Pith Number

pith:RPCS76Y4

pith:2018:RPCS76Y4HKGBVHQBJCBTYGRWKX

not attested not anchored not stored refs pending

Automating the Calculation of Hilbert-Kunz Multiplicities and F-Signatures

Gabriel Johnson, Sandra Spiroff

arxiv:1810.01504 v1 · 2018-10-02 · 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{RPCS76Y4HKGBVHQBJCBTYGRWKX}

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	2026-05-18T00:04:11.949540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8bc52ffb1c3a8c1a9e0148833c1a3655e14f8969ab8d038406f87ca9b406b55c

Aliases

arxiv: 1810.01504 · arxiv_version: 1810.01504v1 · doi: 10.48550/arxiv.1810.01504 · pith_short_12: RPCS76Y4HKGB · pith_short_16: RPCS76Y4HKGBVHQB · pith_short_8: RPCS76Y4

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/RPCS76Y4HKGBVHQBJCBTYGRWKX \
  | 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: 8bc52ffb1c3a8c1a9e0148833c1a3655e14f8969ab8d038406f87ca9b406b55c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "09c8796d3d7f44c6f93abaead99c146c37bef966e196b898d206d5eb381b4a28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-10-02T20:48:04Z",
    "title_canon_sha256": "492ae0a93fe6f37adf98a993158b87f52e5606c6a4e001b3cba923db76608a2a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.01504",
    "kind": "arxiv",
    "version": 1
  }
}