Pith Number

pith:77XTSZ32

pith:2003:77XTSZ32GAC2QLZ3HYY7GQUVEI

not attested not anchored not stored refs pending

A quantum duality principle for subgroups and homogeneous spaces

Fabio Gavarini, Nicola Ciccoli

arxiv:math/0312289 v4 · 2003-12-15 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{77XTSZ32GAC2QLZ3HYY7GQUVEI}

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	2026-05-18T03:42:34.336786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffef39677a3005a82f3b3e31f34295221684255103761a35589e4e7b76693ced

Aliases

arxiv: math/0312289 · arxiv_version: math/0312289v4 · doi: 10.48550/arxiv.math/0312289 · pith_short_12: 77XTSZ32GAC2 · pith_short_16: 77XTSZ32GAC2QLZ3 · pith_short_8: 77XTSZ32

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/77XTSZ32GAC2QLZ3HYY7GQUVEI \
  | 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: ffef39677a3005a82f3b3e31f34295221684255103761a35589e4e7b76693ced

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b131f290b829146f88ad4b1c7ec9697350bdb08b015270748525a0f40f66599",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2003-12-15T15:14:47Z",
    "title_canon_sha256": "0eea49f2c567524bc275cd0864cce31e7dd7cb189b50b01d65203ef11851f97a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312289",
    "kind": "arxiv",
    "version": 4
  }
}