Pith Number

pith:ZRR4V2FX

pith:2009:ZRR4V2FX4QHGX5HJEAD3HACRYP

not attested not anchored not stored refs pending

Heaviness in Circle Rotations

David Ralston

arxiv:0906.4004 v2 · 2009-06-22 · 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{ZRR4V2FX4QHGX5HJEAD3HACRYP}

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	2026-05-18T04:20:50.079728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc63cae8b7e40e6bf4e92007b38051c3fed36b16db9c228c9610980d75ce22ef

Aliases

arxiv: 0906.4004 · arxiv_version: 0906.4004v2 · doi: 10.48550/arxiv.0906.4004 · pith_short_12: ZRR4V2FX4QHG · pith_short_16: ZRR4V2FX4QHGX5HJ · pith_short_8: ZRR4V2FX

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/ZRR4V2FX4QHGX5HJEAD3HACRYP \
  | 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: cc63cae8b7e40e6bf4e92007b38051c3fed36b16db9c228c9610980d75ce22ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2494ccbe107f0f3afddd6a8c9f5cb416e6f0ecf24b3f98cf0e6c221d956a850c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-06-22T13:40:10Z",
    "title_canon_sha256": "5e98125ca1516d00bd1ade273b49656db2cded48956812d645ac6257a7e4078a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.4004",
    "kind": "arxiv",
    "version": 2
  }
}