Pith Number

pith:WWXBGGAB

pith:2017:WWXBGGABGB2XY2VGKF6NZA3U6W

not attested not anchored not stored refs pending

Coexistence of periodic-2 and periodic-3 caustics for nearly circular analytic billiard maps

Jianlu Zhang, Vadim Kaloshin

arxiv:1711.10541 v1 · 2017-11-28 · 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{WWXBGGABGB2XY2VGKF6NZA3U6W}

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	2026-07-05T06:48:43.734244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1

Aliases

arxiv: 1711.10541 · arxiv_version: 1711.10541v1 · doi: 10.48550/arxiv.1711.10541 · pith_short_12: WWXBGGABGB2X · pith_short_16: WWXBGGABGB2XY2VG · pith_short_8: WWXBGGAB

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/WWXBGGABGB2XY2VGKF6NZA3U6W \
  | 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: b5ae13180130757c6aa6517cdc8374f5b886bcfbb1614d5fd9aa8cfea02a9de1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed45af8dad1db24eebca2d69837331d486611f97e8ba0384aaab7baa0f3540d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-11-28T20:26:58Z",
    "title_canon_sha256": "dbd47c2848843d7f7b6b3476751f48189f4e726e9d69732c89dbb826056f264b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.10541",
    "kind": "arxiv",
    "version": 1
  }
}