Pith Number

pith:JMRMIVJZ

pith:2011:JMRMIVJZCK4BCM3FMD2XC2OEC4

not attested not anchored not stored refs pending

The spin of prime ideals

B. Mazur, H. Iwaniec, J. B. Friedlander, K. Rubin

arxiv:1110.6331 v2 · 2011-10-28 · 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{JMRMIVJZCK4BCM3FMD2XC2OEC4}

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	2026-05-18T03:42:44.696123Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b22c4553912b811336560f57169c41728b4c92ccf670d5bd59b7d47ce6c82f2

Aliases

arxiv: 1110.6331 · arxiv_version: 1110.6331v2 · doi: 10.48550/arxiv.1110.6331 · pith_short_12: JMRMIVJZCK4B · pith_short_16: JMRMIVJZCK4BCM3F · pith_short_8: JMRMIVJZ

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/JMRMIVJZCK4BCM3FMD2XC2OEC4 \
  | 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: 4b22c4553912b811336560f57169c41728b4c92ccf670d5bd59b7d47ce6c82f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5d0626e51810b04578a463ed43ad4a6acbd1f4fca85f751d07846d2827814f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-28T13:36:06Z",
    "title_canon_sha256": "32731d5e90787c91ae7606c7d2bc430a4b376309949074c66a6430aef84620f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6331",
    "kind": "arxiv",
    "version": 2
  }
}