Pith Number

pith:XXPIDTB6

pith:2004:XXPIDTB64ZAG52OOD2REUBUSWC

not attested not anchored not stored refs pending

The Hilbert-Kunz function in graded dimension two

Holger Brenner

arxiv:math/0405202 v1 · 2004-05-11 · 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{XXPIDTB64ZAG52OOD2REUBUSWC}

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	2026-05-18T01:05:26.376563Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdde81cc3ee6406ee9ce1ea24a0692b0b0cf2a9e0350b3b1ca653b7ea178927d

Aliases

arxiv: math/0405202 · arxiv_version: math/0405202v1 · doi: 10.48550/arxiv.math/0405202 · pith_short_12: XXPIDTB64ZAG · pith_short_16: XXPIDTB64ZAG52OO · pith_short_8: XXPIDTB6

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/XXPIDTB64ZAG52OOD2REUBUSWC \
  | 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: bdde81cc3ee6406ee9ce1ea24a0692b0b0cf2a9e0350b3b1ca653b7ea178927d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86c7a378946af58de79b32de70b2a1647c11f9604b10346f912f71e286060ab0",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.AC",
    "submitted_at": "2004-05-11T20:46:28Z",
    "title_canon_sha256": "fff979884971c7fdc0cc4c16a9481c4cf540b9e04754e328ea03602d18cc0ddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0405202",
    "kind": "arxiv",
    "version": 1
  }
}