Pith Number

pith:MUWJ25QE

pith:2014:MUWJ25QE3PTMQZ3YA4O6XJ2AVR

not attested not anchored not stored refs pending

The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion point

Robert J. Lemke Oliver, Zev Klagsbrun

arxiv:1406.6745 v1 · 2014-06-26 · 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{MUWJ25QE3PTMQZ3YA4O6XJ2AVR}

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	2026-05-18T02:48:55.987534Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

652c9d7604dbe6c86778071deba740ac57834c09a154b958fa03b58c87b0d525

Aliases

arxiv: 1406.6745 · arxiv_version: 1406.6745v1 · doi: 10.48550/arxiv.1406.6745 · pith_short_12: MUWJ25QE3PTM · pith_short_16: MUWJ25QE3PTMQZ3Y · pith_short_8: MUWJ25QE

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/MUWJ25QE3PTMQZ3YA4O6XJ2AVR \
  | 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: 652c9d7604dbe6c86778071deba740ac57834c09a154b958fa03b58c87b0d525

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93fb42a98302897c11c64dbc2d281045d82add92680f97a749ba5f26e370b67f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-06-26T01:43:33Z",
    "title_canon_sha256": "7ddcc381ca06a2d9539e45f6866feb1a977ceb9f743b1dd1bc298247919b779b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1406.6745",
    "kind": "arxiv",
    "version": 1
  }
}