Pith Number

pith:K4FTHI3J

pith:2015:K4FTHI3JXMLMESGTA67QBIRY6I

not attested not anchored not stored refs pending

A note on the growth of regularity with respect to Frobenius

Wenliang Zhang

arxiv:1512.00049 v1 · 2015-11-30 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4FTHI3JXMLMESGTA67QBIRY6I}

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	2026-05-18T01:25:32.931690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

570b33a369bb16c248d307bf00a238f2058873a447e052361f54e7dd5a9c509f

Aliases

arxiv: 1512.00049 · arxiv_version: 1512.00049v1 · doi: 10.48550/arxiv.1512.00049 · pith_short_12: K4FTHI3JXMLM · pith_short_16: K4FTHI3JXMLMESGT · pith_short_8: K4FTHI3J

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/K4FTHI3JXMLMESGTA67QBIRY6I \
  | 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: 570b33a369bb16c248d307bf00a238f2058873a447e052361f54e7dd5a9c509f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "246963d0b1fb9017eaaac6e1a15fb6004594a6c2b02d476d7f55c576375b7a2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-11-30T21:31:22Z",
    "title_canon_sha256": "2f22c4d5f9bfd50c06f8ba1dbff15e83bfe239257cd54ad5b1918292ee51392c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.00049",
    "kind": "arxiv",
    "version": 1
  }
}