Pith Number

pith:LGX7SU3Q

pith:1996:LGX7SU3QCG4AU5BTT5JFFFAPZV

not attested not anchored not stored refs pending

Closed formula for the matrix elements of the volume operator in canonical quantum gravity

T. Thiemann

arxiv:gr-qc/9606091 v1 · 1996-06-29 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LGX7SU3QCG4AU5BTT5JFFFAPZV}

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.

Cited by

2 papers in Pith

A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity

Receipt and verification

First computed	2026-07-04T16:01:11.470031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59aff9537011b80a74339f5252940fcd6512500c21e3c335911de6b838f681c2

Aliases

arxiv: gr-qc/9606091 · arxiv_version: gr-qc/9606091v1 · doi: 10.48550/arxiv.gr-qc/9606091 · pith_short_12: LGX7SU3QCG4A · pith_short_16: LGX7SU3QCG4AU5BT · pith_short_8: LGX7SU3Q

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/LGX7SU3QCG4AU5BTT5JFFFAPZV \
  | 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: 59aff9537011b80a74339f5252940fcd6512500c21e3c335911de6b838f681c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ac3e473f22dd155e0eb2ba2b1346f1af1154256bccc54e9a2dfefc77c3270e5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1996-06-29T23:29:28Z",
    "title_canon_sha256": "8077f171dbf0ca05f9fed02f65d617bc3545ff5e74d144bd2def3ff732293bd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9606091",
    "kind": "arxiv",
    "version": 1
  }
}