Pith Number

pith:SLH5NPXS

pith:2021:SLH5NPXSVTVMI5EPT5W2HHPZLZ

not attested not anchored not stored refs pending

A new discrete calculus of variations and its applications in statistical physics

Q. H. Liu

arxiv:2104.11075 v1 · 2021-04-21 · physics.gen-ph · physics.chem-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SLH5NPXSVTVMI5EPT5W2HHPZLZ}

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	2026-07-05T02:34:17.378953Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92cfd6bef2aceac4748f9f6da39df95e6dbf30cc91a5b4261390c615c34e86ff

Aliases

arxiv: 2104.11075 · arxiv_version: 2104.11075v1 · doi: 10.48550/arxiv.2104.11075 · pith_short_12: SLH5NPXSVTVM · pith_short_16: SLH5NPXSVTVMI5EP · pith_short_8: SLH5NPXS

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/SLH5NPXSVTVMI5EPT5W2HHPZLZ \
  | 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: 92cfd6bef2aceac4748f9f6da39df95e6dbf30cc91a5b4261390c615c34e86ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3721b09718267a5d59b2160de0997b7f70116ec055036084c314728296a88441",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2021-04-21T08:16:48Z",
    "title_canon_sha256": "da049f6d732c086db3f432f8d238f9818686ad23bcc4cfe1084137e78faff1ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.11075",
    "kind": "arxiv",
    "version": 1
  }
}