Pith Number

pith:IT7GBGGN

pith:2013:IT7GBGGNF2LGDIR2YQKL5IY5G2

not attested not anchored not stored refs pending

Scale-multiplicative semigroups and geometry: automorphism groups of trees

George A. Willis, Jacqui Ramagge, Udo Baumgartner

arxiv:1312.1064 v1 · 2013-12-04 · 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{IT7GBGGNF2LGDIR2YQKL5IY5G2}

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	2026-05-18T03:05:35.043622Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44fe6098cd2e9661a23ac414bea31d369631fc1c85e6b24cb5bf1e3fd8ea0bc8

Aliases

arxiv: 1312.1064 · arxiv_version: 1312.1064v1 · doi: 10.48550/arxiv.1312.1064 · pith_short_12: IT7GBGGNF2LG · pith_short_16: IT7GBGGNF2LGDIR2 · pith_short_8: IT7GBGGN

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/IT7GBGGNF2LGDIR2YQKL5IY5G2 \
  | 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: 44fe6098cd2e9661a23ac414bea31d369631fc1c85e6b24cb5bf1e3fd8ea0bc8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94fc4068e39cf93ba350c6b16a3619c63b228c1d2ef77a7918971536fceb1719",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-12-04T09:03:21Z",
    "title_canon_sha256": "569dc2e53a3e2778e9c89d11bc8e4270dad513fcf58c3ab6881cae47d7e685b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.1064",
    "kind": "arxiv",
    "version": 1
  }
}