Pith Number

pith:WTFGUJ5E

pith:2026:WTFGUJ5EKW3HRU46YG2Z2C2WW4

not attested not anchored not stored refs pending

Visible 2-torsion in the Tate-Shafarevich group of an elliptic curve

Tom Fisher

arxiv:2605.31488 v1 · 2026-05-29 · 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{WTFGUJ5EKW3HRU46YG2Z2C2WW4}

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	2026-06-01T02:04:08.691842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b4ca6a27a455b678d39ec1b59d0b56b7216b3519d9c9f4e871499695c237ec76

Aliases

arxiv: 2605.31488 · arxiv_version: 2605.31488v1 · doi: 10.48550/arxiv.2605.31488 · pith_short_12: WTFGUJ5EKW3H · pith_short_16: WTFGUJ5EKW3HRU46 · pith_short_8: WTFGUJ5E

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/WTFGUJ5EKW3HRU46YG2Z2C2WW4 \
  | 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: b4ca6a27a455b678d39ec1b59d0b56b7216b3519d9c9f4e871499695c237ec76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e18572417a9872d44f23e0b517a7c79df356695f56c0d2db607e984bbb15c4da",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-29T16:12:11Z",
    "title_canon_sha256": "95f86a7b675e4ac14787b514751bfbf9522f9be02481e505b9a8d8807e86ca9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.31488",
    "kind": "arxiv",
    "version": 1
  }
}