Pith Number

pith:3QWBH54L

pith:2012:3QWBH54LBRZ4PV2VZLKD3GWEHX

not attested not anchored not stored refs pending

Porous media equations with two weights: smoothing and decay properties of energy solutions via Poincar\'e inequalities

Gabriele Grillo, Maria Michaela Porzio, Matteo Muratori

arxiv:1204.6159 v2 · 2012-04-27 · 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{3QWBH54LBRZ4PV2VZLKD3GWEHX}

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	2026-05-18T03:41:20.158824Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc2c13f78b0c73c7d755cad43d9ac43df42e26b9c0d69ec2e16de90147f985fa

Aliases

arxiv: 1204.6159 · arxiv_version: 1204.6159v2 · doi: 10.48550/arxiv.1204.6159 · pith_short_12: 3QWBH54LBRZ4 · pith_short_16: 3QWBH54LBRZ4PV2V · pith_short_8: 3QWBH54L

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/3QWBH54LBRZ4PV2VZLKD3GWEHX \
  | 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: dc2c13f78b0c73c7d755cad43d9ac43df42e26b9c0d69ec2e16de90147f985fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd5278d12ec8b93a72caef530b3f20ae8fcae12cbcddc169f4c040279a14deef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-27T09:55:13Z",
    "title_canon_sha256": "5536103c68fbfe7c1b81493000ae5ca2ca87964206187fd0ff6ea62f1a66515d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6159",
    "kind": "arxiv",
    "version": 2
  }
}