Pith Number

pith:J4Y74Q3D

pith:2015:J4Y74Q3DRCNAIJ5ZCE5M3KQMYI

not attested not anchored not stored refs pending

Root operators, root groups and retractions

Petra Schwer

arxiv:1509.03146 v3 · 2015-09-10 · math.RT · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J4Y74Q3DRCNAIJ5ZCE5M3KQMYI}

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	2026-05-18T00:09:42.546572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f31fe4363889a0427b9113acdaa0cc21b7227fbb14cd3f6824b5498d46a4f58

Aliases

arxiv: 1509.03146 · arxiv_version: 1509.03146v3 · doi: 10.48550/arxiv.1509.03146 · pith_short_12: J4Y74Q3DRCNA · pith_short_16: J4Y74Q3DRCNAIJ5Z · pith_short_8: J4Y74Q3D

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/J4Y74Q3DRCNAIJ5ZCE5M3KQMYI \
  | 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: 4f31fe4363889a0427b9113acdaa0cc21b7227fbb14cd3f6824b5498d46a4f58

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c34b404b65e71f2c9deb1c574659bc7e60c9740276de9f26e2ca181755b880c7",
    "cross_cats_sorted": [
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2015-09-10T13:36:47Z",
    "title_canon_sha256": "eefb80fdfbabbdba364cdaea7e4ea9e511a777dae2372b49fb1e40c027cbbfc2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03146",
    "kind": "arxiv",
    "version": 3
  }
}