Pith Number

pith:6HNW7OE5

pith:2020:6HNW7OE5EJMDAEZ2RQLVI6R73Q

not attested not anchored not stored refs pending

Fourier optimization and quadratic forms

Andr\'es Chirre, Emily Quesada-Herrera

arxiv:2012.07781 v2 · 2020-12-14 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6HNW7OE5EJMDAEZ2RQLVI6R73Q}

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	2026-07-05T05:42:17.418752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1db6fb89d225830133a8c17547a3fdc19c57675ecd7e51474f9ee69bbf0e131

Aliases

arxiv: 2012.07781 · arxiv_version: 2012.07781v2 · doi: 10.48550/arxiv.2012.07781 · pith_short_12: 6HNW7OE5EJMD · pith_short_16: 6HNW7OE5EJMDAEZ2 · pith_short_8: 6HNW7OE5

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/6HNW7OE5EJMDAEZ2RQLVI6R73Q \
  | 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: f1db6fb89d225830133a8c17547a3fdc19c57675ecd7e51474f9ee69bbf0e131

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "645c0401acb9f6af78214708fbf739cb043896e7cc718ddfd4cea8c82bc3e991",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-12-14T18:19:33Z",
    "title_canon_sha256": "78edf11241322bc22dac8366ba18460a500182167798a21114795fc5ceac8f1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2012.07781",
    "kind": "arxiv",
    "version": 2
  }
}