed=…"

What you can still check — the live Orszag–Tang beacon's signed record, re-issued every ~32 s:

curl -sf https://ledatic.org/entropy/frame/latest.attestation.json
# → digest + pulse_id + Ed25519 sig, pk_fp=cac5f21a70564aeb

That record signs the solver state, whose bytes we hold but do not publish — it carries bytes_published: false and says so in its own body, rather than naming a URL it cannot honour. So the signature is checkable and the re-hash is not. Stating which half you get is the whole discipline; an attestation that points at bytes it doesn't match would be worse than one that admits the limit.

Lineage

Sits in conversation with the conservation-law numerics tradition (van Leer, Roe, Harten, Toro) and the cryptographic-attestation lineage (Drand, NIST randomness beacon). The intersection — physical chaos plus public Ed25519 provenance plus a self-hosting compiler in the signing path — is what's novel here.

References: