Pith Number

pith:AQVNRXK6

pith:2013:AQVNRXK6RHC3ICPUB2WK3DR3EC

not attested not anchored not stored refs pending

De Branges spaces and Krein's theory of entire operators

Julio H. Toloza, Luis O. Silva

arxiv:1309.1991 v3 · 2013-09-08 · 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{AQVNRXK6RHC3ICPUB2WK3DR3EC}

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	2026-05-18T01:41:00.275192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

042ad8dd5e89c5b409f40eacad8e3b20bd51158618a07156aaa63b93c4547b3a

Aliases

arxiv: 1309.1991 · arxiv_version: 1309.1991v3 · doi: 10.48550/arxiv.1309.1991 · pith_short_12: AQVNRXK6RHC3 · pith_short_16: AQVNRXK6RHC3ICPU · pith_short_8: AQVNRXK6

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/AQVNRXK6RHC3ICPUB2WK3DR3EC \
  | 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: 042ad8dd5e89c5b409f40eacad8e3b20bd51158618a07156aaa63b93c4547b3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "48cfaef257baa8e746a49b6fcb20a0e57b950fa8a81c507a6ec783d7f114c347",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-09-08T18:34:26Z",
    "title_canon_sha256": "a793ad89b2d7e5f655d0289d51a1fc3ebb836d93fd421e5cbafecca69dbe7214"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1991",
    "kind": "arxiv",
    "version": 3
  }
}