Pith Number

pith:Z4CHMDFK

pith:2012:Z4CHMDFKVIRRE2HCCQDHWYOT4E

not attested not anchored not stored refs pending

Decay of the solution to the bipolar Euler-Poisson system with damping in $\mathbb{R}^3$

Weike Wang, Zhigang Wu

arxiv:1212.3754 v2 · 2012-12-16 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z4CHMDFKVIRRE2HCCQDHWYOT4E}

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	2026-05-18T03:38:13.672139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf04760caaaa231268e214067b61d3e10630fc1a2ca6f4e6c42bbffff9f4e532

Aliases

arxiv: 1212.3754 · arxiv_version: 1212.3754v2 · doi: 10.48550/arxiv.1212.3754 · pith_short_12: Z4CHMDFKVIRR · pith_short_16: Z4CHMDFKVIRRE2HC · pith_short_8: Z4CHMDFK

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/Z4CHMDFKVIRRE2HCCQDHWYOT4E \
  | 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: cf04760caaaa231268e214067b61d3e10630fc1a2ca6f4e6c42bbffff9f4e532

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb76e2a958c9200829ed95792ca805da2d455e673b4bf7aa0a2f2f0e202aee1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-12-16T06:19:40Z",
    "title_canon_sha256": "cfe7f47924867dd3fb73b5531e3f247f0f81d44570e82e313a3c7bb2a213a09b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3754",
    "kind": "arxiv",
    "version": 2
  }
}