Pith Number

pith:A77UNKEV

pith:2024:A77UNKEVZFPZXSNJHD5TEWISA5

not attested not anchored not stored refs pending

New bounds for the optimal density of covering single-insertion codes via the Tur\'an density

Maksim Zhukovskii, Oleg Pikhurko, Oleg Verbitsky

arxiv:2409.06425 v3 · 2024-09-10 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A77UNKEVZFPZXSNJHD5TEWISA5}

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	2026-06-23T03:14:26.928701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07ff46a895c95f9bc9a938fb325912077494889f0dcd72b2fcef5dcac738a5ca

Aliases

arxiv: 2409.06425 · arxiv_version: 2409.06425v3 · doi: 10.48550/arxiv.2409.06425 · pith_short_12: A77UNKEVZFPZ · pith_short_16: A77UNKEVZFPZXSNJ · pith_short_8: A77UNKEV

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/A77UNKEVZFPZXSNJHD5TEWISA5 \
  | 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: 07ff46a895c95f9bc9a938fb325912077494889f0dcd72b2fcef5dcac738a5ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8340af9676462066aa511f75d01ab6850aea0cf858fbda102e1a46cb4d2ba07",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-09-10T11:15:33Z",
    "title_canon_sha256": "90a29e4cc974312b75ae796c663a87be5cec5a9d95da0893f07b24aa12ebb443"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.06425",
    "kind": "arxiv",
    "version": 3
  }
}