Pith Number

pith:4UYMRBUM

pith:2012:4UYMRBUMR67XWD377SUIORDQOU

not attested not anchored not stored refs pending

A computational upper bound on Jacobsthal's function

Fintan Costello, Paul Watts

arxiv:1208.5342 v2 · 2012-08-27 · 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{4UYMRBUMR67XWD377SUIORDQOU}

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	2026-05-18T02:20:59.970058Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e530c8868c8fbf7b0f7ffca8874470750371899ef912d56840f1a2d87b8941c1

Aliases

arxiv: 1208.5342 · arxiv_version: 1208.5342v2 · doi: 10.48550/arxiv.1208.5342 · pith_short_12: 4UYMRBUMR67X · pith_short_16: 4UYMRBUMR67XWD37 · pith_short_8: 4UYMRBUM

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/4UYMRBUMR67XWD377SUIORDQOU \
  | 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: e530c8868c8fbf7b0f7ffca8874470750371899ef912d56840f1a2d87b8941c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eebc6c813b32b29c6279e2fbe671a28ab6942c87813849982ebd158960e6eed4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-27T09:24:33Z",
    "title_canon_sha256": "f3f93db369f38f47695e20016a5987a25e7bc8d3ba6d595c4da9e3a95f0c17f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5342",
    "kind": "arxiv",
    "version": 2
  }
}