Pith Number

pith:4PJBIWNG

pith:2014:4PJBIWNGUMQWHUSMO4TFYLTKAW

not attested not anchored not stored refs pending

The reflexive closure of the adjointable operators

Elias G. Katsoulis

arxiv:1401.1143 v3 · 2014-01-06 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4PJBIWNGUMQWHUSMO4TFYLTKAW}

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	2026-05-18T02:28:12.109184Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3d21459a6a32163d24c77265c2e6a05b0c88fa6535b804f3215cd53c93db8a2

Aliases

arxiv: 1401.1143 · arxiv_version: 1401.1143v3 · doi: 10.48550/arxiv.1401.1143 · pith_short_12: 4PJBIWNGUMQW · pith_short_16: 4PJBIWNGUMQWHUSM · pith_short_8: 4PJBIWNG

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/4PJBIWNGUMQWHUSMO4TFYLTKAW \
  | 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: e3d21459a6a32163d24c77265c2e6a05b0c88fa6535b804f3215cd53c93db8a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2de4ee697b88d28a2ecfad10e005684d9e419cbbf494982a2374e53e4287d25f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2014-01-06T17:10:34Z",
    "title_canon_sha256": "32cd2511581b905bb4e36e7dc59827a6e473b755cada334ca4d2df8b6d6ce755"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1143",
    "kind": "arxiv",
    "version": 3
  }
}