Pith Number

pith:AKKLYIOS

pith:2017:AKKLYIOSKKLFL45DOQ3OAGGMW6

not attested not anchored not stored refs pending

A short proof of the middle levels theorem

Jerri Nummenpalo, Petr Gregor, Torsten M\"utze

arxiv:1710.08249 v2 · 2017-10-23 · 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{AKKLYIOSKKLFL45DOQ3OAGGMW6}

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	2026-05-18T00:15:41.989698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0294bc21d2529655f3a37436e018ccb79d8b85bfc3576804ad3e902fc112b388

Aliases

arxiv: 1710.08249 · arxiv_version: 1710.08249v2 · doi: 10.48550/arxiv.1710.08249 · pith_short_12: AKKLYIOSKKLF · pith_short_16: AKKLYIOSKKLFL45D · pith_short_8: AKKLYIOS

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/AKKLYIOSKKLFL45DOQ3OAGGMW6 \
  | 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: 0294bc21d2529655f3a37436e018ccb79d8b85bfc3576804ad3e902fc112b388

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "077e9005b825cb5bd207dc82896f542190a5167c28545f4b4974d15ef53a7344",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-10-23T13:05:21Z",
    "title_canon_sha256": "1090e2013d063c5505b1c6c2a559536aa7257e88a8b3bef7e8ad800781612434"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.08249",
    "kind": "arxiv",
    "version": 2
  }
}