Pith Number

pith:Z2F4EP3D

pith:2011:Z2F4EP3DXA6FO4HYE7H2BND2KE

not attested not anchored not stored refs pending

Self-adjoint commuting differential operators and commutative subalgebras of the Weyl algebra

Andrey E. Mironov

arxiv:1107.3356 v2 · 2011-07-18 · math-ph · math.MP · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Z2F4EP3DXA6FO4HYE7H2BND2KE}

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	2026-05-18T03:58:24.681311Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ce8bc23f63b83c5770f827cfa0b47a513339313c90b86b1a4e1c7075e83829fa

Aliases

arxiv: 1107.3356 · arxiv_version: 1107.3356v2 · doi: 10.48550/arxiv.1107.3356 · pith_short_12: Z2F4EP3DXA6F · pith_short_16: Z2F4EP3DXA6FO4HY · pith_short_8: Z2F4EP3D

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/Z2F4EP3DXA6FO4HYE7H2BND2KE \
  | 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: ce8bc23f63b83c5770f827cfa0b47a513339313c90b86b1a4e1c7075e83829fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb03aa703fe400f287a00321ed4ed9b3e00b625d9a67dd0059dad3361c3889f3",
    "cross_cats_sorted": [
      "math.MP",
      "nlin.SI"
    ],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-07-18T05:29:53Z",
    "title_canon_sha256": "34b0b95f2e3462fbd5ccecc635458f6f1611a05abb4422cd041134f64a78abbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3356",
    "kind": "arxiv",
    "version": 2
  }
}