Pith Number

pith:NJVNRKHV

pith:2012:NJVNRKHVNPM33LY4JWZZFK2ZID

not attested not anchored not stored refs pending

A note on phase transitions for the Smoluchowski equation with dipolar potential

Amic Frouvelle (CEREMADE), Jian-Guo Liu, Pierre Degond (IMT)

arxiv:1212.3920 v1 · 2012-12-17 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NJVNRKHVNPM33LY4JWZZFK2ZID}

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	2026-05-18T03:38:22.057110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a6ad8a8f56bd9bdaf1c4db392ab5940dde662c09f6a5695ea68d4bdb8388999

Aliases

arxiv: 1212.3920 · arxiv_version: 1212.3920v1 · doi: 10.48550/arxiv.1212.3920 · pith_short_12: NJVNRKHVNPM3 · pith_short_16: NJVNRKHVNPM33LY4 · pith_short_8: NJVNRKHV

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/NJVNRKHVNPM33LY4JWZZFK2ZID \
  | 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: 6a6ad8a8f56bd9bdaf1c4db392ab5940dde662c09f6a5695ea68d4bdb8388999

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b34afb45803f6cca971a8162a72795dde7da9e262673fd37ea7cfa178186a33",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-12-17T08:14:52Z",
    "title_canon_sha256": "aa03de270ce21486890e586baeed11ddcf1d59dfeb5c120e2d96b289b2b71366"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3920",
    "kind": "arxiv",
    "version": 1
  }
}