Pith Number

pith:ZGJ4INPR

pith:2024:ZGJ4INPRXZ75A5VSWHQBOJKR7Y

not attested not anchored not stored refs pending

Coupling and Tensorization of Kinetic Theory and Graph Theory

Datong Zhou

arxiv:2412.14512 v2 · 2024-12-19 · math.AP · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZGJ4INPRXZ75A5VSWHQBOJKR7Y}

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	2026-07-05T10:37:40.909679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c993c435f1be7fd076b2b1e0172551fe0eb20282e7f5eed8f27c92751037c6d9

Aliases

arxiv: 2412.14512 · arxiv_version: 2412.14512v2 · doi: 10.48550/arxiv.2412.14512 · pith_short_12: ZGJ4INPRXZ75 · pith_short_16: ZGJ4INPRXZ75A5VS · pith_short_8: ZGJ4INPR

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/ZGJ4INPRXZ75A5VSWHQBOJKR7Y \
  | 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: c993c435f1be7fd076b2b1e0172551fe0eb20282e7f5eed8f27c92751037c6d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa3000d3ac39d2d114e0b3e82c0ad19b76c21a8f016e037cc618681027fa75bd",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-19T04:25:56Z",
    "title_canon_sha256": "6d7cbbb018eee8f19acca3f95882b99055495987429feea3b839bf1f63a150a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.14512",
    "kind": "arxiv",
    "version": 2
  }
}