Pith Number

pith:KWY6GAKE

pith:2016:KWY6GAKEOHYQ3UYR2FXM5NYAYB

not attested not anchored not stored refs pending

Some remarks on the Balog-Wooley decomposition theorem and quantities D^+, D^\times

Ilya D. Shkredov

arxiv:1605.00266 v1 · 2016-05-01 · math.CO · 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{KWY6GAKEOHYQ3UYR2FXM5NYAYB}

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	2026-05-18T01:15:56.306185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55b1e3014471f10dd311d16eceb700c0676869ea3cd9d1757ff004b149801ba3

Aliases

arxiv: 1605.00266 · arxiv_version: 1605.00266v1 · doi: 10.48550/arxiv.1605.00266 · pith_short_12: KWY6GAKEOHYQ · pith_short_16: KWY6GAKEOHYQ3UYR · pith_short_8: KWY6GAKE

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/KWY6GAKEOHYQ3UYR2FXM5NYAYB \
  | 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: 55b1e3014471f10dd311d16eceb700c0676869ea3cd9d1757ff004b149801ba3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddefc5253dccf502eaaaf53820da37a38702b145f31ecd66a032f45cfee57421",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-05-01T15:45:09Z",
    "title_canon_sha256": "549ea0177aee383669fe6d061e1d3b688d2fac31e0c7d21b73072f2d67ea85be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00266",
    "kind": "arxiv",
    "version": 1
  }
}