Pith Number

pith:UQABW5VS

pith:2026:UQABW5VS2KLFNC3SI2GPW3MUBN

not attested not anchored not stored refs pending

Exterior Algebra and an Extension of the Feng-Sun-Xiang Theorem in $p$-groups

Lilu Zhao, Zhi-Wei Sun

arxiv:2606.30506 v1 · 2026-06-29 · 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{UQABW5VS2KLFNC3SI2GPW3MUBN}

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	2026-06-30T02:18:18.083720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4001b76b2d296568b72468cfb6d940b6616b9205b8e42fbe40cedf0cb550df6

Aliases

arxiv: 2606.30506 · arxiv_version: 2606.30506v1 · doi: 10.48550/arxiv.2606.30506 · pith_short_12: UQABW5VS2KLF · pith_short_16: UQABW5VS2KLFNC3S · pith_short_8: UQABW5VS

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/UQABW5VS2KLFNC3SI2GPW3MUBN \
  | 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: a4001b76b2d296568b72468cfb6d940b6616b9205b8e42fbe40cedf0cb550df6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b40382323ee813f354305ba5203bbcd7fda4d609be0d1b3eadddd0db8ef7c27d",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-29T16:12:56Z",
    "title_canon_sha256": "f2ad46f974a588e617091cc8bcb488def8d8739113e97d6c88720d757438f6a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30506",
    "kind": "arxiv",
    "version": 1
  }
}