Pith Number

pith:OV6V5W74

pith:2008:OV6V5W744CFYURCIXNX5VSUJK4

not attested not anchored not stored refs pending

Gradient estimates for $u_t=\Delta F(u)$ on manifolds and some Liouville-type theorems

Xiangjin Xu

arxiv:0805.3676 v3 · 2008-05-23 · math.AP · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OV6V5W744CFYURCIXNX5VSUJK4}

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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	2026-05-18T04:29:54.212089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

757d5edbfce08b8a4448bb6fdaca89573ea1b50f002b4b7f5ce4a9cd0542ae77

Aliases

arxiv: 0805.3676 · arxiv_version: 0805.3676v3 · doi: 10.48550/arxiv.0805.3676 · pith_short_12: OV6V5W744CFY · pith_short_16: OV6V5W744CFYURCI · pith_short_8: OV6V5W74

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/OV6V5W744CFYURCIXNX5VSUJK4 \
  | 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: 757d5edbfce08b8a4448bb6fdaca89573ea1b50f002b4b7f5ce4a9cd0542ae77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28b75b52dd7ef1585d1f6a5813dda6bdb8fa6f15fd9f09e8214098afffae4c20",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2008-05-23T18:14:34Z",
    "title_canon_sha256": "54df4c852264758ac4c3d65c36db82c129e38afbfc9a76a46f3e933757f356b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0805.3676",
    "kind": "arxiv",
    "version": 3
  }
}