Pith Number

pith:TKT6UK56

pith:2011:TKT6UK567MIRPNGTS7ZF2B5JHA

not attested not anchored not stored refs pending

Distribution of Missing Sums in Sumsets

Kevin O'Bryant, Oleg Lazarev, Steven J. Miller

arxiv:1109.4700 v3 · 2011-09-22 · 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{TKT6UK567MIRPNGTS7ZF2B5JHA}

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	2026-05-18T03:38:02.962113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aa7ea2bbefb1117b4d397f25d07a93817bdbe0198785b4a742ef3a1faa1471d

Aliases

arxiv: 1109.4700 · arxiv_version: 1109.4700v3 · doi: 10.48550/arxiv.1109.4700 · pith_short_12: TKT6UK567MIR · pith_short_16: TKT6UK567MIRPNGT · pith_short_8: TKT6UK56

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/TKT6UK567MIRPNGTS7ZF2B5JHA \
  | 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: 9aa7ea2bbefb1117b4d397f25d07a93817bdbe0198785b4a742ef3a1faa1471d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5db86f56e018f6d8d21cd29118ffc9a8fccf8e4d0a2e26a075d7464100130006",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-09-22T04:31:00Z",
    "title_canon_sha256": "b3c2e4f1540840ffb9f978b00ac29c82e3072fdf099c16660cd61d0dd17bcb73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.4700",
    "kind": "arxiv",
    "version": 3
  }
}