Pith Number

pith:4XLXSTGT

pith:2006:4XLXSTGTGAJI7QOLN3K5DAODYS

not attested not anchored not stored refs pending

Approximation and billiards

CPT, FRUMAM), Serge Troubetzkoy (IML

arxiv:math/0611599 v2 · 2006-11-20 · 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{4XLXSTGTGAJI7QOLN3K5DAODYS}

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	2026-05-18T03:39:43.950604Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5d7794cd330128fc1cb6ed5d181c3c49fcb707349676db5e32c5b6f4739562e

Aliases

arxiv: math/0611599 · arxiv_version: math/0611599v2 · doi: 10.48550/arxiv.math/0611599 · pith_short_12: 4XLXSTGTGAJI · pith_short_16: 4XLXSTGTGAJI7QOL · pith_short_8: 4XLXSTGT

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/4XLXSTGTGAJI7QOLN3K5DAODYS \
  | 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: e5d7794cd330128fc1cb6ed5d181c3c49fcb707349676db5e32c5b6f4739562e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d1dae3218876e237bcb3b21c316201b8a7325bef1bd668654ca24c116ec9e331",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2006-11-20T09:09:42Z",
    "title_canon_sha256": "3dd410de41a19a2778e0232bbfb7fc19fc4f48b99e3265bcce36a768cff9cd3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611599",
    "kind": "arxiv",
    "version": 2
  }
}