Pith Number

pith:7TNOPL2Z

pith:2015:7TNOPL2ZMZ4D4ICJCKG6YZQPBJ

not attested not anchored not stored refs pending

Generating countable groups by discrete subsets

Igor Protasov

arxiv:1511.01045 v1 · 2015-11-02 · math.GN · math.CO · 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{7TNOPL2ZMZ4D4ICJCKG6YZQPBJ}

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	2026-05-18T01:27:55.369943Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcdae7af5966783e2049128dec660f0a55a4e23d4923d573f9a0718ecef1ac59

Aliases

arxiv: 1511.01045 · arxiv_version: 1511.01045v1 · doi: 10.48550/arxiv.1511.01045 · pith_short_12: 7TNOPL2ZMZ4D · pith_short_16: 7TNOPL2ZMZ4D4ICJ · pith_short_8: 7TNOPL2Z

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/7TNOPL2ZMZ4D4ICJCKG6YZQPBJ \
  | 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: fcdae7af5966783e2049128dec660f0a55a4e23d4923d573f9a0718ecef1ac59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fae6c298c05f70639fc8a19bbfc65897e68c897ca7bfdbe9af1060e4f92e2724",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2015-11-02T09:29:27Z",
    "title_canon_sha256": "db7cec92a004a260f692f7ab886dca9ea22e4a6d158025bd99f36a347b9f87ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.01045",
    "kind": "arxiv",
    "version": 1
  }
}