Pith Number

pith:GUAMASHS

pith:2025:GUAMASHSKWE5U7C4GUHVOGI2Q6

not attested not anchored not stored refs pending

Efficient numerical methods for the uncertain Boltzmann equation based on a hybrid solver

Liu Liu, Yiwen Lin

arxiv:2507.20316 v1 · 2025-07-27 · math.NA · 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{GUAMASHSKWE5U7C4GUHVOGI2Q6}

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	2026-07-05T11:44:16.962804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3500c048f25589da7c5c350f57191a87af759e966e0beac5d087b4aeb5571fa5

Aliases

arxiv: 2507.20316 · arxiv_version: 2507.20316v1 · doi: 10.48550/arxiv.2507.20316 · pith_short_12: GUAMASHSKWE5 · pith_short_16: GUAMASHSKWE5U7C4 · pith_short_8: GUAMASHS

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/GUAMASHSKWE5U7C4GUHVOGI2Q6 \
  | 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: 3500c048f25589da7c5c350f57191a87af759e966e0beac5d087b4aeb5571fa5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6d0465f15843f0290d38d8cdd803d97e04c474e13f0f303914a6e26956955f7",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-27T15:15:05Z",
    "title_canon_sha256": "488574c3859cd35e0053236b3e80e7610c6a216883265c0abf52467af0e8cdce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.20316",
    "kind": "arxiv",
    "version": 1
  }
}