Pith Number

pith:I3CZIIJH

pith:2011:I3CZIIJHB2UFJ3VAAVFIIWCWU3

not attested not anchored not stored refs pending

Poisson-Furstenberg boundary and growth of groups

Anna G. Erschler, Laurent Bartholdi

arxiv:1107.5499 v2 · 2011-07-27 · 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{I3CZIIJHB2UFJ3VAAVFIIWCWU3}

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	2026-05-18T01:13:45.189637Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46c59421270ea854eea0054a845856a6e3fa1950da4ba38154004f721fa2371c

Aliases

arxiv: 1107.5499 · arxiv_version: 1107.5499v2 · doi: 10.48550/arxiv.1107.5499 · pith_short_12: I3CZIIJHB2UF · pith_short_16: I3CZIIJHB2UFJ3VA · pith_short_8: I3CZIIJH

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/I3CZIIJHB2UFJ3VAAVFIIWCWU3 \
  | 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: 46c59421270ea854eea0054a845856a6e3fa1950da4ba38154004f721fa2371c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c827deddb95ea4e0ea67603ac63ff8e771c49c9ad15d79421f9afdec7a5f2ccd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-07-27T15:02:03Z",
    "title_canon_sha256": "5976e9c9b7a160444e93c66e7d76aeffdb7f933a7dca0163f86817313fcd4e68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5499",
    "kind": "arxiv",
    "version": 2
  }
}