Pith Number

pith:FPGL3B6Q

pith:2009:FPGL3B6QU5DQT7VWVMEJAZTEJS

not attested not anchored not stored refs pending

Probabilistic averages of Jacobi operators

Helge Krueger

arxiv:0904.4226 v1 · 2009-04-27 · math.SP · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FPGL3B6QU5DQT7VWVMEJAZTEJS}

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	2026-05-18T02:13:56.985131Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2bccbd87d0a74709feb6ab089066644c8463bb3763c13f377867a77dcbf151dc

Aliases

arxiv: 0904.4226 · arxiv_version: 0904.4226v1 · doi: 10.48550/arxiv.0904.4226 · pith_short_12: FPGL3B6QU5DQ · pith_short_16: FPGL3B6QU5DQT7VW · pith_short_8: FPGL3B6Q

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/FPGL3B6QU5DQT7VWVMEJAZTEJS \
  | 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: 2bccbd87d0a74709feb6ab089066644c8463bb3763c13f377867a77dcbf151dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a344b9d457427448930dd4dcc6eee21fa71d89c23d4b358654f1dbc358ac85c",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2009-04-27T17:59:38Z",
    "title_canon_sha256": "5bed81d2117b75b128e3611b995e4218ba2a9a7b8273ef340c91b8159887f817"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.4226",
    "kind": "arxiv",
    "version": 1
  }
}