Pith Number

pith:XZOY73OV

pith:2026:XZOY73OVS2LGDO47QSLDVOYW6B

not attested not anchored not stored refs pending

Wave-Particle Decomposition for Kinetic Equations I: Theory and Numerics

Chang Liu, Kun Xu

arxiv:2606.26915 v1 · 2026-06-25 · 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{XZOY73OVS2LGDO47QSLDVOYW6B}

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	2026-06-26T01:16:04.011459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be5d8fedd5969661bb9f84963abb16f054fdcafae38ed367c950b8d5456f3c00

Aliases

arxiv: 2606.26915 · arxiv_version: 2606.26915v1 · doi: 10.48550/arxiv.2606.26915 · pith_short_12: XZOY73OVS2LG · pith_short_16: XZOY73OVS2LGDO47 · pith_short_8: XZOY73OV

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/XZOY73OVS2LGDO47QSLDVOYW6B \
  | 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: be5d8fedd5969661bb9f84963abb16f054fdcafae38ed367c950b8d5456f3c00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96f5d9690f5c053ef6546f87f3b1852621459a1115baeb7a619bef6f3a079e9d",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-06-25T11:53:19Z",
    "title_canon_sha256": "5b3e572fe0451706ab6029bcf99e72a1e480a94fb19fa57a40e1f59ff62dd9e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.26915",
    "kind": "arxiv",
    "version": 1
  }
}