Pith Number

pith:3P4MNKC4

pith:2025:3P4MNKC4JDPVDXDNO3ZGUDJ5MZ

not attested not anchored not stored refs pending

On biquadratic fields: when 5 squares are not enough

Daniel Dombek

arxiv:2506.20820 v1 · 2025-06-25 · 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{3P4MNKC4JDPVDXDNO3ZGUDJ5MZ}

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	2026-05-20T00:05:30.387830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbf8c6a85c48df51dc6d76f26a0d3d66713d90f80925c211396a3552680f983d

Aliases

arxiv: 2506.20820 · arxiv_version: 2506.20820v1 · doi: 10.48550/arxiv.2506.20820 · pith_short_12: 3P4MNKC4JDPV · pith_short_16: 3P4MNKC4JDPVDXDN · pith_short_8: 3P4MNKC4

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/3P4MNKC4JDPVDXDNO3ZGUDJ5MZ \
  | 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: dbf8c6a85c48df51dc6d76f26a0d3d66713d90f80925c211396a3552680f983d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b20f25504ce2e190902150ffd512e2159ca94b04b1c7aeb3e3a230840bddb1ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-06-25T20:35:23Z",
    "title_canon_sha256": "40d92e18c685278e11562669744e8358efd5d0a575c3b39452a209e44645d342"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.20820",
    "kind": "arxiv",
    "version": 1
  }
}