Pith Number

pith:FUPKZC7M

pith:2019:FUPKZC7MP2E77VTS7MJEQ2MOUU

not attested not anchored not stored refs pending

Birational and noncommutative lifts of antichain toggling and rowmotion

Michael Joseph, Tom Roby

arxiv:1909.09658 v3 · 2019-09-20 · 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{FUPKZC7MP2E77VTS7MJEQ2MOUU}

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	2026-07-05T00:58:04.931419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d1eac8bec7e89ffd672fb1248698ea51acf577725c72f6eb06a97fe88a16af9

Aliases

arxiv: 1909.09658 · arxiv_version: 1909.09658v3 · doi: 10.48550/arxiv.1909.09658 · pith_short_12: FUPKZC7MP2E7 · pith_short_16: FUPKZC7MP2E77VTS · pith_short_8: FUPKZC7M

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/FUPKZC7MP2E77VTS7MJEQ2MOUU \
  | 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: 2d1eac8bec7e89ffd672fb1248698ea51acf577725c72f6eb06a97fe88a16af9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d5294f655c963aa2c3569bedfcf4f2f9ae6fb8ad08981f9bc77f08d2843e203",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-09-20T18:08:28Z",
    "title_canon_sha256": "c1718181b9b078003069fb0c393b94a30632da5915f159a6cb20487082f95ae9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.09658",
    "kind": "arxiv",
    "version": 3
  }
}