Pith Number

pith:E56GH3BB

pith:2007:E56GH3BBHMIXTM4EFCLOOYAJK4

not attested not anchored not stored refs pending

Critical points for surface maps and the Benedicks-Carleson theorem

Hiroki Takahasi

arxiv:0704.1599 v4 · 2007-04-12 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E56GH3BBHMIXTM4EFCLOOYAJK4}

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	2026-05-18T04:35:46.431775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

277c63ec213b1179b3842896e760095739ea507f488ac1b684440f8406dd9867

Aliases

arxiv: 0704.1599 · arxiv_version: 0704.1599v4 · doi: 10.48550/arxiv.0704.1599 · pith_short_12: E56GH3BBHMIX · pith_short_16: E56GH3BBHMIXTM4E · pith_short_8: E56GH3BB

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/E56GH3BBHMIXTM4EFCLOOYAJK4 \
  | 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: 277c63ec213b1179b3842896e760095739ea507f488ac1b684440f8406dd9867

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d172ffe6481b6d7bac2e9ae798e9e53e16707448f417e063acd90939d3d8e08",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2007-04-12T15:37:46Z",
    "title_canon_sha256": "649c23b6accadd8f8b98fede72f230a61b405e8be0c3eaca48f99dcdff04c010"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0704.1599",
    "kind": "arxiv",
    "version": 4
  }
}