Pith Number

pith:VCR7EMWL

pith:2017:VCR7EMWLMIA52PJJFNOMA3D7CS

not attested not anchored not stored refs pending

Generalized Commutative Association Schemes, Hypergroups, and Positive Product Formulas

Michael Voit

arxiv:1708.01172 v1 · 2017-08-03 · 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{VCR7EMWLMIA52PJJFNOMA3D7CS}

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	2026-05-18T00:38:40.443649Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8a3f232cb6201dd3d292b5cc06c7f148b5735d1ed992c1e075aa02f5d726e2d

Aliases

arxiv: 1708.01172 · arxiv_version: 1708.01172v1 · doi: 10.48550/arxiv.1708.01172 · pith_short_12: VCR7EMWLMIA5 · pith_short_16: VCR7EMWLMIA52PJJ · pith_short_8: VCR7EMWL

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/VCR7EMWLMIA52PJJFNOMA3D7CS \
  | 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: a8a3f232cb6201dd3d292b5cc06c7f148b5735d1ed992c1e075aa02f5d726e2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a59542ab90098537ae0291b0fd1eeb12d6a646661d3805e0c1b08cc8a9c281ec",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-08-03T15:04:14Z",
    "title_canon_sha256": "72fc86579c5c315aa74cba9fdd8e0033b779eb789ad7fda30133549778ee38b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.01172",
    "kind": "arxiv",
    "version": 1
  }
}