Pith Number

pith:LSHJNYVK

pith:2012:LSHJNYVKBD6C5QJZGQRQV6PQJI

not attested not anchored not stored refs pending

An Improved Lower Bound for Stack Sorting

Luke Schaeffer

arxiv:1212.0836 v1 · 2012-12-04 · cs.DM · 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{LSHJNYVKBD6C5QJZGQRQV6PQJI}

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	2026-05-18T03:39:15.100308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c8e96e2aa08fc2ec13934230af9f04a146f31777be25c31930a3fb5603dfb81

Aliases

arxiv: 1212.0836 · arxiv_version: 1212.0836v1 · doi: 10.48550/arxiv.1212.0836 · pith_short_12: LSHJNYVKBD6C · pith_short_16: LSHJNYVKBD6C5QJZ · pith_short_8: LSHJNYVK

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/LSHJNYVKBD6C5QJZGQRQV6PQJI \
  | 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: 5c8e96e2aa08fc2ec13934230af9f04a146f31777be25c31930a3fb5603dfb81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bc405624cc2d5cafb139aa44d441f2a04fcf6aebd99bfc32c6cbb71248969ca0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2012-12-04T19:40:54Z",
    "title_canon_sha256": "25fb51dfae8c2e5f5f5133eb138c0aa76a6dad457667dea33c112cd9957c2b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0836",
    "kind": "arxiv",
    "version": 1
  }
}