Pith Number

pith:O4UJ3UGK

pith:2011:O4UJ3UGKRBWU6LFIG6UY5HRMZ4

not attested not anchored not stored refs pending

On lower bounds for the Ihara constants A(2) and A(3)

Iwan Duursma, Kit-Ho Mak

arxiv:1102.4127 v4 · 2011-02-21 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O4UJ3UGKRBWU6LFIG6UY5HRMZ4}

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	2026-05-17T23:53:19.453735Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77289dd0ca886d4f2ca837a98e9e2ccf2d34bfe88d3248ac40dee77d85296427

Aliases

arxiv: 1102.4127 · arxiv_version: 1102.4127v4 · doi: 10.48550/arxiv.1102.4127 · pith_short_12: O4UJ3UGKRBWU · pith_short_16: O4UJ3UGKRBWU6LFI · pith_short_8: O4UJ3UGK

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/O4UJ3UGKRBWU6LFIG6UY5HRMZ4 \
  | 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: 77289dd0ca886d4f2ca837a98e9e2ccf2d34bfe88d3248ac40dee77d85296427

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0103a7b9667b9140fd1111fde364e2313b75c36ce5e3ed7734bac36561da43d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-02-21T03:59:30Z",
    "title_canon_sha256": "c7955e73b67266d80f9bec8477a5d1bab91cd85f8f2be530f292dc967dbc4668"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.4127",
    "kind": "arxiv",
    "version": 4
  }
}