Pith Number

pith:WS3ISQ4E

pith:2011:WS3ISQ4EW5SINNSBQWBC35TZD3

not attested not anchored not stored refs pending

Hereditary completeness for systems of exponentials and reproducing kernels

Alexander Borichev, Anton Baranov, Yurii Belov

arxiv:1112.5551 v2 · 2011-12-23 · math.CV · 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{WS3ISQ4EW5SINNSBQWBC35TZD3}

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	2026-05-18T03:59:13.541712Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4b6894384b76486b64185822df6791ee58abc47a3800de33c958d6785b0adf7

Aliases

arxiv: 1112.5551 · arxiv_version: 1112.5551v2 · doi: 10.48550/arxiv.1112.5551 · pith_short_12: WS3ISQ4EW5SI · pith_short_16: WS3ISQ4EW5SINNSB · pith_short_8: WS3ISQ4E

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/WS3ISQ4EW5SINNSBQWBC35TZD3 \
  | 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: b4b6894384b76486b64185822df6791ee58abc47a3800de33c958d6785b0adf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90d536ece55b584b71dd3a88321e173bb4ffe04fac7d87923df1187db5b0c9bd",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-12-23T10:41:12Z",
    "title_canon_sha256": "0141b1c483b094c95f73d5036aed6234114ab07ab23b7ccd29e3d469371fb8fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5551",
    "kind": "arxiv",
    "version": 2
  }
}