Pith Number

pith:PQWYZ3H7

pith:2012:PQWYZ3H7EUNVWGMP2RLDKQTJYK

not attested not anchored not stored refs pending

An Eilenberg-Ganea Phenomenon for Actions with Virtually Cyclic Stabilisers

Ian J. Leary, Martin Fluch

arxiv:1207.1474 v2 · 2012-07-05 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PQWYZ3H7EUNVWGMP2RLDKQTJYK}

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	2026-05-18T02:53:27.325641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c2d8cecff251b5b198fd456354269c2a39a8271da6be4224c413fa7690038b4

Aliases

arxiv: 1207.1474 · arxiv_version: 1207.1474v2 · doi: 10.48550/arxiv.1207.1474 · pith_short_12: PQWYZ3H7EUNV · pith_short_16: PQWYZ3H7EUNVWGMP · pith_short_8: PQWYZ3H7

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/PQWYZ3H7EUNVWGMP2RLDKQTJYK \
  | 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: 7c2d8cecff251b5b198fd456354269c2a39a8271da6be4224c413fa7690038b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "272a519c7ef4143ec5390c9d78c21db6403230b096c1b6052513d18733ffb035",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-05T22:19:17Z",
    "title_canon_sha256": "6f3f5ef241b3cc2889830680c1630e49a619839b19489ad7ee491ce50c8aba5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1474",
    "kind": "arxiv",
    "version": 2
  }
}