Pith Number

pith:Q4S3EDIR

pith:2012:Q4S3EDIRRTS62H4CMZFBDDCCY6

not attested not anchored not stored refs pending

Schoenberg Correspondence on Dual Groups

Michael Sch\"urmann, Stefan Vo\ss

arxiv:1210.1830 v2 · 2012-10-05 · math.OA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q4S3EDIRRTS62H4CMZFBDDCCY6}

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	2026-05-18T03:41:31.896686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8725b20d118ce5ed1f82664a118c42c7816a03fdc841a05b855b378a4bff654a

Aliases

arxiv: 1210.1830 · arxiv_version: 1210.1830v2 · doi: 10.48550/arxiv.1210.1830 · pith_short_12: Q4S3EDIRRTS6 · pith_short_16: Q4S3EDIRRTS62H4C · pith_short_8: Q4S3EDIR

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/Q4S3EDIRRTS62H4CMZFBDDCCY6 \
  | 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: 8725b20d118ce5ed1f82664a118c42c7816a03fdc841a05b855b378a4bff654a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48a0dd7ff8d007d219f49a8c3ca3b7400aedc913e7066a030b0b99207831bd3b",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2012-10-05T18:17:47Z",
    "title_canon_sha256": "4689baf30076d1deac598d5f77398c4784c8e3c64427f1b231fc0a735374c15f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1830",
    "kind": "arxiv",
    "version": 2
  }
}