Pith Number

pith:AFGTFX2O

pith:2016:AFGTFX2OEBK3PG2VVFRJFFFC6V

not attested not anchored not stored refs pending

Cancelation free formula for the antipode of linearized Hopf monoid

Carolina Benedetti, Nantel Bergeron

arxiv:1611.01657 v1 · 2016-11-05 · 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{AFGTFX2OEBK3PG2VVFRJFFFC6V}

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	2026-05-18T01:00:04.752185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

014d32df4e2055b79b55a9629294a2f57e09e3245578bf4511f24749fd961567

Aliases

arxiv: 1611.01657 · arxiv_version: 1611.01657v1 · doi: 10.48550/arxiv.1611.01657 · pith_short_12: AFGTFX2OEBK3 · pith_short_16: AFGTFX2OEBK3PG2V · pith_short_8: AFGTFX2O

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/AFGTFX2OEBK3PG2VVFRJFFFC6V \
  | 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: 014d32df4e2055b79b55a9629294a2f57e09e3245578bf4511f24749fd961567

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54223a59a8922478e9c7ed3bfd1ccf28072b80786df742ba409e37b20ab11be6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-05T15:08:55Z",
    "title_canon_sha256": "8a3cf42e5a2f1d8fcda34ec710c68e0e9dec024b78f1456990222bfc1f4c118a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.01657",
    "kind": "arxiv",
    "version": 1
  }
}