Pith Number

pith:HFGCWWOU

pith:2014:HFGCWWOU4LHZBXYXZEH4QD7HPC

not attested not anchored not stored refs pending

Sums of dilates in ordered groups

Alain Plagne, Salvatore Tringali

arxiv:1403.0934 v3 · 2014-03-04 · math.CO · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFGCWWOU4LHZBXYXZEH4QD7HPC}

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	2026-05-18T00:16:10.042185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

394c2b59d4e2cf90df17c90fc80fe778a046059e91be694a27706a166001000b

Aliases

arxiv: 1403.0934 · arxiv_version: 1403.0934v3 · doi: 10.48550/arxiv.1403.0934 · pith_short_12: HFGCWWOU4LHZ · pith_short_16: HFGCWWOU4LHZBXYX · pith_short_8: HFGCWWOU

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/HFGCWWOU4LHZBXYXZEH4QD7HPC \
  | 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: 394c2b59d4e2cf90df17c90fc80fe778a046059e91be694a27706a166001000b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c153e4a1e9f7ee5c213242042b98d49a51a2bdaf8a03dd472681c5d0f6aedbb8",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-03-04T20:51:56Z",
    "title_canon_sha256": "117a439136bf842bbae9ab86bd708099fec61f79140ba8e8dbc9205bcbba482d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1403.0934",
    "kind": "arxiv",
    "version": 3
  }
}