Pith Number

pith:M3ODX7H3

pith:2013:M3ODX7H3NED4RRSNRY4WEYGXL3

not attested not anchored not stored refs pending

Twins in words and long common subsequences in permutations

Boris Bukh, Lidong Zhou

arxiv:1307.0088 v3 · 2013-06-29 · 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{M3ODX7H3NED4RRSNRY4WEYGXL3}

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	2026-05-18T02:26:01.103973Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66dc3bfcfb6907c8c64d8e396260d75ef470fd0fb013bad61e814d823851988d

Aliases

arxiv: 1307.0088 · arxiv_version: 1307.0088v3 · doi: 10.48550/arxiv.1307.0088 · pith_short_12: M3ODX7H3NED4 · pith_short_16: M3ODX7H3NED4RRSN · pith_short_8: M3ODX7H3

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/M3ODX7H3NED4RRSNRY4WEYGXL3 \
  | 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: 66dc3bfcfb6907c8c64d8e396260d75ef470fd0fb013bad61e814d823851988d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56736471e1a76c9bed1ed37348f75b357ef90f86804ed099d2530ebd9c79c4ac",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/3.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-29T11:11:06Z",
    "title_canon_sha256": "ca3972c97d92843c43a25f4dea926f30195e618c42470c419b0f2c3188491e1d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.0088",
    "kind": "arxiv",
    "version": 3
  }
}