Pith Number

pith:PE642LT3

pith:2026:PE642LT3XM3SDCXEZR6TQQNB77

not attested not anchored not stored refs pending

On the Spatially Homogeneous Boltzmann Equation with Mass Exchange

Jian-Guo Liu, Siwei Luo

arxiv:2607.20684 v1 · 2026-07-22 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PE642LT3XM3SDCXEZR6TQQNB77}

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	2026-07-24T00:23:29.422577Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

793dcd2e7bbb37218ae4cc7d3841a1ffc362f71387aae25aa9323bfd25bbd9ed

Aliases

arxiv: 2607.20684 · arxiv_version: 2607.20684v1 · doi: 10.48550/arxiv.2607.20684 · pith_short_12: PE642LT3XM3S · pith_short_16: PE642LT3XM3SDCXE · pith_short_8: PE642LT3

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/PE642LT3XM3SDCXEZR6TQQNB77 \
  | 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: 793dcd2e7bbb37218ae4cc7d3841a1ffc362f71387aae25aa9323bfd25bbd9ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bfba71319e51d3972d07d4a606f32486ce1c9b1f4156aed07b29675971bea81",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-22T19:33:35Z",
    "title_canon_sha256": "a4370360aad9afd1b5d3d7742b1fc8b03e6627cce9b990f5e5818060bfb504e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20684",
    "kind": "arxiv",
    "version": 1
  }
}