Pith Number

pith:OHATB4IX

pith:2004:OHATB4IX4Z2GJEZOPST6RJTINT

not attested not anchored not stored refs pending

Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards

E. Gutkin, S. Tabachnikov

arxiv:math/0412335 v2 · 2004-12-16 · 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{OHATB4IX4Z2GJEZOPST6RJTINT}

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	2026-05-18T03:39:30.797057Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71c130f117e67464932e7ca7e8a6686ce29305bca5fdb3ed447931651e852f75

Aliases

arxiv: math/0412335 · arxiv_version: math/0412335v2 · doi: 10.48550/arxiv.math/0412335 · pith_short_12: OHATB4IX4Z2G · pith_short_16: OHATB4IX4Z2GJEZO · pith_short_8: OHATB4IX

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/OHATB4IX4Z2GJEZOPST6RJTINT \
  | 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: 71c130f117e67464932e7ca7e8a6686ce29305bca5fdb3ed447931651e852f75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0cfe0d065d5da3dbff31de354f58089ac32a13a0ba287eb9a1686b91c8eb0408",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2004-12-16T21:36:13Z",
    "title_canon_sha256": "ea5d16e208fc814d0d2ac9670594cf6087fd66bec0136660792845e0fd28ac1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412335",
    "kind": "arxiv",
    "version": 2
  }
}