Pith Number

pith:MF6FYKLX

pith:2008:MF6FYKLXDTZLRTDUG7BUUQXCBO

not attested not anchored not stored refs pending

On the validity of Chapman-Enskog expansions for shock waves with small strength

Christian Klingenberg, Nabil Bedjaoui, Philippe G. LeFloch

arxiv:0812.3985 v1 · 2008-12-20 · math.AP · cs.NA · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MF6FYKLXDTZLRTDUG7BUUQXCBO}

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	2026-06-03T23:06:09.988923Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

617c5c29771cf2b8cc7437c34a42e20b9698a59ae50d59d56bf7915778c2adb1

Aliases

arxiv: 0812.3985 · arxiv_version: 0812.3985v1 · doi: 10.48550/arxiv.0812.3985 · pith_short_12: MF6FYKLXDTZL · pith_short_16: MF6FYKLXDTZLRTDU · pith_short_8: MF6FYKLX

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/MF6FYKLXDTZLRTDUG7BUUQXCBO \
  | 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: 617c5c29771cf2b8cc7437c34a42e20b9698a59ae50d59d56bf7915778c2adb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ac3ad108aa0def1601ea024393a1c0dd90f9ff3da01bfb0b40cc3559ae5e5d0",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-12-20T17:41:34Z",
    "title_canon_sha256": "0b4c7fff1a514ec8c449bd4c47b5f7b20ee762ad24d47169cf64b5940a4acf63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.3985",
    "kind": "arxiv",
    "version": 1
  }
}