Pith Number

pith:P77FKKDE

pith:2015:P77FKKDENR77RCDJM2FYG5C7DK

not attested not anchored not stored refs pending

The 12-th roots of the discriminant of an elliptic curve and the torsion points

Kohei Fukuda, Sho Yoshikawa

arxiv:1503.06449 v1 · 2015-03-22 · 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{P77FKKDENR77RCDJM2FYG5C7DK}

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	2026-05-18T00:59:49.417696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ffe5528646c7ff88869668b83745f1a954709a70b6069849c479f82488b9f90

Aliases

arxiv: 1503.06449 · arxiv_version: 1503.06449v1 · doi: 10.48550/arxiv.1503.06449 · pith_short_12: P77FKKDENR77 · pith_short_16: P77FKKDENR77RCDJ · pith_short_8: P77FKKDE

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/P77FKKDENR77RCDJM2FYG5C7DK \
  | 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: 7ffe5528646c7ff88869668b83745f1a954709a70b6069849c479f82488b9f90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "790f83003d4009e589edfaa5d5873ecfa6c8b4b20cb38b84b6e9659f905b42c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-03-22T18:01:36Z",
    "title_canon_sha256": "6a1e8e7c91bc27eb26ddf39ab5b1ca16b0c3760f6d383475504cf36505f40957"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06449",
    "kind": "arxiv",
    "version": 1
  }
}