Pith Number

pith:R7QNBVSA

pith:2012:R7QNBVSACASGTWM5GK4ZBI4MTI

not attested not anchored not stored refs pending

Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff

Fr\'ed\'eric H\'erau (LMJL), Radjesvarane Alexandre (USTH), Wei-Xi Li

arxiv:1212.4632 v4 · 2012-12-19 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R7QNBVSACASGTWM5GK4ZBI4MTI}

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	2026-05-18T00:08:24.437936Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8fe0d0d640102469d99d32b990a38c9a2d0139055195d9127f96c0293248f85f

Aliases

arxiv: 1212.4632 · arxiv_version: 1212.4632v4 · doi: 10.48550/arxiv.1212.4632 · pith_short_12: R7QNBVSACASG · pith_short_16: R7QNBVSACASGTWM5 · pith_short_8: R7QNBVSA

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/R7QNBVSACASGTWM5GK4ZBI4MTI \
  | 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: 8fe0d0d640102469d99d32b990a38c9a2d0139055195d9127f96c0293248f85f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a696937876a6982b9dd3c4ccf462789501eb1006fd6399d640c5da4808eaba8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-19T12:12:58Z",
    "title_canon_sha256": "030dbf5b1289a45a6ce104193aeed2d2c1840dce2fe07acf4bec4f0a4d6287ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4632",
    "kind": "arxiv",
    "version": 4
  }
}