Pith Number

pith:3MHRP3MQ

pith:2016:3MHRP3MQBAPM4NFBYPN6VE7QP5

not attested not anchored not stored refs pending

On the modularity of elliptic curves over a composite field of some real quadratic fields

Sho Yoshikawa

arxiv:1607.05549 v2 · 2016-07-19 · 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{3MHRP3MQBAPM4NFBYPN6VE7QP5}

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	2026-05-18T01:10:45.390920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db0f17ed90081ece34a1c3dbea93f07f71d80a4c33932d3539e54bd037ea03ab

Aliases

arxiv: 1607.05549 · arxiv_version: 1607.05549v2 · doi: 10.48550/arxiv.1607.05549 · pith_short_12: 3MHRP3MQBAPM · pith_short_16: 3MHRP3MQBAPM4NFB · pith_short_8: 3MHRP3MQ

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/3MHRP3MQBAPM4NFBYPN6VE7QP5 \
  | 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: db0f17ed90081ece34a1c3dbea93f07f71d80a4c33932d3539e54bd037ea03ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b2e97daca9b69598cce3f05b81e0b4b7602cb2c2c093a9321af9b3585f7f7be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-07-19T12:38:51Z",
    "title_canon_sha256": "acf5bd32c31a356b37a501d74ac5ec58d84c4982f94749a0394c25118f79ef7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.05549",
    "kind": "arxiv",
    "version": 2
  }
}