Pith Number

pith:XAVVDRIJ

pith:2007:XAVVDRIJPXNYGHNUXJALA6D3PU

not attested not anchored not stored refs pending

Harnack Inequality and Strong Feller Property for Stochastic Fast-Diffusion Equations

Feng-Yu Wang, Wei Liu

arxiv:0712.3136 v1 · 2007-12-19 · math.PR · 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{XAVVDRIJPXNYGHNUXJALA6D3PU}

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	2026-05-18T02:16:02.619187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b82b51c5097ddb831db4ba40b0787b7d10b952e2640d2ed719fbdaa16146412c

Aliases

arxiv: 0712.3136 · arxiv_version: 0712.3136v1 · doi: 10.48550/arxiv.0712.3136 · pith_short_12: XAVVDRIJPXNY · pith_short_16: XAVVDRIJPXNYGHNU · pith_short_8: XAVVDRIJ

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/XAVVDRIJPXNYGHNUXJALA6D3PU \
  | 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: b82b51c5097ddb831db4ba40b0787b7d10b952e2640d2ed719fbdaa16146412c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e0692ec685ba9a0936277f4061f2d33f755d16ed309a6d52c7263c17bf67386",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2007-12-19T09:56:05Z",
    "title_canon_sha256": "0a87fb9c8f6e085973e4d5255445707d95b5a4a09624a5e61c113898e79da889"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3136",
    "kind": "arxiv",
    "version": 1
  }
}