Pith Number

pith:5B6KFQ6P

pith:2013:5B6KFQ6PRE3XHHNX5U3BHPZ76Z

not attested not anchored not stored refs pending

A non-concentration estimate for partially rectangular billiards

Hans Christianson

arxiv:1305.4653 v3 · 2013-05-20 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5B6KFQ6PRE3XHHNX5U3BHPZ76Z}

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	2026-05-18T03:13:21.382114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e87ca2c3cf8937739db7ed3613bf3ff6658811aac31794700396a824f49ebb43

Aliases

arxiv: 1305.4653 · arxiv_version: 1305.4653v3 · doi: 10.48550/arxiv.1305.4653 · pith_short_12: 5B6KFQ6PRE3X · pith_short_16: 5B6KFQ6PRE3XHHNX · pith_short_8: 5B6KFQ6P

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/5B6KFQ6PRE3XHHNX5U3BHPZ76Z \
  | 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: e87ca2c3cf8937739db7ed3613bf3ff6658811aac31794700396a824f49ebb43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bef2926ee5140160a3c95c2e2ed625ecde3b4dc83c39831bf725ab4a29972ae0",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-05-20T20:45:02Z",
    "title_canon_sha256": "5808fd71572c93a2dd0c036ca0fd560567c452eebca4ea482819f7e4fed40539"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4653",
    "kind": "arxiv",
    "version": 3
  }
}