Pith Number

pith:3L3KUTAY

pith:2016:3L3KUTAY4VTMPBW5IH5HPOMTK4

not attested not anchored not stored refs pending

Pattern-Avoiding Polytopes

Bruce Sagan, Robert Davis

arxiv:1609.01782 v3 · 2016-09-06 · math.CO · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3L3KUTAY4VTMPBW5IH5HPOMTK4}

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	2026-05-18T00:10:41.686238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

daf6aa4c18e566c786dd41fa77b99357313007639e488b05d434748fc58751b9

Aliases

arxiv: 1609.01782 · arxiv_version: 1609.01782v3 · doi: 10.48550/arxiv.1609.01782 · pith_short_12: 3L3KUTAY4VTM · pith_short_16: 3L3KUTAY4VTMPBW5 · pith_short_8: 3L3KUTAY

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/3L3KUTAY4VTMPBW5IH5HPOMTK4 \
  | 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: daf6aa4c18e566c786dd41fa77b99357313007639e488b05d434748fc58751b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d26eb22a2905d2acc5f9eca6f1fde0951003092f6724154bfa78dc6fb9080d7",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-06T22:50:54Z",
    "title_canon_sha256": "8c4e83d4a86b46139533d0b203630b357888cb1c592066de2aca2e83d13574aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01782",
    "kind": "arxiv",
    "version": 3
  }
}