Pith Number

pith:KCKQ4I65

pith:2012:KCKQ4I65OREWDWLSTJJLOVA5DQ

not attested not anchored not stored refs pending

Gradient estimates for porous medium and fast diffusion equations by martingale method

Ying Hu (IRMAR), Zhongmin Qian (MI), Zichen Zhang (MI)

arxiv:1206.1394 v2 · 2012-06-07 · 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{KCKQ4I65OREWDWLSTJJLOVA5DQ}

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	2026-05-18T02:03:55.963161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

50950e23dd744961d9729a52b7541d1c142962d9e29ed88b6f9f81fead068123

Aliases

arxiv: 1206.1394 · arxiv_version: 1206.1394v2 · doi: 10.48550/arxiv.1206.1394 · pith_short_12: KCKQ4I65OREW · pith_short_16: KCKQ4I65OREWDWLS · pith_short_8: KCKQ4I65

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/KCKQ4I65OREWDWLSTJJLOVA5DQ \
  | 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: 50950e23dd744961d9729a52b7541d1c142962d9e29ed88b6f9f81fead068123

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9dfcdffb14ec03e72b61018491738cfe64fe0ad2dfff42243592026916a9ab64",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-07T04:32:51Z",
    "title_canon_sha256": "69e634d2aa083f3391efe75eb0f8df7f191f0a1552503a7d96d100d296ca87d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1394",
    "kind": "arxiv",
    "version": 2
  }
}