Pith Number

pith:QKKPJFQX

pith:2016:QKKPJFQXEU4TCGIMTST4KJISSC

not attested not anchored not stored refs pending

Selmer groups of twists of elliptic curves over K with K-rational torsion points

Jackson S. Morrow

arxiv:1601.05348 v3 · 2016-01-20 · 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{QKKPJFQXEU4TCGIMTST4KJISSC}

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	2026-05-18T01:20:55.458665Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8294f49617253931190c9ca7c52512908c823b5631e9d44f10f38e336b8f4d67

Aliases

arxiv: 1601.05348 · arxiv_version: 1601.05348v3 · doi: 10.48550/arxiv.1601.05348 · pith_short_12: QKKPJFQXEU4T · pith_short_16: QKKPJFQXEU4TCGIM · pith_short_8: QKKPJFQX

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/QKKPJFQXEU4TCGIMTST4KJISSC \
  | 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: 8294f49617253931190c9ca7c52512908c823b5631e9d44f10f38e336b8f4d67

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a6c1772ac8800a4786f7e909108adc3729bf0b35069d9797f078d9cdaed6f21",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-01-20T17:51:55Z",
    "title_canon_sha256": "3ead8ecca42ea09be4b061ee030880d6ea2d17095497ee7cb8d05bdb5da07fe1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05348",
    "kind": "arxiv",
    "version": 3
  }
}