Pith Number

pith:7KMSVQD6

pith:2012:7KMSVQD65PQNXUKIQPFYGHQRWD

not attested not anchored not stored refs pending

Sharp short and long time $\mathbf L^{\boldsymbol \infty}$ bounds for solutions to porous media equations with Neumann boundary conditions

Gabriele Grillo, Matteo Muratori

arxiv:1206.5332 v1 · 2012-06-22 · 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{7KMSVQD65PQNXUKIQPFYGHQRWD}

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	2026-05-18T03:52:40.398810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa992ac07eebe0dbd14883cb831e11b0dddf92fb4e20b8ca0ab67936c00c03f5

Aliases

arxiv: 1206.5332 · arxiv_version: 1206.5332v1 · doi: 10.48550/arxiv.1206.5332 · pith_short_12: 7KMSVQD65PQN · pith_short_16: 7KMSVQD65PQNXUKI · pith_short_8: 7KMSVQD6

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/7KMSVQD65PQNXUKIQPFYGHQRWD \
  | 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: fa992ac07eebe0dbd14883cb831e11b0dddf92fb4e20b8ca0ab67936c00c03f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "880616464923602b903aaaa2dd281a8692df1a239a98e2a515d84dc8200e5256",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-06-22T22:20:36Z",
    "title_canon_sha256": "3c8468c3e35b618e71ef0cd163bdde6227692c7208cb1b2f3de2cf748dc59a00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.5332",
    "kind": "arxiv",
    "version": 1
  }
}