Pith Number

pith:4ZXHSOL4

pith:2003:4ZXHSOL4CEO4H7J5JXZAQ7WHM6

not attested not anchored not stored refs pending

Lipschitz Flow-box Theorem

Axel Boldt, Craig Calcaterra

arxiv:math/0305207 v4 · 2003-05-14 · math.DS · math.DG · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZXHSOL4CEO4H7J5JXZAQ7WHM6}

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.

Cited by

3 papers in Pith

A Theory of Saddle Escape in Deep Nonlinear Networks

Receipt and verification

First computed	2026-07-04T15:35:00.109939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e66e79397c111dc3fd3d4df2087ec76785844656030f865a22319b2748a956bf

Aliases

arxiv: math/0305207 · arxiv_version: math/0305207v4 · doi: 10.48550/arxiv.math/0305207 · pith_short_12: 4ZXHSOL4CEO4 · pith_short_16: 4ZXHSOL4CEO4H7J5 · pith_short_8: 4ZXHSOL4

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/4ZXHSOL4CEO4H7J5JXZAQ7WHM6 \
  | 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: e66e79397c111dc3fd3d4df2087ec76785844656030f865a22319b2748a956bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86cd71a6a9dcb6353177e6f40adddf2d5109ee5c4ac948f0499bafd5ff519f3f",
    "cross_cats_sorted": [
      "math.DG",
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2003-05-14T19:08:25Z",
    "title_canon_sha256": "65a0970eeaa81c5d363b58fe9c0bc1dfe0d2adca15da8688c30b9455098afc33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0305207",
    "kind": "arxiv",
    "version": 4
  }
}