Pith Number

pith:7ZWR24QZ

pith:2016:7ZWR24QZQ4GYXQPIP5TDZNKEJM

not attested not anchored not stored refs pending

Groups with positive rank gradient and their actions

Mark Shusterman

arxiv:1602.00144 v1 · 2016-01-30 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZWR24QZQ4GYXQPIP5TDZNKEJM}

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	2026-05-18T01:21:36.196071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe6d1d7219870d8bc1e87f663cb5444b23ddca8ea9ad2cecd9c27f2bd6421128

Aliases

arxiv: 1602.00144 · arxiv_version: 1602.00144v1 · doi: 10.48550/arxiv.1602.00144 · pith_short_12: 7ZWR24QZQ4GY · pith_short_16: 7ZWR24QZQ4GYXQPI · pith_short_8: 7ZWR24QZ

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/7ZWR24QZQ4GYXQPIP5TDZNKEJM \
  | 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: fe6d1d7219870d8bc1e87f663cb5444b23ddca8ea9ad2cecd9c27f2bd6421128

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0682ce537ac7b114c82e5bb88b713f912d93c4537840bf01f8c94ba46a45b82",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-01-30T17:38:45Z",
    "title_canon_sha256": "b268dc0591786a6cd6a2fd266497da61332aa784bcf5f24919f053b490ecb997"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.00144",
    "kind": "arxiv",
    "version": 1
  }
}