Pith Number

pith:XDHC4U5H

pith:2018:XDHC4U5HNSCF4W3EYXKKJHVZBW

not attested not anchored not stored refs pending

Minimizing GCD sums and applications to non-vanishing of theta functions and to Burgess' inequality

Marc Munsch, R\'egis de la Bret\`eche

arxiv:1812.03788 v5 · 2018-12-10 · 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{XDHC4U5HNSCF4W3EYXKKJHVZBW}

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	2026-05-17T23:41:53.633949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8ce2e53a76c845e5b64c5d4a49eb90d9cefadffed79c6cc74bad8631dce6ec7

Aliases

arxiv: 1812.03788 · arxiv_version: 1812.03788v5 · doi: 10.48550/arxiv.1812.03788 · pith_short_12: XDHC4U5HNSCF · pith_short_16: XDHC4U5HNSCF4W3E · pith_short_8: XDHC4U5H

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/XDHC4U5HNSCF4W3EYXKKJHVZBW \
  | 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: b8ce2e53a76c845e5b64c5d4a49eb90d9cefadffed79c6cc74bad8631dce6ec7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f20849c3915e7f032a313398a196b2f06cee4308bc9ba9d50115e358fa4a767e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-12-10T13:40:14Z",
    "title_canon_sha256": "182df56a04cdcbb8e2edf21d870a691185a0467fdbed0606b67931a17ef6664e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.03788",
    "kind": "arxiv",
    "version": 5
  }
}