Pith Number

pith:HAAXDKGE

pith:2018:HAAXDKGEVNUPTNXV7TSVFJ6LZ4

not attested not anchored not stored refs pending

Orders of Tate-Shafarevich groups for the cubic twists of $X_0(27)$

Andrzej D\k{a}browski, Lucjan Szymaszkiewicz

arxiv:1803.06932 v1 · 2018-03-15 · 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{HAAXDKGEVNUPTNXV7TSVFJ6LZ4}

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	2026-05-18T00:20:40.818217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

380171a8c4ab68f9b6f5fce552a7cbcf3fad60b2b92c5a5c968f43892d1ba5d2

Aliases

arxiv: 1803.06932 · arxiv_version: 1803.06932v1 · doi: 10.48550/arxiv.1803.06932 · pith_short_12: HAAXDKGEVNUP · pith_short_16: HAAXDKGEVNUPTNXV · pith_short_8: HAAXDKGE

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/HAAXDKGEVNUPTNXV7TSVFJ6LZ4 \
  | 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: 380171a8c4ab68f9b6f5fce552a7cbcf3fad60b2b92c5a5c968f43892d1ba5d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "304b09f6e673f4f97eeb8a00d9498d7209847fba11e5eba48bb835b0c236eca5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-03-15T23:02:34Z",
    "title_canon_sha256": "ffe47e3b61b9a97d893d2913a56d63c357be25e18badfce50846fdb60206f7c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.06932",
    "kind": "arxiv",
    "version": 1
  }
}