Pith Number

pith:45OLPPTH

pith:2011:45OLPPTHJNSWTPXSPPDVKVZK22

not attested not anchored not stored refs pending

Binary Quadratic Forms and Counterexamples to Hasse's Local-Global Principle

Franz Lemmermeyer

arxiv:1108.5687 v1 · 2011-08-29 · 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{45OLPPTHJNSWTPXSPPDVKVZK22}

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	2026-05-18T04:14:36.969501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e75cb7be674b6569bef27bc755572ad6a02421530edd048a724e44e867fe1299

Aliases

arxiv: 1108.5687 · arxiv_version: 1108.5687v1 · doi: 10.48550/arxiv.1108.5687 · pith_short_12: 45OLPPTHJNSW · pith_short_16: 45OLPPTHJNSWTPXS · pith_short_8: 45OLPPTH

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/45OLPPTHJNSWTPXSPPDVKVZK22 \
  | 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: e75cb7be674b6569bef27bc755572ad6a02421530edd048a724e44e867fe1299

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9beceb92edb4a09e9f081f2853f21947c63ceb20657855f7347afab738754a2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-08-29T18:17:38Z",
    "title_canon_sha256": "7b339c39a541db058c2ebf9e31f6c6685102a1f0f171ffd984553b9c9653f7a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.5687",
    "kind": "arxiv",
    "version": 1
  }
}