Pith Number

pith:V2CCBWLT

pith:2019:V2CCBWLTZKKNNROFMUWLPEBPQM

not attested not anchored not stored refs pending

Remarks on the energy inequality of a global $L^{\infty}$ solution to the compressible Euler equations for the isentropic nozzle flow

Naoki Tsuge

arxiv:1908.03209 v1 · 2019-08-08 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V2CCBWLTZKKNNROFMUWLPEBPQM}

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	2026-07-04T23:52:37.531606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae8420d973ca94d6c5c5652cb7902f833d432535d0ce719d1491d1ec80930973

Aliases

arxiv: 1908.03209 · arxiv_version: 1908.03209v1 · doi: 10.48550/arxiv.1908.03209 · pith_short_12: V2CCBWLTZKKN · pith_short_16: V2CCBWLTZKKNNROF · pith_short_8: V2CCBWLT

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/V2CCBWLTZKKNNROFMUWLPEBPQM \
  | 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: ae8420d973ca94d6c5c5652cb7902f833d432535d0ce719d1491d1ec80930973

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eb20311a5c64613b1f14894528c9a276c97950d53addc391d062e4256b2e5e4",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-08T15:42:53Z",
    "title_canon_sha256": "8d8852c43e96727f4bb43fa3e9e756316062494f02f6bd0eb8e9d42f7d9ce2a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03209",
    "kind": "arxiv",
    "version": 1
  }
}