Pith Number

pith:VGSIAGBR

pith:2011:VGSIAGBRXZL3GVXWWBBUSWIOHR

not attested not anchored not stored refs pending

Symbolic integration with respect to the Haar measure on the unitary group

Jaros{\l}aw Adam Miszczak, Zbigniew Pucha{\l}a

arxiv:1109.4244 v2 · 2011-09-20 · physics.comp-ph · cs.SC · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGSIAGBRXZL3GVXWWBBUSWIOHR}

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

Mitigating Barren Plateaus in Quantum Denoising Diffusion Probabilistic Model

Probabilistic and approximate universal quantum purification machines

Receipt and verification

First computed	2026-07-05T01:23:06.679090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a4801831be57b356f6b04349590e3c65c9609d404984b83581301f6c6d6bcd

Aliases

arxiv: 1109.4244 · arxiv_version: 1109.4244v2 · doi: 10.48550/arxiv.1109.4244 · pith_short_12: VGSIAGBRXZL3 · pith_short_16: VGSIAGBRXZL3GVXW · pith_short_8: VGSIAGBR

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/VGSIAGBRXZL3GVXWWBBUSWIOHR \
  | 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: a9a4801831be57b356f6b04349590e3c65c9609d404984b83581301f6c6d6bcd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "272d3d4b76fca05e2500dbd2cf4e1f146fb7885fc6cbfa23afa14058b90e9e6a",
    "cross_cats_sorted": [
      "cs.SC",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.comp-ph",
    "submitted_at": "2011-09-20T09:07:33Z",
    "title_canon_sha256": "6a43be10fd44b8e7b1336d57b675bf1e704a369c7f18dab153765d7dfa19428e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4244",
    "kind": "arxiv",
    "version": 2
  }
}