Pith Number

pith:2P45Q3ZY

pith:2013:2P45Q3ZYEYQNOALE3JPSGHX7TB

not attested not anchored not stored refs pending

Resolvent-Techniques For Multiple Exercise Problems

Jukka Lempa, S\"oren Christensen

arxiv:1309.7210 v1 · 2013-09-27 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2P45Q3ZYEYQNOALE3JPSGHX7TB}

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	2026-05-18T00:56:53.645640Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3f9d86f382620d70164da5f231eff987a070ba56b008e9cf063d9a8675d9051

Aliases

arxiv: 1309.7210 · arxiv_version: 1309.7210v1 · doi: 10.48550/arxiv.1309.7210 · pith_short_12: 2P45Q3ZYEYQN · pith_short_16: 2P45Q3ZYEYQNOALE · pith_short_8: 2P45Q3ZY

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/2P45Q3ZYEYQNOALE3JPSGHX7TB \
  | 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: d3f9d86f382620d70164da5f231eff987a070ba56b008e9cf063d9a8675d9051

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5c0f134cbb5f148dae063fa4ab6346a4322c8b63f7e99433e064fd1d8e75b73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-27T11:50:05Z",
    "title_canon_sha256": "2abc0883ba9294b0a6401fe5031039a60dd69370b2c7cf69bb9572a97c00b3d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7210",
    "kind": "arxiv",
    "version": 1
  }
}