Pith Number

pith:4MYG2CVT

pith:2005:4MYG2CVTXS3HUNES4GGXH3JE6F

not attested not anchored not stored refs pending

Ternary expansions of powers of 2

Jeffrey C. Lagarias

arxiv:math/0512006 v4 · 2005-12-01 · math.DS · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4MYG2CVTXS3HUNES4GGXH3JE6F}

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	2026-05-18T02:57:51.012590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3306d0ab3bcb67a3492e18d73ed24f17da24ffe6ffb3a25704d77db02c8d9b6

Aliases

arxiv: math/0512006 · arxiv_version: math/0512006v4 · doi: 10.48550/arxiv.math/0512006 · pith_short_12: 4MYG2CVTXS3H · pith_short_16: 4MYG2CVTXS3HUNES · pith_short_8: 4MYG2CVT

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/4MYG2CVTXS3HUNES4GGXH3JE6F \
  | 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: e3306d0ab3bcb67a3492e18d73ed24f17da24ffe6ffb3a25704d77db02c8d9b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0a23537018851ebf1c8655a988a91a6ba1314ff1abfa1d72af818171a6412f8",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2005-12-01T05:06:13Z",
    "title_canon_sha256": "dd228b11ba28937bc41bf0f9cdfa510b98139a4c2b0a3deb6a05911f3cf68a90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512006",
    "kind": "arxiv",
    "version": 4
  }
}