Pith Number

pith:4RICZPIY

pith:2012:4RICZPIYSQ2EG3II3ZSXYKUUEE

not attested not anchored not stored refs pending

Examples of dynamical degree equals arithmetic degree

Joseph H. Silverman, Shu Kawaguchi

arxiv:1212.3015 v1 · 2012-12-12 · math.NT · 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{4RICZPIYSQ2EG3II3ZSXYKUUEE}

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	2026-05-18T03:38:33.936908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4502cbd189434436d08de657c2a9421224bf5b9837e41ebd7e012b1f6a3bfab

Aliases

arxiv: 1212.3015 · arxiv_version: 1212.3015v1 · doi: 10.48550/arxiv.1212.3015 · pith_short_12: 4RICZPIYSQ2E · pith_short_16: 4RICZPIYSQ2EG3II · pith_short_8: 4RICZPIY

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/4RICZPIYSQ2EG3II3ZSXYKUUEE \
  | 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: e4502cbd189434436d08de657c2a9421224bf5b9837e41ebd7e012b1f6a3bfab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b82498b0425496e5560661b569c5a5ea2891568047fed1e4ab7b0635ce0771c2",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-12T23:45:54Z",
    "title_canon_sha256": "407302610a1dd3da2ead293224d9ecb2a8270bf4d1f55ec97c0a9cace7545d63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3015",
    "kind": "arxiv",
    "version": 1
  }
}