Pith Number

pith:22ZCVG7P

pith:2015:22ZCVG7PHJM2ZKNHYZ3HWC5DGG

not attested not anchored not stored refs pending

On families of 9-congruent elliptic curves

Tom Fisher

arxiv:1504.07891 v1 · 2015-04-29 · 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{22ZCVG7PHJM2ZKNHYZ3HWC5DGG}

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	2026-05-18T02:17:31.976337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6b22a9bef3a59aca9a7c6767b0ba331979ccb27a1e1dcdf8d575eef88cee1aa

Aliases

arxiv: 1504.07891 · arxiv_version: 1504.07891v1 · doi: 10.48550/arxiv.1504.07891 · pith_short_12: 22ZCVG7PHJM2 · pith_short_16: 22ZCVG7PHJM2ZKNH · pith_short_8: 22ZCVG7P

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/22ZCVG7PHJM2ZKNHYZ3HWC5DGG \
  | 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: d6b22a9bef3a59aca9a7c6767b0ba331979ccb27a1e1dcdf8d575eef88cee1aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "878e3e47122ede3aa0c235156d1d3fa42f52834b85fcdbed36d80f1fcb67a9ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-29T15:30:27Z",
    "title_canon_sha256": "722a390b5ebe304790ac01424462a2314118216ae4ddbc2b22a5a77c0addf1c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07891",
    "kind": "arxiv",
    "version": 1
  }
}