Pith Number

pith:XO75TM7L

pith:2016:XO75TM7LTXHJJOE6TCKCLZVLHC

not attested not anchored not stored refs pending

One-sided convergence in the Boltzmann-Grad limit

Isabelle Gallagher (IMJ), Laure Saint-Raymond (DMA), Sergio Simonella, Thierry Bodineau (CMAP)

arxiv:1612.03722 v1 · 2016-12-12 · math.PR · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XO75TM7LTXHJJOE6TCKCLZVLHC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T00:55:18.487161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbbfd9b3eb9dce94b89e989425e6ab38a1cf9f250c3ee64b4c0290a5fffa836e

Aliases

arxiv: 1612.03722 · arxiv_version: 1612.03722v1 · doi: 10.48550/arxiv.1612.03722 · pith_short_12: XO75TM7LTXHJ · pith_short_16: XO75TM7LTXHJJOE6 · pith_short_8: XO75TM7L

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/XO75TM7LTXHJJOE6TCKCLZVLHC \
  | 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: bbbfd9b3eb9dce94b89e989425e6ab38a1cf9f250c3ee64b4c0290a5fffa836e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1524932267f4d24c1def62e7216320ec8e4fb218b8703fb5a1c14e7fc314ebde",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-12T14:52:22Z",
    "title_canon_sha256": "d59772085ae07f4b24276fe85ba3973d31588bc38b897394a94a5b03981965ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03722",
    "kind": "arxiv",
    "version": 1
  }
}