Pith Number

pith:3NKT2HGK

pith:2026:3NKT2HGK57J5ARAW6DUZMO73UC

not attested not anchored not stored refs pending

GRACE-DG: A Discontinuous Galerkin method-based code for general non-linear coagulation-fragmentation equations

Jing Yang, Xue-Ning Bai, Zhuo Chen

arxiv:2607.13740 v1 · 2026-07-15 · astro-ph.EP · astro-ph.IM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NKT2HGK57J5ARAW6DUZMO73UC}

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	2026-07-16T01:23:03.758489Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db553d1ccaefd3d04416f0e9963bfba0983f8ccd68b48ee9379acb62cf099e62

Aliases

arxiv: 2607.13740 · arxiv_version: 2607.13740v1 · doi: 10.48550/arxiv.2607.13740 · pith_short_12: 3NKT2HGK57J5 · pith_short_16: 3NKT2HGK57J5ARAW · pith_short_8: 3NKT2HGK

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/3NKT2HGK57J5ARAW6DUZMO73UC \
  | 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: db553d1ccaefd3d04416f0e9963bfba0983f8ccd68b48ee9379acb62cf099e62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13589c5c2935a52cc76027e50908d1fc574fd0b384bc91766e7c016a329968fd",
    "cross_cats_sorted": [
      "astro-ph.IM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.EP",
    "submitted_at": "2026-07-15T11:55:59Z",
    "title_canon_sha256": "40b16efe817e0cc1fcecd3d7d38231f816992d4fc5ce703da84e8d988bfff407"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.13740",
    "kind": "arxiv",
    "version": 1
  }
}