Pith Number

pith:T52OE3ND

pith:2025:T52OE3ND7P3UNVS2KTGXVTMXUU

not attested not anchored not stored refs pending

The asymptotic Mahler measure of Gaussian periods

Berend Ringeling, David Hokken, Gunther Cornelissen

arxiv:2507.09303 v3 · 2025-07-12 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T52OE3ND7P3UNVS2KTGXVTMXUU}

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	2026-06-23T01:12:46.387788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f74e26da3fbf746d65a54cd7acd97a517cafcc514d3c0f535c8880dc2cdc624

Aliases

arxiv: 2507.09303 · arxiv_version: 2507.09303v3 · doi: 10.48550/arxiv.2507.09303 · pith_short_12: T52OE3ND7P3U · pith_short_16: T52OE3ND7P3UNVS2 · pith_short_8: T52OE3ND

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/T52OE3ND7P3UNVS2KTGXVTMXUU \
  | 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: 9f74e26da3fbf746d65a54cd7acd97a517cafcc514d3c0f535c8880dc2cdc624

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e66e2a5994e73a0c257631652e86bb717bd781e629f5896ce234b772b3d18ee",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-07-12T14:43:46Z",
    "title_canon_sha256": "23cd1bd8f27729ce50034dd4f36aeb74cfdc569fded12e71099c5de1eaa9afa3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.09303",
    "kind": "arxiv",
    "version": 3
  }
}