Pith Number

pith:QAB6EEVY

pith:2013:QAB6EEVY45Z4R6UASMN64JJFFP

not attested not anchored not stored refs pending

Infinite product representations for kernels and iterations of functions

D. Alpay, I. Lewkowicz, I. Martziano, P. Jorgensen

arxiv:1301.4626 v1 · 2013-01-20 · 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{QAB6EEVY45Z4R6UASMN64JJFFP}

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	2026-05-18T03:35:56.111572Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8003e212b8e773c8fa80931bee25252bc1750b6752546ab2d3b2c18e0b4de5aa

Aliases

arxiv: 1301.4626 · arxiv_version: 1301.4626v1 · doi: 10.48550/arxiv.1301.4626 · pith_short_12: QAB6EEVY45Z4 · pith_short_16: QAB6EEVY45Z4R6UA · pith_short_8: QAB6EEVY

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/QAB6EEVY45Z4R6UASMN64JJFFP \
  | 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: 8003e212b8e773c8fa80931bee25252bc1750b6752546ab2d3b2c18e0b4de5aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7b5ca67c18e3a4e2e1e7aca0c308667bb7217fb801fbc95b1c6bdd2a7dcdd87",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-01-20T04:30:14Z",
    "title_canon_sha256": "c22c7dd5744133ac4d8eeefa9ac3cde6c22946da0b153890b66713fa9f4724b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.4626",
    "kind": "arxiv",
    "version": 1
  }
}