Pith Number

pith:JFHXUCV6

pith:2020:JFHXUCV6XEAQNGEDAM3XZ2PZ7H

not attested not anchored not stored refs pending

The Sperner property for $132$-avoiding intervals in the weak order

Christian Gaetz, Katherine Tung

arxiv:2006.16359 v2 · 2020-06-29 · 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{JFHXUCV6XEAQNGEDAM3XZ2PZ7H}

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	2026-07-05T03:30:49.952003Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

494f7a0abeb90106988303377ce9f9f9e4890d2830976a6c2cc83ea851b63c92

Aliases

arxiv: 2006.16359 · arxiv_version: 2006.16359v2 · doi: 10.48550/arxiv.2006.16359 · pith_short_12: JFHXUCV6XEAQ · pith_short_16: JFHXUCV6XEAQNGED · pith_short_8: JFHXUCV6

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/JFHXUCV6XEAQNGEDAM3XZ2PZ7H \
  | 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: 494f7a0abeb90106988303377ce9f9f9e4890d2830976a6c2cc83ea851b63c92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92fb87cfeffb32601ccda7829412dcdfd37917efd34e864aa1379f1d16dac371",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-06-29T20:22:25Z",
    "title_canon_sha256": "7a69f55bfb200fc145fab30ab5ef007ded2cd38680034a4777f66b0844527206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.16359",
    "kind": "arxiv",
    "version": 2
  }
}