Pith Number

pith:ZMEUP74E

pith:2015:ZMEUP74EXANBGS2DFJBPAURRKK

not attested not anchored not stored refs pending

Canonical Trees, Compact Prefix-free Codes and Sums of Unit Fractions: A Probabilistic Analysis

Clemens Heuberger, Daniel Krenn, Stephan Wagner

arxiv:1503.08791 v2 · 2015-03-30 · math.NT · math.CO · 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{ZMEUP74EXANBGS2DFJBPAURRKK}

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	2026-05-18T01:33:06.029387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb0947ff84b81a134b432a42f0523152bb212846cb7e3f2e41db6191c5e09f78

Aliases

arxiv: 1503.08791 · arxiv_version: 1503.08791v2 · doi: 10.48550/arxiv.1503.08791 · pith_short_12: ZMEUP74EXANB · pith_short_16: ZMEUP74EXANBGS2D · pith_short_8: ZMEUP74E

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/ZMEUP74EXANBGS2DFJBPAURRKK \
  | 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: cb0947ff84b81a134b432a42f0523152bb212846cb7e3f2e41db6191c5e09f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b9e6a679c01015522a90e013eb088343a257d8af626a4c358f0505c25333ba3",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-30T18:55:52Z",
    "title_canon_sha256": "2bd71d490d069d53d38525dd46a6572a74c55c8f3bed9f67fe4818ae6404a6cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08791",
    "kind": "arxiv",
    "version": 2
  }
}