Pith Number

pith:HBVD64PT

pith:2018:HBVD64PTHJFHLBJ4HFLJTTT2OU

not attested not anchored not stored refs pending

Cycles in the supersingular $\ell$-isogeny graph and corresponding endomorphisms

Catalina Camacho-Navarro, Efrat Bank, Jennifer Park, Kirsten Eisentraeger, Travis Morrison

arxiv:1804.04063 v2 · 2018-04-11 · 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{HBVD64PTHJFHLBJ4HFLJTTT2OU}

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	2026-05-18T00:05:05.042332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

386a3f71f33a4a75853c395699ce7a753ffc99df10e0fa38eafe323ef41448da

Aliases

arxiv: 1804.04063 · arxiv_version: 1804.04063v2 · doi: 10.48550/arxiv.1804.04063 · pith_short_12: HBVD64PTHJFH · pith_short_16: HBVD64PTHJFHLBJ4 · pith_short_8: HBVD64PT

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/HBVD64PTHJFHLBJ4HFLJTTT2OU \
  | 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: 386a3f71f33a4a75853c395699ce7a753ffc99df10e0fa38eafe323ef41448da

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7458aceeecab464c8a2c2e7e540383b833a5f9716dc4b6a823fcc73a3ad4c02",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-04-11T15:57:51Z",
    "title_canon_sha256": "ccb9c4d8e7519434321283b6659004545dd777cb5c6cd38421e1bdd3db532ca8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.04063",
    "kind": "arxiv",
    "version": 2
  }
}