Pith Number

pith:M7OOHY6C

pith:2025:M7OOHY6CHYSHAZ5CGJ5BMAQO23

not attested not anchored not stored refs pending

Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle

Yongqi Liang, Yufan Liu

arxiv:2504.18293 v2 · 2025-04-25 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7OOHY6CHYSHAZ5CGJ5BMAQO23}

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	2026-07-05T11:33:23.322135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67dce3e3c23e247067a2327a16020ed6c33517ba046bc3ed50ba1534d6bf1a79

Aliases

arxiv: 2504.18293 · arxiv_version: 2504.18293v2 · doi: 10.48550/arxiv.2504.18293 · pith_short_12: M7OOHY6CHYSH · pith_short_16: M7OOHY6CHYSHAZ5C · pith_short_8: M7OOHY6C

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/M7OOHY6CHYSHAZ5CGJ5BMAQO23 \
  | 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: 67dce3e3c23e247067a2327a16020ed6c33517ba046bc3ed50ba1534d6bf1a79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d09ba8d774a3af18a552a983a448be8418d9a4b97439a43cca1d5c3cde171e5",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-04-25T12:07:27Z",
    "title_canon_sha256": "c0905cac31fa6225132ccc03538bbae19c928b8cf1ac4ff70dab1b2de0761e29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.18293",
    "kind": "arxiv",
    "version": 2
  }
}