Pith Number

pith:TJTNX3GS

pith:2000:TJTNX3GS2GYPOAGLV3BEF56AFE

not attested not anchored not stored refs pending

Phase space observables and isotypic spaces

A. Levrero, E. De Vito, G. Cassinelli, P. Lahti

arxiv:quant-ph/0004032 v1 · 2000-04-07 · quant-ph · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TJTNX3GS2GYPOAGLV3BEF56AFE}

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	2026-05-18T01:38:03.284797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a66dbecd2d1b0f700cbaec242f7c02912fb562502d4eef62ebc4038adee185e

Aliases

arxiv: quant-ph/0004032 · arxiv_version: quant-ph/0004032v1 · doi: 10.48550/arxiv.quant-ph/0004032 · pith_short_12: TJTNX3GS2GYP · pith_short_16: TJTNX3GS2GYPOAGL · pith_short_8: TJTNX3GS

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/TJTNX3GS2GYPOAGLV3BEF56AFE \
  | 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: 9a66dbecd2d1b0f700cbaec242f7c02912fb562502d4eef62ebc4038adee185e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9061eb14d4d47af0ae6faf215452d6c20c3ff9aa6da0319457b697d11ccbc64a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "quant-ph",
    "submitted_at": "2000-04-07T08:33:22Z",
    "title_canon_sha256": "5c1495a7c4acb6241828b527a071dc1e1d627900cae83875df1d8cf987f0c250"
  },
  "schema_version": "1.0",
  "source": {
    "id": "quant-ph/0004032",
    "kind": "arxiv",
    "version": 1
  }
}