Pith Number

pith:4CFPXG2J

pith:2016:4CFPXG2JHJAH7ODSXSZIBEQDN7

not attested not anchored not stored refs pending

Gradients of sequences of subgroups in a direct product

Mark Shusterman, Nikolay Nikolov, Zvi Shemtov

arxiv:1609.08900 v2 · 2016-09-28 · 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{4CFPXG2JHJAH7ODSXSZIBEQDN7}

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	2026-05-18T00:44:38.832961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e08afb9b493a407fb872bcb28092036fe68153a16a3706b6fab89b5a2e907a6f

Aliases

arxiv: 1609.08900 · arxiv_version: 1609.08900v2 · doi: 10.48550/arxiv.1609.08900 · pith_short_12: 4CFPXG2JHJAH · pith_short_16: 4CFPXG2JHJAH7ODS · pith_short_8: 4CFPXG2J

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/4CFPXG2JHJAH7ODSXSZIBEQDN7 \
  | 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: e08afb9b493a407fb872bcb28092036fe68153a16a3706b6fab89b5a2e907a6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6c169e51435dcaeb30cf7d214105527f95959bcf94e4c5b4b5d66622a501aa7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-09-28T13:14:34Z",
    "title_canon_sha256": "46feb16c9ac4f847eed0c25711d6751f33e2e2f51fe0f2548dcb794b9ad8a0db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08900",
    "kind": "arxiv",
    "version": 2
  }
}