Pith Number

pith:ZDUGUH6R

pith:2011:ZDUGUH6R4IJ736ZRV2XU5FCYCE

not attested not anchored not stored refs pending

Product-free sets with high density

Carl Pomerance, Jeffrey C. Lagarias, Par Kurlberg

arxiv:1107.5589 v2 · 2011-07-27 · 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{ZDUGUH6R4IJ736ZRV2XU5FCYCE}

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	2026-05-18T03:40:38.769398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8e86a1fd1e213fdfb31aeaf4e9458113a6495d9b970b94f84e774c4d277aba3

Aliases

arxiv: 1107.5589 · arxiv_version: 1107.5589v2 · doi: 10.48550/arxiv.1107.5589 · pith_short_12: ZDUGUH6R4IJ7 · pith_short_16: ZDUGUH6R4IJ736ZR · pith_short_8: ZDUGUH6R

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/ZDUGUH6R4IJ736ZRV2XU5FCYCE \
  | 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: c8e86a1fd1e213fdfb31aeaf4e9458113a6495d9b970b94f84e774c4d277aba3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f31df0c50db592e73901a49297961fd8bdda1ba03d70e7c2a929e1021fa40482",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-27T20:23:02Z",
    "title_canon_sha256": "c2959cd51cca5e34f13dd132bac11f5c3c661e1e0468bf01afda8954deeafa37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5589",
    "kind": "arxiv",
    "version": 2
  }
}