Pith Number

pith:R4VKFF4Y

pith:2013:R4VKFF4YNUT7X6NL5FKRKOYARV

not attested not anchored not stored refs pending

On the rank of the intersection of free subgroups in virtually free groups

Alexander Zakharov

arxiv:1301.3115 v2 · 2013-01-14 · 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{R4VKFF4YNUT7X6NL5FKRKOYARV}

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	2026-05-18T03:08:14.370697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f2aa297986d27fbf9abe955153b008d6785ebd24fa99c7297eee65d9e3183d5

Aliases

arxiv: 1301.3115 · arxiv_version: 1301.3115v2 · doi: 10.48550/arxiv.1301.3115 · pith_short_12: R4VKFF4YNUT7 · pith_short_16: R4VKFF4YNUT7X6NL · pith_short_8: R4VKFF4Y

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/R4VKFF4YNUT7X6NL5FKRKOYARV \
  | 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: 8f2aa297986d27fbf9abe955153b008d6785ebd24fa99c7297eee65d9e3183d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e4abfff0f4df00dccd719104063b5aa1a9af7c3579775591d65634b8931c978",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-01-14T20:27:02Z",
    "title_canon_sha256": "35227e7b2e05502ddd4edda764f9ddd5c3adbaeb90f8cd9d9d5beb78e861fe75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3115",
    "kind": "arxiv",
    "version": 2
  }
}