Pith Number

pith:7PFLA3YT

pith:2012:7PFLA3YTU7E2GRT6PFYC2JUYSD

not attested not anchored not stored refs pending

Notes on Thin Matrix Groups

Peter Sarnak

arxiv:1212.3525 v1 · 2012-12-14 · math.NT · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7PFLA3YTU7E2GRT6PFYC2JUYSD}

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	2026-05-18T03:38:24.398683Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbcab06f13a7c9a3467e79702d269890f0493c3f91ee13a9b86a0b2087d02490

Aliases

arxiv: 1212.3525 · arxiv_version: 1212.3525v1 · doi: 10.48550/arxiv.1212.3525 · pith_short_12: 7PFLA3YTU7E2 · pith_short_16: 7PFLA3YTU7E2GRT6 · pith_short_8: 7PFLA3YT

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/7PFLA3YTU7E2GRT6PFYC2JUYSD \
  | 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: fbcab06f13a7c9a3467e79702d269890f0493c3f91ee13a9b86a0b2087d02490

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "486de4ccfc106823797e7670d0d1dda86cee43c3c56eb1d0d1f77707446b3276",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-14T16:48:27Z",
    "title_canon_sha256": "833ee00544bebf6135b0adbb012af32a52bcb0a90cdd1c9641a8c90ac616a390"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.3525",
    "kind": "arxiv",
    "version": 1
  }
}