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Pith Number

pith:F7QRUX25

pith:2024:F7QRUX25JSFI3S454ZDI7RAGBW
not attested not anchored not stored refs pending

Long time derivation of the Boltzmann equation from hard sphere dynamics

Xiao Ma, Yu Deng, Zaher Hani

arxiv:2408.07818 v3 · 2024-08-14 · math.AP

Add to your LaTeX paper
\usepackage{pith}
\pithnumber{F7QRUX25JSFI3S454ZDI7RAGBW}

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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.

Cited by

10 papers in Pith

Receipt and verification
First computed 2026-07-05T11:39:42.467938Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

2fe11a5f5d4c8a8dcb9de6468fc4060d982c903ab7f6c98a6767967e95629637

Aliases

arxiv: 2408.07818 · arxiv_version: 2408.07818v3 · doi: 10.48550/arxiv.2408.07818 · pith_short_12: F7QRUX25JSFI · pith_short_16: F7QRUX25JSFI3S45 · pith_short_8: F7QRUX25
Agent API
Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/F7QRUX25JSFI3S454ZDI7RAGBW \
  | 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: 2fe11a5f5d4c8a8dcb9de6468fc4060d982c903ab7f6c98a6767967e95629637
Canonical record JSON
{
  "metadata": {
    "abstract_canon_sha256": "c90641e633277b9bd4b1116abfbd606f87296d54aa356341a2ad03d9ce6270ce",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-08-14T21:14:18Z",
    "title_canon_sha256": "1a21500ad319b5bacea39b4c2916b18048bc51ad597d103a4245213e72847ac5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.07818",
    "kind": "arxiv",
    "version": 3
  }
}