Pith Number

pith:YPWFTBXZ

pith:2012:YPWFTBXZ4O7B7ZRQZ35RCMEQSM

not attested not anchored not stored refs pending

Hilbert-Kunz functions of 2 x 2 determinantal rings

Irena Swanson, Lance Edward Miller

arxiv:1206.1015 v2 · 2012-06-05 · math.AC · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YPWFTBXZ4O7B7ZRQZ35RCMEQSM}

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	2026-05-18T03:43:27.065530Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ec5986f9e3be1fe630cefb11309093252634be43ac31f948f0b5ea962585c8

Aliases

arxiv: 1206.1015 · arxiv_version: 1206.1015v2 · doi: 10.48550/arxiv.1206.1015 · pith_short_12: YPWFTBXZ4O7B · pith_short_16: YPWFTBXZ4O7B7ZRQ · pith_short_8: YPWFTBXZ

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/YPWFTBXZ4O7B7ZRQZ35RCMEQSM \
  | 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: c3ec5986f9e3be1fe630cefb11309093252634be43ac31f948f0b5ea962585c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "833a89f4e8b7adef5a62d43737de77d6753f70d22009f76af2440164de2e6ba4",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-06-05T18:25:53Z",
    "title_canon_sha256": "113461acc2a54a2c80d91a7b900bb79be02479b98008c16f33056d33ffa783d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1015",
    "kind": "arxiv",
    "version": 2
  }
}