Pith Number

pith:AIL7LVVW

pith:2004:AIL7LVVW2OLGAD4GGJPBNAFNTV

not attested not anchored not stored refs pending

Duality symmetry for star products

G. Marmo, P. Vitale, V. I. Man'ko

arxiv:hep-th/0407131 v1 · 2004-07-15 · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AIL7LVVW2OLGAD4GGJPBNAFNTV}

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

1 paper in Pith

From classical probability densities to quantum states: quantization of Gaussians for arbitrary orderings

Receipt and verification

First computed	2026-07-04T14:49:33.953406Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0217f5d6b6d396600f86325e1680ad9d6fc68dfa32c1aa9f1235bfb7bfd9fb11

Aliases

arxiv: hep-th/0407131 · arxiv_version: hep-th/0407131v1 · doi: 10.48550/arxiv.hep-th/0407131 · pith_short_12: AIL7LVVW2OLG · pith_short_16: AIL7LVVW2OLGAD4G · pith_short_8: AIL7LVVW

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/AIL7LVVW2OLGAD4GGJPBNAFNTV \
  | 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: 0217f5d6b6d396600f86325e1680ad9d6fc68dfa32c1aa9f1235bfb7bfd9fb11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3be2fb2e5a8efca3784bc12b6013936efa15a251ca43d2564d498437410d6970",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "2004-07-15T10:08:12Z",
    "title_canon_sha256": "3532943c6f08ebd329389faa0de39658da74d6ca8a1a7e797c15f8e90c6de6e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/0407131",
    "kind": "arxiv",
    "version": 1
  }
}