Pith Number

pith:O4VJ5QVM

pith:2003:O4VJ5QVM4XRAKDH2U3Q76WN5R3

not attested not anchored not stored refs pending

On the symmetry of commuting differential operators with singularities along hyperplanes

Kenji Taniguchi

arxiv:math-ph/0309011 v2 · 2003-09-03 · 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{O4VJ5QVM4XRAKDH2U3Q76WN5R3}

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	2026-05-18T03:04:07.106238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

772a9ec2ace5e2050cfaa6e1ff59bd8ef7168276a8c3a7246efb68e5df491ec1

Aliases

arxiv: math-ph/0309011 · arxiv_version: math-ph/0309011v2 · doi: 10.48550/arxiv.math-ph/0309011 · pith_short_12: O4VJ5QVM4XRA · pith_short_16: O4VJ5QVM4XRAKDH2 · pith_short_8: O4VJ5QVM

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/O4VJ5QVM4XRAKDH2U3Q76WN5R3 \
  | 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: 772a9ec2ace5e2050cfaa6e1ff59bd8ef7168276a8c3a7246efb68e5df491ec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8b69eb7cefa6409b37e78b7c05b08bfb0aed4fc9b6e61f74f3004e55a3d9e84",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2003-09-03T10:50:29Z",
    "title_canon_sha256": "412ca580a1bb57ceaa0ede6f36702953b5722a7766e5469dd98e83540751e748"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0309011",
    "kind": "arxiv",
    "version": 2
  }
}