Pith Number

pith:PB5J72W5

pith:2026:PB5J72W5T6UCZANTY7IYS6YBVH

not attested not anchored not stored refs pending

Hilbert-Kunz multiplicity of quadrics decreases

Cheng Meng

arxiv:2606.04346 v1 · 2026-06-03 · 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{PB5J72W5T6UCZANTY7IYS6YBVH}

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	2026-06-04T01:09:04.372462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

787a9feadd9fa82c81b3c7d1897b01a9c3720e2f83c53d64759e5851916f60bc

Aliases

arxiv: 2606.04346 · arxiv_version: 2606.04346v1 · doi: 10.48550/arxiv.2606.04346 · pith_short_12: PB5J72W5T6UC · pith_short_16: PB5J72W5T6UCZANT · pith_short_8: PB5J72W5

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/PB5J72W5T6UCZANTY7IYS6YBVH \
  | 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: 787a9feadd9fa82c81b3c7d1897b01a9c3720e2f83c53d64759e5851916f60bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d49c9958230f4ad5ec8280d59662b614438079eff3d572660dac8286fbab5fbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-06-03T02:04:39Z",
    "title_canon_sha256": "bc48b797422fc3671d435c63bfc1ba0d47ff533588f3aefb23acb5fcdc0d6383"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.04346",
    "kind": "arxiv",
    "version": 1
  }
}