Pith Number

pith:4Y2MRHZ2

pith:2011:4Y2MRHZ2XIJKG2UI6S6YJBQUIV

not attested not anchored not stored refs pending

Local-global compatibility for l=p, I

David Geraghty, Richard Taylor, Thomas Barnet-Lamb, Toby Gee

arxiv:1105.2240 v1 · 2011-05-11 · 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{4Y2MRHZ2XIJKG2UI6S6YJBQUIV}

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	2026-05-18T04:22:21.220054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e634c89f3aba12a36a88f4bd84861445498c4d16b9bfa90ab3bb87dae6759b03

Aliases

arxiv: 1105.2240 · arxiv_version: 1105.2240v1 · doi: 10.48550/arxiv.1105.2240 · pith_short_12: 4Y2MRHZ2XIJK · pith_short_16: 4Y2MRHZ2XIJKG2UI · pith_short_8: 4Y2MRHZ2

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/4Y2MRHZ2XIJKG2UI6S6YJBQUIV \
  | 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: e634c89f3aba12a36a88f4bd84861445498c4d16b9bfa90ab3bb87dae6759b03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "771feedcffa51829adfeabe1c37c703a579490293aefd988fbb51cd1914ca3e6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-05-11T16:27:02Z",
    "title_canon_sha256": "7338d5cff60243e748f0e98365422e7f42d05e093d8410b24bb319c1df15fc8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2240",
    "kind": "arxiv",
    "version": 1
  }
}