Pith Number

pith:WX2W7W3X

pith:2010:WX2W7W3XNEJX2I7E5VICEUVFPX

not attested not anchored not stored refs pending

Adjoint Operators on Banach Spaces

Francis Mensah, Tepper L Gill, Woodford W. Zachary

arxiv:1010.4922 v1 · 2010-10-24 · math-ph · math.FA · 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{WX2W7W3XNEJX2I7E5VICEUVFPX}

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	2026-05-18T04:38:49.830195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5f56fdb7769137d23e4ed502252a57dd02e190f2f76d4c2eb224475c2b48964

Aliases

arxiv: 1010.4922 · arxiv_version: 1010.4922v1 · doi: 10.48550/arxiv.1010.4922 · pith_short_12: WX2W7W3XNEJX · pith_short_16: WX2W7W3XNEJX2I7E · pith_short_8: WX2W7W3X

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/WX2W7W3XNEJX2I7E5VICEUVFPX \
  | 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: b5f56fdb7769137d23e4ed502252a57dd02e190f2f76d4c2eb224475c2b48964

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49d325e3af20388b0d51c7308e3207a3571c8da49688f5adc986a116039bab6c",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-10-24T02:00:22Z",
    "title_canon_sha256": "841bacf30cd2f5235db9ca7f08b49aba93f82399b21d03e0babbd4632ef113af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4922",
    "kind": "arxiv",
    "version": 1
  }
}