Pith Number

pith:PBTZL2TY

pith:2013:PBTZL2TY7VAI2GQQEKXHVAM2IK

not attested not anchored not stored refs pending

On the $\pi$$\mathfrak{F}$-norm and the $\mathfrak{H}$-$\mathfrak{F}$-norm of a finite group

Wenbin Guo, Xiaoyu Chen

arxiv:1308.0948 v2 · 2013-08-05 · 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{PBTZL2TY7VAI2GQQEKXHVAM2IK}

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	2026-05-18T01:35:57.540561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

786795ea78fd408d1a1022ae7a819a42b86e2cdac84ef4b656610852f0ad913e

Aliases

arxiv: 1308.0948 · arxiv_version: 1308.0948v2 · doi: 10.48550/arxiv.1308.0948 · pith_short_12: PBTZL2TY7VAI · pith_short_16: PBTZL2TY7VAI2GQQ · pith_short_8: PBTZL2TY

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/PBTZL2TY7VAI2GQQEKXHVAM2IK \
  | 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: 786795ea78fd408d1a1022ae7a819a42b86e2cdac84ef4b656610852f0ad913e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2824581b5c650ac36711919798e4ef9b9b51e64fa71a37a8f75dad29dac391d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-08-05T11:44:34Z",
    "title_canon_sha256": "e918c814ab0d3da8ed2ecd0ad854fa9d13f582803e8e5b2cd1b297366f990f08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.0948",
    "kind": "arxiv",
    "version": 2
  }
}