Pith Number

pith:6OXAMDKI

pith:2011:6OXAMDKINME32MLSYPVV7UMHD5

not attested not anchored not stored refs pending

Splitting theorems for pro-$p$ groups acting on pro-$p$ trees and 2-generated subgroups of free pro-$p$ products with procyclic amalgamations

Pavel Zalesskii, Theo Zapata, Wolfgang Herfort

arxiv:1103.2955 v2 · 2011-03-15 · 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{6OXAMDKINME32MLSYPVV7UMHD5}

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	2026-05-18T03:20:57.239882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3ae060d486b09bd3172c3eb5fd1871f5872512f39c855eaf1a15d933e807702

Aliases

arxiv: 1103.2955 · arxiv_version: 1103.2955v2 · doi: 10.48550/arxiv.1103.2955 · pith_short_12: 6OXAMDKINME3 · pith_short_16: 6OXAMDKINME32MLS · pith_short_8: 6OXAMDKI

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/6OXAMDKINME32MLSYPVV7UMHD5 \
  | 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: f3ae060d486b09bd3172c3eb5fd1871f5872512f39c855eaf1a15d933e807702

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f78f9bdfe46dfba69fef4efa6453be0a8e04e87efbf4c18f3ba55e2815e7adf0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-03-15T16:40:12Z",
    "title_canon_sha256": "db8b70bb09514f57dcd737f76134d6405dc8bc1e6ec3dca80f7f749b8ff11c43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2955",
    "kind": "arxiv",
    "version": 2
  }
}