Pith Number

pith:3UXXCC2G

pith:2014:3UXXCC2GV6FZ2D4QT44ME6HIZN

not attested not anchored not stored refs pending

Palindromic Automorphisms of Free Groups

Krishnendu Gongopadhyay, Mahender Singh, Valeriy G. Bardakov

arxiv:1411.0240 v2 · 2014-11-02 · 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{3UXXCC2GV6FZ2D4QT44ME6HIZN}

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	2026-05-18T00:45:59.066900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd2f710b46af8b9d0f909f38c278e8cb5d05ee967e5dfa4cb599ce27a55fc399

Aliases

arxiv: 1411.0240 · arxiv_version: 1411.0240v2 · doi: 10.48550/arxiv.1411.0240 · pith_short_12: 3UXXCC2GV6FZ · pith_short_16: 3UXXCC2GV6FZ2D4Q · pith_short_8: 3UXXCC2G

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/3UXXCC2GV6FZ2D4QT44ME6HIZN \
  | 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: dd2f710b46af8b9d0f909f38c278e8cb5d05ee967e5dfa4cb599ce27a55fc399

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67214b4eff0fead0a6cd0deb840726c0ed6df21212021453a07e07c949296f03",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-11-02T10:45:02Z",
    "title_canon_sha256": "fd180bfdf5210ec2a4d0d277836d7a881fa0223e4736c398df698cd32de9454f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0240",
    "kind": "arxiv",
    "version": 2
  }
}