Pith Number

pith:TMYZVVZL

pith:2017:TMYZVVZLSLI667CKAB2BNJBAX4

not attested not anchored not stored refs pending

Hilbert-Kunz density function and asymptotic Hilbert-Kunz multiplicity for projective toric varieties

Mandira Mondal, V. Trivedi

arxiv:1707.05959 v3 · 2017-07-19 · math.AG · 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{TMYZVVZLSLI667CKAB2BNJBAX4}

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	2026-05-18T00:38:08.439738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b319ad72b92d1ef7c4a007416a420bf0f62b40284c9ec8b10145a2acdf98d26

Aliases

arxiv: 1707.05959 · arxiv_version: 1707.05959v3 · doi: 10.48550/arxiv.1707.05959 · pith_short_12: TMYZVVZLSLI6 · pith_short_16: TMYZVVZLSLI667CK · pith_short_8: TMYZVVZL

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/TMYZVVZLSLI667CKAB2BNJBAX4 \
  | 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: 9b319ad72b92d1ef7c4a007416a420bf0f62b40284c9ec8b10145a2acdf98d26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68dd42494de2a0395560fa821b7c63271d78c8328f819807daddae7493313ae5",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-07-19T07:29:35Z",
    "title_canon_sha256": "5c8a56b253e1f58bd08298b6af72cd69a1e31a99be6ccb5b400219a803768259"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.05959",
    "kind": "arxiv",
    "version": 3
  }
}