Pith Number

pith:ZXAPURNC

pith:2016:ZXAPURNCR7UL326M4BOK6K3XWV

not attested not anchored not stored refs pending

On the structure of subsets of the discrete cube with small edge boundary

David Ellis, Nathan Keller, Noam Lifshitz

arxiv:1612.06680 v4 · 2016-12-20 · 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{ZXAPURNCR7UL326M4BOK6K3XWV}

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	2026-05-18T00:15:00.152815Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdc0fa45a28fe8bdebcce05caf2b77b56ba95433bb2bf691a1f349fcc1e8b7df

Aliases

arxiv: 1612.06680 · arxiv_version: 1612.06680v4 · doi: 10.48550/arxiv.1612.06680 · pith_short_12: ZXAPURNCR7UL · pith_short_16: ZXAPURNCR7UL326M · pith_short_8: ZXAPURNC

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/ZXAPURNCR7UL326M4BOK6K3XWV \
  | 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: cdc0fa45a28fe8bdebcce05caf2b77b56ba95433bb2bf691a1f349fcc1e8b7df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b816c84ca7efdf13770eee711fd413c4e21a393aea8a05cf7ea9096a260b85b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-12-20T14:36:29Z",
    "title_canon_sha256": "0bcc26879b4042bef799ed246215bccf248e8e7b0eb4842e4d7f3cc319c56538"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06680",
    "kind": "arxiv",
    "version": 4
  }
}