Pith Number

pith:J22SNUYB

pith:2019:J22SNUYBHQXOG64SUZXEE5IQU2

not attested not anchored not stored refs pending

Geodesic growth in virtually abelian groups

Alex Bishop

arxiv:1908.07294 v4 · 2019-08-20 · 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{J22SNUYBHQXOG64SUZXEE5IQU2}

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	2026-07-05T01:58:53.899335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4eb526d3013c2ee37b92a66e427510a69453235aab6a4f1ca320cf4114b51e8c

Aliases

arxiv: 1908.07294 · arxiv_version: 1908.07294v4 · doi: 10.48550/arxiv.1908.07294 · pith_short_12: J22SNUYBHQXO · pith_short_16: J22SNUYBHQXOG64S · pith_short_8: J22SNUYB

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/J22SNUYBHQXOG64SUZXEE5IQU2 \
  | 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: 4eb526d3013c2ee37b92a66e427510a69453235aab6a4f1ca320cf4114b51e8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c83f513789433418cf81a4208f599af19f467eef909fba1b7798a8cb7bf8e64d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-08-20T12:09:13Z",
    "title_canon_sha256": "c9a7371e3bde4251da83b469201d7304bc66fd9aa2affd8c5f7d0a6de3f05219"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07294",
    "kind": "arxiv",
    "version": 4
  }
}