Pith Number

pith:Q3JFW7YS

pith:2015:Q3JFW7YSY67TSBA54F43B753OU

not attested not anchored not stored refs pending

Global existence and $L^{p}$ convergence rates of planar waves for three-dimensional bipolar Euler-Poisson systems

Jie Liao, Yeping Li

arxiv:1501.06008 v1 · 2015-01-24 · 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{Q3JFW7YSY67TSBA54F43B753OU}

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	2026-05-18T02:28:47.076746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86d25b7f12c7bf39041de179b0ffbb7514c6cbe8c116105df5f52acfe43bfc23

Aliases

arxiv: 1501.06008 · arxiv_version: 1501.06008v1 · doi: 10.48550/arxiv.1501.06008 · pith_short_12: Q3JFW7YSY67T · pith_short_16: Q3JFW7YSY67TSBA5 · pith_short_8: Q3JFW7YS

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/Q3JFW7YSY67TSBA54F43B753OU \
  | 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: 86d25b7f12c7bf39041de179b0ffbb7514c6cbe8c116105df5f52acfe43bfc23

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce14d2b8ddd0241d0a793dfe515aa5b2230a19678fea07d3a4484048706940a4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-01-24T06:43:34Z",
    "title_canon_sha256": "0e21a62874ae9caaef5d4982e641f1c74d38172a5a0c2a7df7fcd156bbe0d36e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06008",
    "kind": "arxiv",
    "version": 1
  }
}