Pith Number

pith:ZVWXGTII

pith:2012:ZVWXGTIIZRPSDZWACDIWQXUL43

not attested not anchored not stored refs pending

On a theorem of Livsic

A. Aleman, R.T.W. Martin, W.T. Ross

arxiv:1209.4497 v1 · 2012-09-20 · 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{ZVWXGTIIZRPSDZWACDIWQXUL43}

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	2026-05-18T03:45:11.517208Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cd6d734d08cc5f21e6c010d1685e8be6fd59c5cd79c1655aa8e0c822c7c110b9

Aliases

arxiv: 1209.4497 · arxiv_version: 1209.4497v1 · doi: 10.48550/arxiv.1209.4497 · pith_short_12: ZVWXGTIIZRPS · pith_short_16: ZVWXGTIIZRPSDZWA · pith_short_8: ZVWXGTII

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/ZVWXGTIIZRPSDZWACDIWQXUL43 \
  | 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: cd6d734d08cc5f21e6c010d1685e8be6fd59c5cd79c1655aa8e0c822c7c110b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "da35e0019222c860f3ef4991dc873ccfb897276f6bd99a179ecf04ad016f6472",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-20T11:24:18Z",
    "title_canon_sha256": "5b9d9c82c02d40eefac8b981790395b8a95eff41951cba46fdc7b0ae2859d181"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4497",
    "kind": "arxiv",
    "version": 1
  }
}