Pith Number

pith:KQ4WD6W7

pith:2025:KQ4WD6W76X2KBO3OQNYAOWHS3T

not attested not anchored not stored refs pending

A Conservative and Positivity-Preserving Discontinuous Galerkin Method for the Population Balance Equation

Guanyang Liu, Yong-Tao Zhang, Ziyao Xu

arxiv:2507.16631 v1 · 2025-07-22 · 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{KQ4WD6W76X2KBO3OQNYAOWHS3T}

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	2026-07-05T11:41:28.034792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

543961fadff5f4a0bb6e83700758f2dceb440f5dd27b20551cbf3dca146aff6f

Aliases

arxiv: 2507.16631 · arxiv_version: 2507.16631v1 · doi: 10.48550/arxiv.2507.16631 · pith_short_12: KQ4WD6W76X2K · pith_short_16: KQ4WD6W76X2KBO3O · pith_short_8: KQ4WD6W7

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/KQ4WD6W76X2KBO3OQNYAOWHS3T \
  | 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: 543961fadff5f4a0bb6e83700758f2dceb440f5dd27b20551cbf3dca146aff6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "acaf4d3a2dcf5dc836cb9fd0f2dce5fa9c90de4b03acc6a1b8ba1453879477e0",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-22T14:23:29Z",
    "title_canon_sha256": "6e97b26278847d2f37846567e8bc0d2a30b011f68e65459dcb85ef16355e2ae6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16631",
    "kind": "arxiv",
    "version": 1
  }
}