Pith Number

pith:B2SHNH2G

pith:2026:B2SHNH2GAOYSN7NRHVV7VA7UJE

not attested not anchored not stored refs pending

Two-Step MV-DeepONet: Probabilistic Operator Learning for Uncertainty Propagation Driven by Random Input Fields

Jiasen Liu, Lei Wang, Yupei Nie

arxiv:2608.09071 v1 · 2026-08-10 · math.NA · cs.AI · cs.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B2SHNH2GAOYSN7NRHVV7VA7UJE}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-08-11T02:21:43.912931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ea4769f4603b126fdb13d6bfa83f4491b9025791ec185e5d9b04c30942afe36

Aliases

arxiv: 2608.09071 · arxiv_version: 2608.09071v1 · doi: 10.48550/arxiv.2608.09071 · pith_short_12: B2SHNH2GAOYS · pith_short_16: B2SHNH2GAOYSN7NR · pith_short_8: B2SHNH2G

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/B2SHNH2GAOYSN7NRHVV7VA7UJE \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0ea4769f4603b126fdb13d6bfa83f4491b9025791ec185e5d9b04c30942afe36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b7710c3bffa13d7a772f5966e0424a6b8e1388d4201a4b557c0d4cee37fe54e",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-08-10T03:21:10Z",
    "title_canon_sha256": "6fd433c78002343b99e01a7b20cb67834b8d7079101de8692250d9f08267f893"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.09071",
    "kind": "arxiv",
    "version": 1
  }
}