Pith Number

pith:P3DE6WY7

pith:2015:P3DE6WY7ZO3YTLE67H7T7FCIBB

not attested not anchored not stored refs pending

Quantum isometry group of dual of finitely generated discrete groups- $\textrm{II}$

Arnab Mandal

arxiv:1504.02240 v2 · 2015-04-09 · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P3DE6WY7ZO3YTLE67H7T7FCIBB}

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	2026-05-18T01:20:26.220424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ec64f5b1fcbb789ac9ef9ff3f944808797dbe736b25888ada1056bc6e3e6570

Aliases

arxiv: 1504.02240 · arxiv_version: 1504.02240v2 · doi: 10.48550/arxiv.1504.02240 · pith_short_12: P3DE6WY7ZO3Y · pith_short_16: P3DE6WY7ZO3YTLE6 · pith_short_8: P3DE6WY7

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/P3DE6WY7ZO3YTLE67H7T7FCIBB \
  | 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: 7ec64f5b1fcbb789ac9ef9ff3f944808797dbe736b25888ada1056bc6e3e6570

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a28529162a7a13f37c10962c55ff628a59f4bc36e89fc856dd55d12a158581f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-04-09T10:09:43Z",
    "title_canon_sha256": "fbdf42b15701448d5469c8a19d7ba6a8ac67ffd3b6ab7062df222f55f68a6f66"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.02240",
    "kind": "arxiv",
    "version": 2
  }
}