Pith Number

pith:KKSHONMI

pith:2016:KKSHONMIQMYZEGMXFVP7ALLCHF

not attested not anchored not stored refs pending

Torsion points and Galois representations on CM elliptic curves

Abbey Bourdon, Pete L. Clark

arxiv:1612.03229 v4 · 2016-12-10 · 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{KKSHONMIQMYZEGMXFVP7ALLCHF}

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	2026-07-05T00:48:35.764492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52a477358883319219972d5ff02d62395ab4438011a61ca2d7086bcd914ec7c2

Aliases

arxiv: 1612.03229 · arxiv_version: 1612.03229v4 · doi: 10.48550/arxiv.1612.03229 · pith_short_12: KKSHONMIQMYZ · pith_short_16: KKSHONMIQMYZEGMX · pith_short_8: KKSHONMI

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/KKSHONMIQMYZEGMXFVP7ALLCHF \
  | 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: 52a477358883319219972d5ff02d62395ab4438011a61ca2d7086bcd914ec7c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bef895654d4f6c2ee4ef1858242c70a598b8ececac6bef403b91c8be84276114",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-12-10T00:19:18Z",
    "title_canon_sha256": "b216528e9984bc593388e76ad527e912eff1ca0fa7a4c96500940ec81527cbb2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.03229",
    "kind": "arxiv",
    "version": 4
  }
}