Pith Number

pith:23ZWJJCR

pith:2010:23ZWJJCRYKD5YI52CIUXR6HXSU

not attested not anchored not stored refs pending

Compactness properties of weighted summation operators on trees - the critical case

Mikhail Lifshits, Werner Linde

arxiv:1009.2339 v1 · 2010-09-13 · 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{23ZWJJCRYKD5YI52CIUXR6HXSU}

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	2026-05-18T03:39:29.457966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6f364a451c287dc23ba122978f8f79510e177b21729dd85c62fbeaa7bdc54b0

Aliases

arxiv: 1009.2339 · arxiv_version: 1009.2339v1 · doi: 10.48550/arxiv.1009.2339 · pith_short_12: 23ZWJJCRYKD5 · pith_short_16: 23ZWJJCRYKD5YI52 · pith_short_8: 23ZWJJCR

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/23ZWJJCRYKD5YI52CIUXR6HXSU \
  | 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: d6f364a451c287dc23ba122978f8f79510e177b21729dd85c62fbeaa7bdc54b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47ec9c75ff9091e6ec94ab1ea9a29c19a399e30dee090ec88e64f069a56ddc80",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2010-09-13T09:50:53Z",
    "title_canon_sha256": "8c5a245c34917b61210fddb2e9d9386bde28347ddb9d053805e97bc46154bf20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.2339",
    "kind": "arxiv",
    "version": 1
  }
}