Pith Number

pith:GFDENK7I

pith:2015:GFDENK7ITYEOJVTWJGSRDOTJXZ

not attested not anchored not stored refs pending

Antipode formulas for some combinatorial Hopf algebras

Rebecca Patrias

arxiv:1501.00710 v2 · 2015-01-04 · 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{GFDENK7ITYEOJVTWJGSRDOTJXZ}

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	2026-05-18T01:04:09.536264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

314646abe89e08e4d67649a511ba69be503d6dd39b2a4379827e29136ffb56bc

Aliases

arxiv: 1501.00710 · arxiv_version: 1501.00710v2 · doi: 10.48550/arxiv.1501.00710 · pith_short_12: GFDENK7ITYEO · pith_short_16: GFDENK7ITYEOJVTW · pith_short_8: GFDENK7I

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/GFDENK7ITYEOJVTWJGSRDOTJXZ \
  | 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: 314646abe89e08e4d67649a511ba69be503d6dd39b2a4379827e29136ffb56bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86ee40eea5b3dcb0d26823db416354a9dd15767ca253a1f71bd8a9d8e7a2588f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-04T19:30:21Z",
    "title_canon_sha256": "7ca2d4f18f5356cb8be756e918b3dd78528190c2fc4fc26dd7b2cbb7bfa91ef7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.00710",
    "kind": "arxiv",
    "version": 2
  }
}