Pith Number

pith:P26SKHO5

pith:2012:P26SKHO57PCS3WNYETERZ24EBS

not attested not anchored not stored refs pending

Quotients, automorphisms and differential operators

Gerald W. Schwarz

arxiv:1201.6369 v9 · 2012-01-30 · math.GR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P26SKHO57PCS3WNYETERZ24EBS}

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	2026-05-18T02:57:53.852881Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ebd251dddfbc52dd9b824c91ceb840cbe630c5736826a732317bb32ac754fd7

Aliases

arxiv: 1201.6369 · arxiv_version: 1201.6369v9 · doi: 10.48550/arxiv.1201.6369 · pith_short_12: P26SKHO57PCS · pith_short_16: P26SKHO57PCS3WNY · pith_short_8: P26SKHO5

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/P26SKHO57PCS3WNYETERZ24EBS \
  | 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: 7ebd251dddfbc52dd9b824c91ceb840cbe630c5736826a732317bb32ac754fd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc365563967456b15c0884e8f8f78d6c9b82586551b792f0f1d3197a5208bb49",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-01-30T21:00:47Z",
    "title_canon_sha256": "ed34e884c87116e6558765ec89272eba2393d242db788110608fb440557146eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6369",
    "kind": "arxiv",
    "version": 9
  }
}