Pith Number

pith:JM5UP4X2

pith:2007:JM5UP4X2WWGRD3L4543T3MYVGJ

not attested not anchored not stored refs pending

Critical points of inner functions, nonlinear partial differential equations, and an extension of Liouville's theorem

Daniela Kraus, Oliver Roth

arxiv:0708.4001 v1 · 2007-08-29 · math.CV · 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{JM5UP4X2WWGRD3L4543T3MYVGJ}

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	2026-05-18T02:58:12.405706Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b3b47f2fab58d11ed7cef373db315326d271bfb3fac2f1d19f56f298598a57b

Aliases

arxiv: 0708.4001 · arxiv_version: 0708.4001v1 · doi: 10.48550/arxiv.0708.4001 · pith_short_12: JM5UP4X2WWGR · pith_short_16: JM5UP4X2WWGRD3L4 · pith_short_8: JM5UP4X2

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/JM5UP4X2WWGRD3L4543T3MYVGJ \
  | 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: 4b3b47f2fab58d11ed7cef373db315326d271bfb3fac2f1d19f56f298598a57b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35028d2cdb8177e6ed91386fc8043d28cf5b5429dff53d7a95176c40c3672f8f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.CV",
    "submitted_at": "2007-08-29T18:19:19Z",
    "title_canon_sha256": "d33f8c4bf73a082f8558ed61194ba031d5fca48187c845a78f6f9d1153cb63c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.4001",
    "kind": "arxiv",
    "version": 1
  }
}