Pith Number

pith:N2UJIEXF

pith:2014:N2UJIEXFOR4TAXT7AMGH6VFDLF

not attested not anchored not stored refs pending

Upper semi-continuity of the Hilbert-Kunz multiplicity

Ilya Smirnov

arxiv:1407.6476 v1 · 2014-07-24 · 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{N2UJIEXFOR4TAXT7AMGH6VFDLF}

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	2026-05-17T23:53:34.781405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ea89412e57479305e7f030c7f54a35940bf3e4bb8be9a747cab46ef01d09ec1

Aliases

arxiv: 1407.6476 · arxiv_version: 1407.6476v1 · doi: 10.48550/arxiv.1407.6476 · pith_short_12: N2UJIEXFOR4T · pith_short_16: N2UJIEXFOR4TAXT7 · pith_short_8: N2UJIEXF

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/N2UJIEXFOR4TAXT7AMGH6VFDLF \
  | 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: 6ea89412e57479305e7f030c7f54a35940bf3e4bb8be9a747cab46ef01d09ec1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3843143a393676c6da2bbbf518428ff4210b5534ce40ec457d6efa917ae287bb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2014-07-24T08:04:35Z",
    "title_canon_sha256": "253cab62a64932e034207d3683eac3a751a0b3d721e6a75e9ad5ff96957283ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.6476",
    "kind": "arxiv",
    "version": 1
  }
}