Pith Number

pith:PGT45LFA

pith:2015:PGT45LFAD64UVNGTGL6YXBHZXX

not attested not anchored not stored refs pending

On Mittag-Leffler moments for the Boltzmann equation for hard potentials without cutoff

Irene M. Gamba, Maja Taskovi\'c, Nata\v{s}a Pavlovi\'c, Ricardo J. Alonso

arxiv:1512.06769 v2 · 2015-12-21 · 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{PGT45LFAD64UVNGTGL6YXBHZXX}

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	2026-05-18T00:49:36.832607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79a7ceaca01fb94ab4d332fd8b84f9bdff6ecb238afbb4dd4f70c922cdf7adf1

Aliases

arxiv: 1512.06769 · arxiv_version: 1512.06769v2 · doi: 10.48550/arxiv.1512.06769 · pith_short_12: PGT45LFAD64U · pith_short_16: PGT45LFAD64UVNGT · pith_short_8: PGT45LFA

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/PGT45LFAD64UVNGTGL6YXBHZXX \
  | 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: 79a7ceaca01fb94ab4d332fd8b84f9bdff6ecb238afbb4dd4f70c922cdf7adf1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cda15ac10161d941ad99fa04e2eb9b8846657a48b567455808f221c0f44a3ae5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-12-21T19:00:07Z",
    "title_canon_sha256": "4e316a2bdf040a8f235b07c47f65c90807040fa1677c353df695fcd33f38b213"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06769",
    "kind": "arxiv",
    "version": 2
  }
}