Pith Number

pith:Z4BJZ3MX

pith:2024:Z4BJZ3MX3YABKVZCXVZOARGFRQ

not attested not anchored not stored refs pending

Explicit bounds on common projective torsion points of elliptic curves

Christian B\"ohning, David Hubbard, Hans-Christian Graf von Bothmer

arxiv:2412.20174 v1 · 2024-12-28 · 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{Z4BJZ3MX3YABKVZCXVZOARGFRQ}

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	2026-07-05T09:54:55.579846Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf029ced97de00155722bd72e044c58c0a1d16c3f82ec6537ff86e5a3783a05b

Aliases

arxiv: 2412.20174 · arxiv_version: 2412.20174v1 · doi: 10.48550/arxiv.2412.20174 · pith_short_12: Z4BJZ3MX3YAB · pith_short_16: Z4BJZ3MX3YABKVZC · pith_short_8: Z4BJZ3MX

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/Z4BJZ3MX3YABKVZCXVZOARGFRQ \
  | 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: cf029ced97de00155722bd72e044c58c0a1d16c3f82ec6537ff86e5a3783a05b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "134bb3ddde055ec04bd32d335aa656002e9f51419f2b1ac8b2cbfe737f45d5cd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-12-28T15:06:15Z",
    "title_canon_sha256": "d7165bab0d2f9f39717db34b1134a6b32b7d2d3306a27ea3972c720b70f3ec07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.20174",
    "kind": "arxiv",
    "version": 1
  }
}