Pith Number

pith:VMRNNOZP

pith:1994:VMRNNOZP2SLPIBIRYYXVEUDJKH

not attested not anchored not stored refs pending

Quasi-Exactly-Solvable Differential Equations

Alexander Turbiner

arxiv:hep-th/9409068 v2 · 1994-09-12 · hep-th · funct-an · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMRNNOZP2SLPIBIRYYXVEUDJKH}

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	2026-07-04T15:07:49.850387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab22d6bb2fd496f40511c62f52506951e6a415aa1700550274e2f7a5dea054bd

Aliases

arxiv: hep-th/9409068 · arxiv_version: hep-th/9409068v2 · doi: 10.48550/arxiv.hep-th/9409068 · pith_short_12: VMRNNOZP2SLP · pith_short_16: VMRNNOZP2SLPIBIR · pith_short_8: VMRNNOZP

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/VMRNNOZP2SLPIBIRYYXVEUDJKH \
  | 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: ab22d6bb2fd496f40511c62f52506951e6a415aa1700550274e2f7a5dea054bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "061664a3c78304db28a8cf5d33a0b3f38921f305f071d64e931e92f047ad6b14",
    "cross_cats_sorted": [
      "funct-an",
      "math.FA"
    ],
    "license": "",
    "primary_cat": "hep-th",
    "submitted_at": "1994-09-12T17:30:59Z",
    "title_canon_sha256": "816400ca9d16859751ade4da5c4f6e1b4e58a43dd2a83eb6b82de00cae67104d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "hep-th/9409068",
    "kind": "arxiv",
    "version": 2
  }
}