Pith Number

pith:PW6RRSBG

pith:2018:PW6RRSBGIFULH3PWNB5P5J2AGM

not attested not anchored not stored refs pending

On the Erd\H{o}s Covering Problem: the density of the uncovered set

B\'ela Bollob\'as, Julian Sahasrabudhe, Marius Tiba, Paul Balister, Robert Morris

arxiv:1811.03547 v1 · 2018-11-08 · math.NT · 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{PW6RRSBGIFULH3PWNB5P5J2AGM}

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	2026-05-18T00:01:15.773752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dbd18c8264168b3edf6687afea740330115d8068bb7ba0e4c79589e3efd289e

Aliases

arxiv: 1811.03547 · arxiv_version: 1811.03547v1 · doi: 10.48550/arxiv.1811.03547 · pith_short_12: PW6RRSBGIFUL · pith_short_16: PW6RRSBGIFULH3PW · pith_short_8: PW6RRSBG

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/PW6RRSBGIFULH3PWNB5P5J2AGM \
  | 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: 7dbd18c8264168b3edf6687afea740330115d8068bb7ba0e4c79589e3efd289e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90be58d15367b4cb49b45f40d41d7f383894b4018fa4d47e6eaf42cbcb4e27a2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-11-08T16:52:31Z",
    "title_canon_sha256": "b7a4a9c28b2e15f8b32a23af31ad33f9024f9befd90e7cab464fa95f32dd8457"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.03547",
    "kind": "arxiv",
    "version": 1
  }
}