Pith Number

pith:4REYDWOQ

pith:2003:4REYDWOQTYH3NJCD7UT7RXVUOO

not attested not anchored not stored refs pending

Covariant Wigner Function Approach to the Boltzmann Equation for Mixing Fermions in Curved Spacetime

Kazuhiro Yamamoto

arxiv:astro-ph/0305390 v1 · 2003-05-21 · astro-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{4REYDWOQTYH3NJCD7UT7RXVUOO}

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	2026-05-18T04:13:37.337411Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9

Aliases

arxiv: astro-ph/0305390 · arxiv_version: astro-ph/0305390v1 · doi: 10.48550/arxiv.astro-ph/0305390 · pith_short_12: 4REYDWOQTYH3 · pith_short_16: 4REYDWOQTYH3NJCD · pith_short_8: 4REYDWOQ

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/4REYDWOQTYH3NJCD7UT7RXVUOO \
  | 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: e44981d9d09e0fb6a443fd27f8deb4738f71b7de9716081a1c717bcd8a3f6bf9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a47d6ed2c3987fa3091fbb157f5a505137ee685407aace16db94bf7dfce4386",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2003-05-21T07:31:55Z",
    "title_canon_sha256": "399f3aa813522111271d570c876b9550604cb566783cdc1e663a0b6e0ee60ead"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0305390",
    "kind": "arxiv",
    "version": 1
  }
}