Pith Number

pith:ZPRSBCGS

pith:2006:ZPRSBCGSWQTFN2LBYYCLYV47QI

not attested not anchored not stored refs pending

Automorphisms of finite Abelian groups

Christopher J. Hillar, Darren Rhea

arxiv:math/0605185 v1 · 2006-05-08 · math.GR · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZPRSBCGSWQTFN2LBYYCLYV47QI}

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.

Cited by

1 paper in Pith

Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories

Receipt and verification

First computed	2026-07-04T14:55:02.738482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbe32088d2b42656e961c604bc579f82206cd98ffe70f1eeae3a5fde3133f406

Aliases

arxiv: math/0605185 · arxiv_version: math/0605185v1 · doi: 10.48550/arxiv.math/0605185 · pith_short_12: ZPRSBCGSWQTF · pith_short_16: ZPRSBCGSWQTFN2LB · pith_short_8: ZPRSBCGS

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/ZPRSBCGSWQTFN2LBYYCLYV47QI \
  | 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: cbe32088d2b42656e961c604bc579f82206cd98ffe70f1eeae3a5fde3133f406

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c337a3e2551a5d2d3cfc45a1a1cc02a8564c85087b9d8407881d8588801f9760",
    "cross_cats_sorted": [
      "math.HO"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-05-08T01:13:06Z",
    "title_canon_sha256": "027145c0f6b0fc2e08ff396c1150376d948045673dac1eb9e2ed1a13c3c6335f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605185",
    "kind": "arxiv",
    "version": 1
  }
}