Pith Number

pith:ZQHUMIPO

pith:2025:ZQHUMIPOAET6I7JJ4VQDOEF3T6

not attested not anchored not stored refs pending

Two $t$-analogues of the tree inversion enumerator

Sam Hopkins

arxiv:2510.22385 v2 · 2025-10-25 · 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{ZQHUMIPOAET6I7JJ4VQDOEF3T6}

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.

Cited by

2 papers in Pith

Short Proofs in Algebraic and Enumerative Combinatorics

Receipt and verification

First computed	2026-05-22T02:04:37.434218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cc0f4621ee0127e47d29e5603710bb9f9a5ba4c50693d22b055164e3bc8aaf61

Aliases

arxiv: 2510.22385 · arxiv_version: 2510.22385v2 · doi: 10.48550/arxiv.2510.22385 · pith_short_12: ZQHUMIPOAET6 · pith_short_16: ZQHUMIPOAET6I7JJ · pith_short_8: ZQHUMIPO

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/ZQHUMIPOAET6I7JJ4VQDOEF3T6 \
  | 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: cc0f4621ee0127e47d29e5603710bb9f9a5ba4c50693d22b055164e3bc8aaf61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "715c1e36dc58e3d86e1561c6301db3d5f5185b4dc7a6b55459c0e79689659842",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-10-25T18:03:10Z",
    "title_canon_sha256": "a7ad4f379f2b8463d24a317769e6fcba12c903c0e95f6e2f6e26bed06b563e0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.22385",
    "kind": "arxiv",
    "version": 2
  }
}