Pith Number

pith:4WY45HPN

pith:2016:4WY45HPNA5DUCSMJRDXK2UAL5E

not attested not anchored not stored refs pending

Cauchy-Davenport Theorem for linear maps: Simplification and Extension

Aditya Potukuchi, John Kim

arxiv:1612.09217 v1 · 2016-12-29 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4WY45HPNA5DUCSMJRDXK2UAL5E}

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	2026-05-18T00:53:46.225011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5b1ce9ded074741498988eead500be93bb794f8e57c8e85d2942bf81ca0202a

Aliases

arxiv: 1612.09217 · arxiv_version: 1612.09217v1 · doi: 10.48550/arxiv.1612.09217 · pith_short_12: 4WY45HPNA5DU · pith_short_16: 4WY45HPNA5DUCSMJ · pith_short_8: 4WY45HPN

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/4WY45HPNA5DUCSMJRDXK2UAL5E \
  | 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: e5b1ce9ded074741498988eead500be93bb794f8e57c8e85d2942bf81ca0202a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de8452941543ef9ca04753b5b17f49732321af4de76e42689594b376b8afd137",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-29T17:55:54Z",
    "title_canon_sha256": "1349b0f1764b2b8a00f557d8156e9d8b6dc4a9e248ebd99aff8272d3a0262c47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09217",
    "kind": "arxiv",
    "version": 1
  }
}