Pith Number

pith:YNQWZLF2

pith:2010:YNQWZLF2YSA7OHVEJ7J76Q3GIF

not attested not anchored not stored refs pending

Productivity of sequences with respect to a given weight function

Dikran Dikranjan, Dmitri Shakhmatov, Jan Sp\v{e}v\'ak

arxiv:1011.1524 v1 · 2010-11-05 · math.GN · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YNQWZLF2YSA7OHVEJ7J76Q3GIF}

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	2026-05-18T04:32:11.438151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3616cacbac481f71ea44fd3ff4366415728474d859dfffef5da661b178a201c

Aliases

arxiv: 1011.1524 · arxiv_version: 1011.1524v1 · doi: 10.48550/arxiv.1011.1524 · pith_short_12: YNQWZLF2YSA7 · pith_short_16: YNQWZLF2YSA7OHVE · pith_short_8: YNQWZLF2

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/YNQWZLF2YSA7OHVEJ7J76Q3GIF \
  | 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: c3616cacbac481f71ea44fd3ff4366415728474d859dfffef5da661b178a201c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b37e52a16ca34ccdfe000f26a2333cf4b8f4674a7d80bb23715a7f9babf1b0c7",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2010-11-05T22:25:17Z",
    "title_canon_sha256": "96b7aeda61e5b20dc303817dd2539e62df14fb9d42087c16b3a06698b803702f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.1524",
    "kind": "arxiv",
    "version": 1
  }
}