Pith Number

pith:77MCHFXF

pith:2015:77MCHFXFDSGPUISK44V6IX7RSD

not attested not anchored not stored refs pending

ATmenability of some graphs of groups with cyclic edge groups

Daniel J. Woodhouse, Daniel T. Wise, Mathieu Carette

arxiv:1512.04599 v2 · 2015-12-14 · 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{77MCHFXFDSGPUISK44V6IX7RSD}

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	2026-05-18T00:53:40.451772Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffd82396e51c8cfa224ae72be45ff190f19e5dd193376647dc46da1ccc5b6236

Aliases

arxiv: 1512.04599 · arxiv_version: 1512.04599v2 · doi: 10.48550/arxiv.1512.04599 · pith_short_12: 77MCHFXFDSGP · pith_short_16: 77MCHFXFDSGPUISK · pith_short_8: 77MCHFXF

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/77MCHFXFDSGPUISK44V6IX7RSD \
  | 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: ffd82396e51c8cfa224ae72be45ff190f19e5dd193376647dc46da1ccc5b6236

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "395cf2be6093bafefbdf852f3fba9259b824943f0727706be53ba92f9ff941f1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-14T23:31:03Z",
    "title_canon_sha256": "9318fbb6353d03dd5a25e1787e2386b3863404aa5a7400aca80292c49006bd84"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04599",
    "kind": "arxiv",
    "version": 2
  }
}