Pith Number

pith:CKH5DJRY

pith:2016:CKH5DJRYPJ5YXIGE6XWOWOX7GX

not attested not anchored not stored refs pending

A badly expanding set on the $2$-torus

Rene R\"uhr

arxiv:1608.02881 v1 · 2016-08-08 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CKH5DJRYPJ5YXIGE6XWOWOX7GX}

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	2026-05-18T01:09:33.433980Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

128fd1a6387a7b8ba0c4f5eceb3aff35d9d873a0f8eeab09fb19e04ce792dd3d

Aliases

arxiv: 1608.02881 · arxiv_version: 1608.02881v1 · doi: 10.48550/arxiv.1608.02881 · pith_short_12: CKH5DJRYPJ5Y · pith_short_16: CKH5DJRYPJ5YXIGE · pith_short_8: CKH5DJRY

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/CKH5DJRYPJ5YXIGE6XWOWOX7GX \
  | 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: 128fd1a6387a7b8ba0c4f5eceb3aff35d9d873a0f8eeab09fb19e04ce792dd3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0d3fc03a83458dc6379d9c029c59e4f16b0dedfe135633dec48482af027ef4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-08T15:06:16Z",
    "title_canon_sha256": "2b1b1b1baef33cbb5b64a2921cc4a6a7149e7fc90b8146ca5d0fc0dd5abed73a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.02881",
    "kind": "arxiv",
    "version": 1
  }
}