Pith Number

pith:H3FVBVCJ

pith:2011:H3FVBVCJWPLO2C7BD2XZJEFGQD

not attested not anchored not stored refs pending

On convergence to equilibrium distribution for Dirac equation

Alexander Komech, Elena Kopylova

arxiv:1201.6221 v1 · 2011-12-05 · 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{H3FVBVCJWPLO2C7BD2XZJEFGQD}

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	2026-05-18T04:03:33.329638Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ecb50d449b3d6ed0be11eaf9490a680fb01ac163cea4da6b035d1e1b38b64a3

Aliases

arxiv: 1201.6221 · arxiv_version: 1201.6221v1 · doi: 10.48550/arxiv.1201.6221 · pith_short_12: H3FVBVCJWPLO · pith_short_16: H3FVBVCJWPLO2C7B · pith_short_8: H3FVBVCJ

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/H3FVBVCJWPLO2C7BD2XZJEFGQD \
  | 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: 3ecb50d449b3d6ed0be11eaf9490a680fb01ac163cea4da6b035d1e1b38b64a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8fd9e3a896e1784936bd1622aa1dcd98c11807e50b64d01cf455351fe6500bb",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-12-05T19:21:23Z",
    "title_canon_sha256": "5a6449f4f7a7b06de71bff14253a42fd563c5882744448dfdc3b1d17b20d1097"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6221",
    "kind": "arxiv",
    "version": 1
  }
}