Pith Number

pith:PZI77HWB

pith:2012:PZI77HWBLD4ZW3EROEQ4DSI5EW

not attested not anchored not stored refs pending

$W^{1,q}$ estimates for the extremal solution of reaction-diffusion problems

Manel Sanchon

arxiv:1209.1526 v1 · 2012-09-07 · 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{PZI77HWBLD4ZW3EROEQ4DSI5EW}

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	2026-05-18T03:46:04.581885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e51ff9ec158f99b6c917121c1c91d25a167518f4ee35263c29ef44abf277bc4

Aliases

arxiv: 1209.1526 · arxiv_version: 1209.1526v1 · doi: 10.48550/arxiv.1209.1526 · pith_short_12: PZI77HWBLD4Z · pith_short_16: PZI77HWBLD4ZW3ER · pith_short_8: PZI77HWB

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/PZI77HWBLD4ZW3EROEQ4DSI5EW \
  | 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: 7e51ff9ec158f99b6c917121c1c91d25a167518f4ee35263c29ef44abf277bc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3db3320ae5d866da205a1d322d7c97a60f662306f6cf76d12859401da8eb1493",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-07T13:11:41Z",
    "title_canon_sha256": "8458c09278856231ca4fb3cf91b1cf04bd876800e287e7bedc3f77d11d3e8729"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1526",
    "kind": "arxiv",
    "version": 1
  }
}